Prasanna

Students can download 6th Social Science Term 3 Geography Chapter 2 Globe Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science Geography Solutions Term 3 Chapter 2 Globe

Samacheer Kalvi 6th Social Science Globe Text Book Back Questions and Answers

I. Fill in the blanks

1. The line of latitude which is known as the Great Circle is ……………..
2. The imaginary lines drawn horizontally on Earth from the West to East are called ……………..
3. The 90° lines of latitude on the Earth are called ……………..
4. The Prime Meridian is also called ……………..
5. The world is divided into …………….. time zones.

Answer:

1. Equator
2. lines or parallels of latitude
3. Poles
4. Greenwich meridian
5. 24

II. Choose the best answer

Question 1.
The shape of the Earth is ……………..
(a) Square
(b) Rectangle
(c) Geoid
(d) Circle
Answer:
(c) Geoid

Question 2.
The North Pole is _______.
(a) 90° N Latitude
(b) 90° S latitude
(c) 90° W Longitude
(d) 90° E longitude
Answer:
(a) 90° N Latitude

Question 3.
The area found between 0° and 180° E lines of longitude is called ……………..
(a) Southern Hemisphere
(b) Western Hemisphere
(c) Northern Hemisphere
(d) Eastern Hemisphere
Answer:
(d) Eastern Hemisphere

Question 4.
The 23 ° N line of latitude is called _______.
(a) Tropic of Capricorn
(b) Tropic of Cancer
(c) Arctic Circle
(d) Antarctic Circle
Answer:
(b) Tropic of Cancer

Question 5.
180° line of longitude is ……………..
(a) Equator
(b) International Date Line
(c) Prime Meridian
(d) North Pole
Answer:
(b) International Date Line

Question 6.
The Sun is found overhead the Greenwich Meridian at ________
(a) 12 midnight
(b) 12 noon
(c) 1 p.m.
(d) 11 a.m.
Answer:
(b) 12 noon

Question 7.
A day has ……………
(a) 1240 minutes
(b) 1340 minutes
(c) 1440 minutes
(d) 1140 minutes
Answer:
(c) 1440 minutes

Question 8.
Which of the following lines of longitude is considered for the Indian Standard Time?
(a) 82 1/2° E
(b) 82 1/2° W
(c) 811/2° E
(d) 81 1/2° W
Answer:
(a) 82 1/2° E

Question 9.
The total number of lines of latitude are ……………
(a) 171
(b) 161
(c) 181
(d) 191
Answer:
(c) 181

Question 10.
The total number of lines of longitude are ________
(a) 370
(b) 380
(c) 360
(d) 390
Answer:
(c) 360

III. pic the odd one Answer

Question 1.
North Pole, South Pole, Equator, International Date Line.
Answer:
International Dateline

Question 2.
Tropic of Capricorn, Tropic of Cancer, Equator, Prime Meridian.
Answer:
Prime Meridian

Question 3.
Torrid Zone, Time Zone, Temperate Zone, Frigid Zone
Answer:
Time Zone

Question 4.
Royal Astronomical Observatory, Prime Meridian, Royal Astronomical Greenwich Meridian, International Date Line.
Answer:
Royal Astronomical observatory

Question 5.
10° North, 20° South, 30°, North, 40° West
Answer:
40° west.

IV. Match the following

Answer:
1. – d
2. – c
3. – b
4. – a

V. Examine the following statements

1. The Earth is spherical in shape.
2. The shape of the Earth is called a geoid.
3. The Earth is flat.
Look at the options given below and choose the correct answer
(a) 1 and 3 are correct
(b) 2 and 3 are correct
(c) 1 and 2 are correct
(d) 1, 2, and 3 are correct
Answer:
(c) 1 and 2 are correct

VI. Examine the following statements

Question 1.
Statement I: The lines of latitude on Earth are used to find the location of a place and define the heat zones on Earth.
Statement II: The lines of longitudes on Earth are used to find the location of a place and to calculate time.
Choose the correct option:
(a) Statement I is correct; II is wrong
(b) Statement I is wrong; II correct
(c) Both the statements are correct
(d) Both the statements are wrong
Answer:
(a) Statement I is correct; II is wrong

VII. Name the following

Question 1.
The imaginary lines are drawn horizontally on Earth
Answer:
Lines of latitude/parallels

Question 2.
The imaginary lines are drawn vertically on Earth.
Answer:
Lines of longitude /Meridians

Question 3.
The three dimensional model of the Earth.
Answer:
Globe

Question 4.
India is located in this hemisphere based on lines of longitude.
Answer:
Southern Hemisphere

Question 5.
The network of lines of latitude and longitude.
Answer:
Earth grid / Geographic grid

VIII. Answer briefly

Question 1.
What is a geoid?
Answer:

1. The Earth cannot be compared with any other geometrical shape as it has a very unique shape.
2. Hence, its shape is called a geoid (earth shaped).

Question 2.
What is the local time?
Answer:

1. When the sun is overhead on a particular line of longitude, it is 12 moon at all the places located on that line of longitude.
2. This is called local time.

Question 3.
How many times would the sun pass overhead a line of longitude?
Answer:
The sun is overhead on a line of longitude only once a day.

Question 4.
What are lines of latitude and longitude?
Answer:

1. There are imaginary lines which are drawn on the globe horizontally and vertically to find a location and calculate distance and time.
2. These imaginary lines are called lines of latitudes and longitudes.

Question 5.
Name the four hemispheres of the Earth.
Answer:

1. Northern Hemisphere,
2. Southern Hemisphere,
3. Eastern Hemisphere and
4. Western Hemisphere.

IX. Give reason

Question 1.
The 0° line or longitude is called the Greenwich Meridian.
Answer:
The 0° line of longitude is called the Greenwich Meridian because it passes through Greenwich.

Question 2.
The regions on Earth between North & South lines of latitude (66 Vi°) and poles (90°) is called Frigid Zone.
Answer:

1. From the Arctic circle (66 ‘A° N) to the North Pole (90° N) and from the Antarctic circle (66 Vi0 S) to the South Pole (90° S) the sun’s rays full further inclined, through out the year.
2. The temperature is very low.
3. Hence this region is known as Frigid Zone.

Question 3.
The International Date Line runs zigzag.
Answer:
If the International Date line is drawn straight, two places in the same country would have different dates. So the International date line is found Zig Zag to avoid confusion.

X. Answer in detail

Question 1.
What are the uses of globe?
Answer:

1. Since the Earth is huge and we live on a very area, we are not able to see the Earth as a whole.
2. But when we travel to space, we can see the Earth as a whole.
3. So, in order to see the shape of the Earth as a whole and to know its unique features, a three-dimensional model of the Earth was created with a specific scale in the name of the globe.

Question 2.
How are the hemispheres divided on the basis of lines of latitude and longitude? Explain with diagrams.
Answer:
Northern Hemisphere:
Northern Hemisphere. The area of the Earth found between the Equator (Oo) and the North pole (90oN) is called the Northern Hemisphere.

Southern Hemisphere:
Southern Hemisphere. The area of the Earth from the Equator (0°) and the South pole (90°S) is called the Southern Hemisphere.

Eastern Hemisphere:
Eastern Hemisphere. The part of the Earth between the 0° line of longitude and 180° East line of longitude is known as the Eastern Hemisphere.

Western Hemisphere
Western Hemisphere. The part of the Earth from Oo line of longitude and 180° West line of longitude is called as Western Hemisphere.

Question 3.
What are the significant lines of latitude? Explain the zones found between them.
Answer:

1. The significant lines of latitude are
2. Equator 0°
3. Tropic of cancer 23 1/2° N
4. Tropic of Capricorn 23 1/2° S
5. Arctic Circle 66 1/22°N
6. Antarctic Circle 66 1/2° S
7. North Pole 90° N
8. South Pole 90° S
9. Based on the amount of heat received from the sun, our world is broadly divided into three heat zones.

1. The Torrid Zone : On both sides of the equator, the region lying between the Tropic of cancer and Tropic of Capricorn is called the Torrid zone. This zone gets the direct rays of the sun all the year round. Hence the climate is hot and humid.

2. The Temperature Zone : This zone is neither hot nor very cold. It lies between the Torrid zone and Frigid zone in both the hemispheres.

3. The Frigid Zone : The region lying between the Arctic circle and North pole and between Antarctic circle and south pole is called the frigid zone. It receives very slanting rays of the sun and is therefore very cold.

Question 4.
Explain : Indian Stanard Time.
Answer:

1. The longitudinal extent of India is from 68° 7’E to 97° 25’E
2. Twenty nine lines of longitude pass through India.
3. Having 29 standard time is not logical
4. Hence 821/2° E line of longitude is observed as the prime meridian to calculate the Indian standard Time (IST)

XI. Activity

There are five Posistion marked on the grid given below. Look at them carefully and fill the blanks with reference to the lines of latitude and longitude. The first one is done for you.

1. The latitudinal and longitudinal reference of point A 40° N 30°W
2. The latitudinal and longitudinal reference of point B 20° N 10°W
3. The latitudinal and longitudinal reference of point C 10° N 20°W
4. The latitudinal and longitudinal reference of point D 40° N 50°W
5. The latitudinal and longitudinal reference of point E 20° N 20°W

Samacheer Kalvi 6th Social Science Globe Additional Important Questions and Answers

I. Fill in the blanks Answer

1. The surface area of the Earth is ………….. million square kilometres.
2. ………….. was the first person to draw the lines of latitude and longitude on a map
3. The Royal Astronomical observatory is located at …………..
4. The directions on the ground are always shown with respect to the …………..
5. There are four ………….. directions.

Answer:

1. 510.1
2. Ptolemy
3. Greenwich
4. North
5. Cardinal

II. Answer the following questions

Question 1.
Who said this? The stars in the sky seem to move towards the west because of the Earth’s rotation on its axis
Answer:
Aryabhata – The Indian astronomer

Question 2.
Who wrote the book ‘Geographia’?
Answer:
Ptolemy, (a Greco – Roman mathematician (astronomer and geographer)

Question 3.
Name the country that has 7 time zones.
Answer:
Russia

III. Answer in briefly

Question 1.
Define Meridian
Answer:
The word meridian is derived from the latin word ‘Meridianus’. It means mid day. So, meridian means the postion of the sun overhead at the place at noon.

Question 2.
What is an axis?
Answer:

1. An imaginary line around which a large round object such as the Earth turns.
2. The Earth rotates on its axis between the north and South Poles.

Question 3.
What is hemisphere?
Answer:
A half of the earth usually as divided into Northern and Southern halves by the equator or into Western and Eastern halves by an imaginary line passing through the poles.

IV. Choose the correct answer

Question 1.
23 1/220° N and S 66 1/220° N and S lines of latitudes are called ……………..
(a) Low latitudes
(b) Middle latitudes
(c) High latitudes
Answer:
(b) Middle latitudes

Question 2.
The Sun’s rays fall vertically in this region.
(a) Frigid Zone
(b) Temperate Zone
(c) Torrid Zone
Answer:
(c) Torrid Zone

Question 3.
High latitudes are there between
(a) 66 1/2°N and S – 90°N and S
(b) 231/2°N and S and 66f°N and S
(c) 0° – 23 1/2°N and S
(d) North poles
Answer:
(a) 66 1/2° N and S – 90°N and S

Question 4.
Latitudes are also known as ……………..
(a) Nilavangu
(b) Ahalangu
(c) Nettangu
Answer:
(b) Ahalangu

Question 5.
Lines of latitudes merge
(a) at poles
(b) at the equator
(c) at International Date line
(d) do not merge
Answer:
(d) do not merge

V. Match the following

Answer:
1. – b
2. – d
3. – e
4. – a
5. – c

VI. Answer in detail

Question 1.
Draw the Heat Zones of the Earth
Answer:

VII. Mind map

Students can Download Tamil Nadu 11th Physics Model Question Paper 1 English Medium Pdf, Tamil Nadu 11th Physics Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 11th Physics Model Question Paper 1 English Medium

General Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 15 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 16 to 24 in Part II are two-mark questions. These are to be answered in about one or two sentences.
6. Question numbers 25 to 33 in Part III are three-mark questions. These are to be answered in about three to five short sentences.
7. Question numbers 34 to 38 in Part IV are five-mark questions. These are to be answered in detail Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 70

PART – I

Answer all the questions: [15 × 1 = 15]

Question 1.
A cyclist moving on a circular track of radius 40 m completes half a revolution in 40 sec average velocity is ………………..
(a) 0
(b) 2 m/s
(c) 4 m/s
(d) 2π m/s
Hint:
Displacement of the cyclist in half revolution is
d = diameter of the circular track
i.e., d= 80 m
Time taken, t = 40 s
Average velocity, V =  = \(\frac{80}{40}\)
V = 2 m/s
Answer:
(b) 2 m/s

Question 2.
A wheel has angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2 seconds it has rotated through an angle of (in radian) ………………..
(a) 10
(b) 12
(c) 4
(d) 6
Answer:
(a) 10

Question 3.
If the origin of co-ordinate system lies at the centre of mass. The sum of the moments of the masses of the system about the centre of mass is …………………
(a) May be greater than zero
(b) May be less than zero
(c) May be equal to zero
(d) Always zero
Answer:
(d) Always zero

Question 4.
Dimensional formula for co-efficient of viscousity
(a) ML^-2 T^-2
(b) ML^-2 T^-1
(c) ML^-1 T^-1
(d) M^-1 L^-1 T^-1
Answer:
(c) ML^-1 T^-1

Question 5.
Action and reaction …………………
(a) Acts on same object
(b) Acts on two different objects
(c) Have resultant not zero
(d) Acts on the same direction
Answer:
(b) Acts on two different objects

Question 6.
A spring is stretched by applying load to its free end. The strain produced in the spring is …………………
(a) Volumetric
(b) Shear
(c) Longitudinal
(d) Longitudinal and shear
Answer:
(d) Longitudinal and shear

Question 7.
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?
(a) 0.25 rad s^-2
(b) 25 rad s^-2
(c) 5 ms^-2
(d) 25 ms^-2

Hint:
τ = F × r
Iα = F × r
MR² × α = 30 × \(\frac{40}{100}\); \(\frac { 3\times 40\times 40\times \alpha }{ 100\times 100 } \) = 12
\(\frac { 3\times 16\times \alpha }{ 100 } \) = 12; α = 25 rad/s²
Answer:
(b) 25 rad s^-2

Question 8.
The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (E is total energy) ………………
(a) \(\frac{2}{3}\) E
(b) \(\frac{1}{3}\) E
(c) \(\frac{1}{4}\) E
(d) \(\frac{1}{2}\) E
Hint:
PE = \(\frac{1}{2}\) kx²
⇒ \(P E_{V_{2}}=\frac{1}{2} K\left(\frac{A}{2}\right)^{2}=\frac{1}{4}\left(\frac{1}{2} K A^{2}\right)\)
Answer:
(c) \(\frac{1}{4}\) E

Question 9.
A particle executes simple harmonic motion with an angular velocity and maximum acceleration of 3.5 rad/s and 7.5 m/s² respectively. Amplitude of the oscillation is ………………
(a) 0.36
(b) 0.28
(c) 0.61
(d) 0.53
Hint:
x = A sin ωt
∴ a = \(\frac { d^{ 2 }x }{ dt^{ 2 } } \) = -Aω² sinωt
∴Maximum acceleration |a_max| = Aω²
Now Aω² = 7.5
A = \(\frac { 7.5 }{ \omega ^{ 2 } } \) = \(\frac { 7.5 }{ (3.5)^{ 2 } } \) = 0.61
Answer:
(c) 0.61

Question 10.
If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved, then its fundamental frequency will become ………………….
(a) \(\frac{n}{4}\)
(b) \(\sqrt{2n}\)
(c) n
(d) \(\frac { n }{ \sqrt { 2 } } \)
Hint:

Answer:
(c) n

Question 11.
The theory of refrigerator is based on …………….
(a) Joule-Thomson effect
(b) Newton’s particle theory
(c) Joule’s effect
(d) None of the above
Answer:
(d) None of the above

Question 12.
Work done by 0.1 mole of a gas at 27°C to double its volume at constant pressure is ………………..
(a) 54 cal
(b) 60 cal
(c) 546 cal
(d) 600 cal
Hint:
Workdone (W) = – p.dv = nRT
= 0.1 × (0.2 cal) × (273 + 27) = 0.1 × 2 × 300
W = 60 cal
Answer:
(b) 60 cal

Question 13.
When a lift is moving upwards with acceleration a, then time period of simple pendulum in it will ………………..
(a) 2π\(\sqrt { \frac { 1 }{ g+a } } \)
(b) 2π\(\sqrt { \frac { g+a }{ l } } \)
(c) \(\frac{1}{2π}\)\(\sqrt { \frac { 1 }{ g+a } } \)
(d) \(\frac{1}{2π}\)\(\sqrt { \frac { g+a }{ l } } \)
Answer:
(a) 2π\(\sqrt { \frac { 1 }{ g+a } } \)

Question 14.
A disc is rotating with angular speed ω. If a child sits on it, what is conserved?
(a) Linear momentum
(b) Angular momentum
(c) Kinetic energy
(d) Potential energy
Answer:
(b) Angular momentum

Question 15.
The vectors \(\vec { A } \) and \(\vec { B } \) are such that |\(\vec { A } \) + \(\vec { B } \)| = |\(\vec { A } \) – \(\vec { B } \)|. The angle between the two vector is ………………..
(a) 45°
(b) 60°
(c) 75°
(d) 90°
Hint:
The angle between two vector is always 90°.
Answer:
(d) 90°

PART – II

Answer any six questions in which Q. No 23 is compulsory. [6 × 2 = 12]

Question 16.
Velocity – time graph of a moving object is shown below. What is the acceleration of the object? Also draw displacement – time graph for the motion of the object?
Answer:
The given graph shows that the velocity of the object is constant. That is, the velocity of the object is not changing, so the acceleration of the object is zero. Since the acceleration of an object is given by


Displacement – time graph for the motion of the object is shown in the figure above.

Question 17.
Can a body subjected to a uniform acceleration always move in a straight line?
Answer:
It will be a straight line in one dimensional motion but not applicable for two dimensional motion because the projectile has a parabolic path but it has a uniform acceleration.

Question 18.
Calculate the viscous force on a ball of radius 1mm moving through a liquid of viscosity 0.2 Nsm^-2 at a speed of 0.07 ms^–
Answer:
Radius of the ball (a) = 1mm = 1 × 10^-3m
Co-effecient of viscosity of liquid (η) = 0.2 Nsm^-2
Speed of the ball (v) = 0.07 ms^-1
According to Stoke’s law
Viscous force F = 6 π η av
= 6 × 3.14 × 1 × 10^-3 × 0.2 × 0.07
= 0.26376 × 10^-3 = 2.64 × 10^-4N

Question 19.
Calculate the work done by a force of 30 N in lifting a load of 2 kg to a height of 10 m (g = 10ms^-2)
Answer:
Given data: F = 30 N, load (m) 2 kg; height = 10m, g = 10 ms^-2
Gravitational forcc F = mg = 30 N
The distance moved h = 10 m
Work done on the object W = Fh = 30 × 10 = 300 J

Question 20.
Why are shockers used in automobiles like car?
Answer:
In the event of jump or jerk, the lime of action of force increases. Since the product of force aid time is constant in a given situation. therefore the force decreases.

Question 21.
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighted 250 N on the surface?
Answer:
As g_d = g (1 – \(\frac{d}{R}\)) ⇒ mg_d = mg(1 – \(\frac{d}{R}\))
Here d = \(\frac{R}{2}\)
∴mg_d = (250) × (1 – \(\frac { R/2 }{ R } \)) = 250 × \(\frac{1}{2}\) = 125N

Question 22.
How do you deduce that two vectors are perpendicular?
Answer:
If two vectors \(\vec { A } \) and \(\vec { B } \) are perpendicular to each other than their scalar product \(\vec { A } \).\(\vec { B } \) = O because cos 90° = 0. Then the vectors \(\vec { A } \) and \(\vec { B } \) are said to be mutually orthogonal.

Question 23.
An air bubble of radius r in water is at a depth of h below the water surface at some instant. If P is atmospheric pressure and d and T are the density and surface tension of ater respectively. Calculate the pressure P inside the bubble?
Answer:
Excess ot pressure inside the air bubble in water = \(\frac{2T}{r}\)
∴ Total pressure inside the air bubble
= atmospheric pressure + pressure due to liquid column + Excess pressure due to surface tension
= P + hρg + \(\frac{2T}{r}\)

Question 24.
Define beats?
Answer:
Formation of beats: When two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed. This phenomenon is known as beats. The number of amplitude maxima per second is called beat frequency. If we have two sources, then their difference in frequency gives the beat frequency. Number of beats per second.
n = |f₁ – f₂| per second.

PART – III

Answer any six questions in which Q.No. 29 is compulsory. [6 × 3 = 18]

Question 25.
Define centripetal acceleration and give any two examples?
Answer:
The acceleration that is directed towards the centre of the circle along the radius and perpendicular to the velocity of the particle is known as centripetal or radial or normal acceleration.
Example:-

1. In the case of planets revolving round the Sun or the moon revolving round the earth, the centripetal force is provided by the gravitational force of attraction between them.
2. For an electron revolving round the nucleus in a circular path, the electrostatic force of attraction between the electron and the nucleus provides the necessary centripetal force.

Question 26.
Write any six properties of vector product of two vectors?
Answer:
(I) The vector product of any two vectors is always another vector whose direction is perpendicular to the plane containing these two vectors, i.e., orthogonal to both the vectors \(\vec { A } \) and \(\vec { B } \), even though the vectors \(\vec { A } \) and \(\vec { B } \) may or may not be mutually orthogonal.

(II) The vector product of two vectors is not commutative, i.e., \(\vec { A } \) × \(\vec { B } \) ≠ \(\vec { B } \) × \(\vec { A } \). But, \(\vec { A } \) × \(\vec { B } \) = – \(\vec { B } \) × \(\vec { A } \) .
Here it is worthwhile to note that |\(\vec { A } \) × \(\vec { B } \)| = |\(\vec { B } \) × \(\vec { A } \)| = AB sin θ i.e., in the case of the product vectors \(\vec { A } \) × \(\vec { B } \) and \(\vec { B } \) × \(\vec { A } \), the magnitudes are equal but directions are opposite to each other.

(III) The vector product of two vectors will have maximum magnitude when sin θ = 1, i.e., θ = 90° i.e., when the vectors \(\vec { A } \) and \(\vec { B } \) are orthogonal to each other.
(\(\vec { A } \) × \(\vec { B } \))_max = AB\(\hat { n } \)

(IV) The vector product of two non-zero vectors will be minimum when sin θ = 0, i.e., θ = 0° or θ = 180°
(\(\vec { A } \) × \(\vec { B } \))_min = 0
i.e., the vector product of two non-zero vectors vanishes, if the vectors are either parallel or antiparallel.

(V) The self-cross product, i.e., product of a vector with itself is the null vector
\(\vec { A } \) × \(\vec { A } \) = AA sin 0° \(\hat { n } \) = \(\vec { 0 } \)
In physics the null vector \(\vec { 0 } \) is simply denoted as zero.

(VI) The self-vector products of unit vectors are thus zero.
\(\hat { i } \) × \(\hat { i } \) = \(\hat { j } \) × \(\hat { j } \) = \(\hat { k } \) × \(\hat { k } \) = 0

Question 27.
Show that the pressure of the gas is equal to two third of mean kinetic energy per unit volume?
Answer:
The internal energy of the gas is given by
U = \(\frac{3}{2}\) NkT
The above equation can also be written as
U = \(\frac{3}{2}\) PV
Since PV = NkT
P = \(\frac{2}{3}\) \(\frac{U}{V}\) = \(\frac{2}{3}\) u
From the equation (1), we can state that the pressure of the gas is equal to two thirds of internal energy per unit volume or internal energy density (u = \(\frac{U}{V}\))
Writing pressure in terms of mean kinetic energy density using equation.
P = \(\frac{1}{3}\) nm\(\overline { V^{ 2 } } \) = \(\frac{1}{3}\) ρ\(\overline { V^{ 2 } } \)
where ρ = nm = mass density (Note n is number density)
Multiply and divide R.H.S of equation (2) by 2, we get
P = \(\frac{2}{3}\)(\(\frac{ρ}{2}\) \(\overline { V^{ 2 } } \))
P = \(\frac{2}{3}\) \(\overline { KE } \)
From the equation (3), pressure is equal to \(\frac{2}{3}\) of mean kinetic energy per unit volume.

Question 28.
Derive an expression for gravitational potential energy?
Answer:
The gravitational tbrce is a conservative force and hence we can define a gravitational potential energy associated with this conservative force field.
Two masses m₁ and m₂, are initially separated by a distance r’. Assuming m₁ to be fixed in its position. work must be done on m₂ to move the distance from r’ to r.


To move the mass m₂, through an infinitesimal displacement d\(\vec { r } \) from \(\vec { r } \) to \(\vec { r } \) + d\(\vec { r } \) , work has to be done externally. This infinitesimal work is given by
dW = \(\vec { F } \)_ext . d\(\vec { r } \) ……………….. (1)
The work is done against the gravitational force, therefore,
\(\vec { F } \)_ext = \(\frac { Gm_{ 1 }m_{ 2 } }{ r^{ 2 } } \hat { r } \) ………………. (2)
Substituting equation (2) in (1), we get
dW = \(\frac { Gm_{ 1 }m_{ 2 } }{ r^{ 2 } } \hat { r } \).d\(\vec { r } \) ………………… (3)
d\(\vec { r } \) = dr \(\hat { r } \) ⇒ dW = \(\frac { Gm_{ 1 }m_{ 2 } }{ r^{ 2 } } \hat { r } \).(dr \(\hat { r } \))
\(\hat { r } \).\(\hat { r } \) = 1 (Since both are unit vectors)
∴ dW = \(\frac { Gm_{ 1 }m_{ 2 } }{ r^{ 2 } } \) dr …………….. (4)
Thus the total work done for displacing the particle from r’ to r is

This work done W gives the gravitational potential energy difference of the system of masses and m₁ and m₂ when the separation between them are r and r’ respectively.

Question 29.
A satellite orbiting the Earth in a circular orbit of radius 1600 km above the surface of the Earth. What is the acceleration experienced by satellite due to Earth’s gravitational force?
Answer:
g’ = g(1 – \(\frac { 2h }{ R_{ e } } \))
= g(\(\frac { 1-2\times 1600\times 10^{ 3 } }{ 6400\times 10^{ 3 } } \)) = g(1 – \(\frac{2}{4}\))
g’ = g (1 – \(\frac{1}{2}\)) = \(\frac{g}{2}\)
g’ = g (1- \(\frac{1}{2}\)) = \(\frac{g}{2}\)
g’ = \(\frac{8}{2}\) (or) g’ = \(\frac{9.8}{2}\) = 4.9ms^-2

Question 30.
Explain the v ariation of a g with latitude?
Answer:
When an object is on the surface fo the Earth, it experiences a centrifugal force that depends on the latitude of the object on Earth. If the Earth were not spinning, the force on the object would have been mg. However, the object experiences an additional centrifugal force due to spinning of the Earth.
This centrifugal force is given by mωR’.
\(\mathrm{OP}_{z}, \cos \lambda=\frac{\mathrm{PZ}}{\mathrm{OP}}=\frac{\mathrm{R}^{\prime}}{\mathrm{R}}\)
R’ = R cos λ
where λ is the latitude. The component of centrifugal acceleration experienced by the object in the direction opposite to g is
\(a_{\mathrm{PQ}}=\omega^{2} \mathrm{R} \cos \lambda=\omega^{2} \mathrm{R} \cos ^{2} \lambda\)
Since R’ = R cos λ

Therefore, g = g – ω²R cos² λ
From the above expression, we can infer that at equator, λ = 0, g’ = g – ω²R. The acceleration due to gravity is minimum. At poles λ = 90; g’ = g, it is maximum. At the equator, g’ is minimum.

Question 31.
A bullet of mass 50g is fired from below into a suspended object of mass 450 g. The object rises through a height of 1.8 m with bullet remaining inside the object. Find the speed of the bullet. Take g = 10 ms^-2
Answer:
m₁ = 50 g = 0.05 kg; m₂ = 450 g = 0.45 kg
The speed of the bullet is u₁ The second body is at rest (u₂ = 0). Let the common velocity of the bullet and the object after the bullet is embedded into the object is v.
v = \(\frac{m_{1} u_{1}+m_{2} u_{2}}{\left(m_{1}+m_{2}\right)}\)
v = \(\frac{0.05 u_{1}+(0.45 \times 0)}{(0.05+0.45)}\) = \(\frac{0.05}{0.50}\)u₁
The combined velocity is the initial velocity for the vertical upward motion of the combined bullet and the object. From second equation of motion,
v = \(\sqrt{2gh}\)
v = \(\sqrt{2 \times 10 \times 1.8}\) = \(\sqrt{36}\)
v = 6 ms^-1
Substituting this in the above equation, the value of u₁ is
6 = \(\frac{0.05}{0.50}\)u₁ or u₁ = \(\frac{0.05}{0.50}\) × 6 = 10 × 6
u₁ = 60ms^-1

Question 32.
If the piston of a container is pushed fast inward. Will the ideal gas equation be valid in the intermediate stage? If not, why?
Answer:
When the piston is compressed so quickly that there is no time to exchange heat to the surrounding, the temperature of the gas increases rapidly. In this intermediate stage the ideal gas equation be not valid. Because this equation can be relates the pressure, volume and temperature of thermodynamic system at equilibrium.

Question 33.
Calculate how many times more intense is 90 dB sound compared to 40 dB sound?
Answer:
Given Data:
L = log \(\frac { I }{ I_{ 0 } } \) = log I – log I₀
We get 90 dB = 9 B = log I₁ – log I₀ ……………….. (1)
40 dB = 4 B = logI₂ – logI₀ ………………….. (2)
Subtract (2) from (1)
50 dB = 5B = log I₁ – logI₂
5 = log₁₀ (\(\frac{I_{1}}{I_{2}}\))
\(\frac{I_{1}}{I_{2}}\) = 10⁵

PART – IV

Answer all the questions. [ 5 × 5 = 25]

Question 34 (a)
Obtain an expression for the time period T of a simple pendulum. The time period T depends on

1. Mass of the bob(m)
2. Length of the pendulum (l)
3. Acceleration due to gravity (g) at the place where the pendulum is suspended, (constant k = 2π)

Answer:
Example:
An expression for the time period T of a simple pendulum can be obtained by using this method as follows.
Let true period T depend upon

1. Mass m of the bob
2. Length l of the pendulum and
3. Acceleration due to gravity g at the place where the pendulum is suspended. Let the constant involved is k = 2π.

Solution:

Here k is the dimensionless constant. Rewriting the above equation with dimensions.

Comparing the powers of M, L and T on both sides, a = 0, b + c = 0, -2c = 1
Solving for a, b and c ⇒ a = 0, b = 1/2, and c = -1/2
From the above equation
T = \(\mathrm{k} \mathrm{m}^{0} l^{1}=g^{-1}-2\)
T = \(k\left(\frac{1}{g}\right)^{1}\) = \(k \sqrt{1 / g}\)
Experimentally k = 2π, hence
T = \(2 \pi \sqrt{1 / g}\)

[OR]

(b) Obtain an expression for the escape speed in detail?
Answer:
Consider an object of mass M on the surface of the Earth. When it is thrown up with an initial speed v_i the initial total energy of the object is
\(\mathrm{E}_{i}=\frac{1}{2} \mathrm{M} v_{i}^{2}-\frac{\mathrm{GMM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{E}}}\) ………………. (1)
where, M_E is the mass of the Earth and R_E the radius of the Earth.
The term \(-\frac{\mathrm{GMM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{E}}}\) is the potential energy of the mass M.
When the object reaches a height far away from Earth and hence treated as approaching infinity, the gravitational potential energy becomes zero [U(∞) = 0] and the kinetic energy becomes zero as well. Therefore the final total energy of the object becomes zero. This is for minimum energy and for minimum speed to escape. Otherwise kinetic energy can be nonzero.
E_F = 0
E_i = E_f ……………….. (2)
Substituting (1) in (2) we get,

Consider the escape speed, the minimum speed required by an object to escape Earth’s gravitational field, hence replace v_i with v_e i.e..

From equation (4) the escape speed depends on two factors acceleration due to gravity and radius of the Earth. It is completely independent of the mass of the object. By substituting the values of g (9.8 ms^-2) and R_e = 6400 km, the escape speed of the Earth is v_e = 11.2 kms^-1. The escape speed is independent of the direction in which the object is thrown. Irrespective of whether the object is thrown vertically up, radially outwards or tangentially it requires the same initial speed to escape Earth’s gravity.

Question 35 (a).
Derive an expression for loss of kinetic energy in perfect inelastic collision?
Answer:
In perfectly inelastic collision, the loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, heat, light etc. Let KE_i be the total kinetic energy before collision and KE_f be the total kinetic energy after collision.
Total kinetic energy before collision,
\(\mathrm{KE}_{i}=\frac{1}{2} m_{1} u_{1}^{2}+\frac{1}{2} m_{2} u_{2}^{2}\) …………….. (1)
Total kinetic energy after collision
KE_f = \(\frac{1}{2}\) (m₁ + m₂)v² …………….. (2)
Then the loss of kinetic energy is
Loss of KE, ∆Q = KE_f – KE_i = \(\frac{1}{2}\) (m₁ + m₂)v² – \(\frac{1}{2}\) m₁ u₁² – \(\frac{1}{2}\) m₂ u₂² ………………. (3)
Substituting equation v = \(\frac{m_{1} u_{1}+m_{2} u_{2}}{\left(m_{1}+m_{2}\right)}\) in equation (3), and on simplying (expand v by using the algebra) (a + b)² = a² + b² + 2ab, we get
Loss of KE, ∆Q = \(\frac{1}{2}\) \(\left(\frac{m_{1} m_{2}}{m_{1}+m_{2}}\right)\) (u₁ – u₂)²

(b) A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. Calculate the initial velocity of the shell?
Answer:
Given Data :
m = 200 gm = 0.2 kg; M = 4 kg.
Energy generated = 1.05 KJ = 1.05 × 10³ J
According to law of Conservation of linear momentum
mv = Mv’
∴v’ = (\(\frac{m}{M}\)) v
Total K.E of the gun and bullet

[OR]

(c) State parallel axis theorem?
Answer:
Parallel axis theorem: Parallel axis theorem states that the moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis through its center of mass and the product of the mass of the body and the square of the perpendicular distance between the two axes.

If I_C is the moment of inertia of the body of mass M about an axis passing through the center of mass, then the moment of inertia I about a parallel axis at a distance d from it is given by the relation,
I = I_C + Md²

(d) Calculate the moment of inertia of uniform circular disc of mass 500 G radius 10 cm about

1. The diameter of the disc
2. The axis, tangent to the disc and parallel to its diameter
3. The axis through the centre of the disc and perpendicular to its plane

Answer:
1. Given Data: M = 500 g = 0.5 kg. R = 10 cm = 10 × 10^-2 m
Moment of inertia of disc about diameter = Id = \(\frac{1}{4}\) MR²
Id = \(\frac{1}{4}\) × 0.5 × 0.1 kg m² = 0.0125 kg m²

2. Apply a parallel axes theorem, moment of inertia of the disc about a tangent to the disc and parallel to the diameter of the disc
= \(\frac{1}{4}\) MR² + MR² = \(\frac{5}{4}\) MR² = \(\frac{5}{4}\) × 0.5 × 1
= 0.0625 kgm²

3. Moment of inertia of the disc about an axis passing through the centre of disc and perpendicular to the plane of the disc
= \(\frac{1}{2}\) MR² = \(\frac{1}{2}\) × 0.5 × 0.1 = 0.025 kgm²

Question 36 (a).
Prove the law of conservation of linear momentum. Use it to find the recoil velocity of a gun when a bullet is fired from it?
Answer:
In nature, conservation laws play a very important role. The dynamics of motion of bodies can be analysed very effectively using conservation laws. There are three conservation laws in mechanics. Conservation of total energy, conservation of total linear momentum, and conservation of angular momentum. By combining Newton’s second and third laws, we can derive the law of conservation of total linear momentum.

When two particles interact with each other, they exert equal and opposite forces on each other. The particle 1 exerts force \(\vec { F } \)₁₂ on particle 2 and particle 2 exerts an exactly equal and opposite force \(\vec { F } \)₁₂ on particle 1 according to Newton’s third law.
\(\vec { F } \)₂₁ = –\(\vec { F } \)₁₂ …………… (1)
In terms of momentum of particles, the force on each particle (Newton’s second law) can be written as
\(\vec { F } \)₁₂ = \(\frac{d \bar{p}_{1}}{d t}\) and \(\vec { F } \)₂₁ = \(\frac{d \vec{p}_{2}}{d t}\) ……………… (2)

Here \(\vec { P } \)₁ is the momentum of particle 1 which changes due to the force \(\vec { F } \)₁₂ exerted by particle 2. Further \(\vec { P } \)₂ is the momentum of particle 2. This changes due to \(\vec { F } \)₂₁ exerted by particle 1.
Substitute equation (2) in equation (1)

It implies that \(\vec { P } \)₁ + \(\vec { P } \)₂ = (constant vector always)

\(\vec { P } \)₁ + \(\vec { P } \)₂ is the total linear momentum of the two particles ( \(\vec { P } \)_tot = \(\vec { P } \)₁ + \(\vec { P } \)₂). It is also called as total linear momentum of the system. Flere, the two particles constitute the system. From this result, the law of conservation of linear momentum can be stated as follows.

If there are no external forces acting on the system, then the total linear momentum of the system ( \(\vec { P } \)_tot) is always a constant vector. In other words, the total linear momentum of the system is conserved in time. Here the word ‘conserve’ means that \(\vec { P } \)₁ and \(\vec { P } \)₂ can vary,
in such a way that \(\vec { P } \)₁ + \(\vec { P } \)₂ is a constant vector.

The forces \(\vec { F } \)₁₂ and \(\vec { F } \)₁₂ are called the internal forces of the system, because they act only between the two particles. There is no external force acting on the two particles from outside. In such a case the total linear momentum of the system is a constant vector or is conserved.

To find the recoil velocity of a gun when a bullet is fired from it:
Consider the firing of a gun. Here the system is Gun + bullet. Initially the gun and bullet are at rest, hence the total linear momentum of the system is zero. Let \(\vec { P } \)₁ be the momentum of the bullet and \(\vec { P } \)₂ the momentum of the gun before firing. Since initially both are at rest.

\(\vec { P } \)₁ = 0, \(\vec { P } \)₂ = 0.

Total momentum before firing the gun is zero, \(\vec { P } \)₁ + \(\vec { P } \)₂ = 0

According to the law of conservation of linear momentum, total linear momemtum has to be zero after the firing also.

When the gun is fired, a force is exerted by the gun on the bullet in forward direction. Now the momentum of the bullet changes from \(\vec { P } \)₁ + \(\vec { P } \)₂. To conserve the total linear momentum of the system, the momentum of the gun must also change from \(\vec { P } \)₂ to \(\vec { P } \)₂. Due to the conservation of linear momentum, \(\vec { P } \)₁+ \(\vec { P } \)₂‘= 0. It implies that \(\vec { P } \)₁‘ = –\(\vec { P } \)₂ the momentum of the gun is exactly equal, but in the opposite direction to the momentum of the bullet. This is the reason after firing, the gun suddenly moves backward with the momentum \(\vec { P } \)₂. It is called ‘recoil momentum’. This is an example of conservation of total linear momentum.

[OR]

(b) Derive an expression for escape speed?
Answer:
Consider an object of mass M on the surface of the Earth. When it is thrown up with an initial speed v;, the initial total energy of the object is
\(E_{i}=\frac{1}{2} M v_{i}^{2}-\frac{G M M_{E}}{R_{E}}\) ………………. (1)
where, M_E is the mass of the Earth and RE the radius of the Earth. The term \(-\frac{\mathrm{GMM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{E}}}\) is the potential energy of the mass M.

When the object reaches a height far away from Earth and hence treated as approaching infinity, the gravitational potential energy becomes zero [U(∞) = 0] and the kinetic energy becomes zero as well. Therefore the final total energy of the object becomes zero. This is for minimum energy and for minimum speed to escape. Otherwise kinetic energy can be nonzero.
E_f = 0

According to the law of energy conservation,
E_i – E_f = 0 …………….. (2)

Substituting (1) in (2) we get,
\(\frac{1}{2} \mathrm{M} v_{i}^{2}-\frac{\mathrm{GMM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{F}}}=0\)
\(\frac{1}{2} \mathrm{M} v_{i}^{2}=\frac{\mathrm{GMM}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{E}}}\) …………….. (3)

Consider the escape speed, the minimum speed required by an object to escape Earth’s gravitational field, hence replace v_i with v_e, i.e.,

From equation (4) the escape speed depends on two factors acceleration due to gravity and radius of the Earth. It is completely independent of the mass of the object. By substituting the values of g (9.8 ms^-2) and R_e = 6400 km, the escape speed of the Earth is v_e = 11.2 kms^-1. The escape speed is independent of the direction in which the object is thrown. Irrespective of whether the object is thrown vertically up, radially outwards or tangentially it requires the same initial speed to escape Earth’s gravity.

Question 37 (a).
Explain in detail Newton’s law of cooling?
Answer:
Newton’s law of cooling: Newton’s law of cooling states that the rate of loss of heat of a body is directly proportional to the difference in the temperature between that body and its surroundings.
\(\frac{dQ}{dt}\) ∝ (T – T_s) …………….. (1)

The negative sign indicates that the quantity of heat lost by liquid goes on decreasing with time. Where,

T = Temperature of the object
T_s = Temperature of the surrounding

From the graph in figure it is clear that the rate of cooling is high initially and decreases with falling temperature.

Let us consider an object of mass m and specific heat capacity s at temperature T. Let T_s be the temperature of the surroundings. If the temperature falls by a small amount of T in time dt, then the amount of heat lost is,
dQ = msdT ………………. (2)
Dividing both sides of equation (2) by dt
\(\frac{dQ}{dt}\) = \(\frac{msdT}{dt}\) ……………….. (3)
From Newton’s of cooling
\(\frac{dQ}{dt}\) ∝ (T – T_s)
\(\frac{dQ}{dt}\) = -a(T – T_s) ……………….. (4)

Where a is some positive constant.
From equation (3) and (4)

Integrating equation (5) on both sides,

Where b₁ is the constant of integration. Taking exponential both sides, we get
\(\mathrm{T}=\mathrm{T}_{\mathrm{s}}+b_{2} e^{\frac{-a}{m s}}\) ……………. (6)
Here b₂ = _e^b1 = Constant

[OR]

(b) Derive an expression for pressure exerted by the gas on the wall of the container?
Answer:
Expression for pressure exerted by a gas:
Consider a monoatomic gas of N molecules each having a mass m inside a cubical container of side l.
The molecules of the gas are in random motion. They collide with each other and also with the walls of the container. As the collisions are elastic in nature, there is no loss of energy, but a change in momentum occurs.

The molecules of the gas exert pressure on the walls of the container due to collision on it. During each collision. the molecules impart certain momentum to the wall. Due to transfer of momentum, the walls experience a continuous force. The force experienced per unit area of the walls of the container determines the pressure exerted by the gas. It is essential to determine the total momentum transferred by the molecules in a short interval of time.

A molecule of mass in moving with a velocity \(\vec { v } \) having components (v_x v_y, v_z) hits the right side wall. Since we have assumed that the collision is elastic, the particle rebounds with sanie speed and its x-component is reversed. This is shown in the figure. The components of velocity of the molecule after collision are (-v_x, v_y, v_z)
The x-component of momentum of the molecule bêfore collision = mv_x
The x-component of momentum of the molecule after collision = -mv_x
The change in momentum of the molecule in x direction
= Final momentum – initial momentum = -mv_x – mv_x = -2mv_x
According to law of conservation of linear momentum, the change in momentum of the wall = 2mv_x

The number of molecules hitting the right side wall in a small interval of time ∆t.

The molecules within the distance of v_x ∆t from the right side wall and moving towards the right will hit the wall in the time interval &. The number of molecules that will hit the right side wall in a time interval ∆t is equal to the product of volume (Av_x∆t) and number density of the molecules n). Here A is area of the wall and ii is number of molecules per
unit volume \(\frac{N}{V}\) We have assumed that the number density is the same throughout the cube.

Not all the n molecules will move to the right, therefore on an average only half of the n molecules move to the right and the other half moves towards left side.

Te no.of molecules that hit the right side wall in a time interval ∆t

= \(\frac{n}{2} \mathrm{A} v_{x} \Delta t\) ……………….. (1)
In the same interval of time ∆t, the total momentum transferred by the molecules
\(\Delta \mathrm{P}=\frac{n}{2} \mathrm{A} v_{x} \Delta t \times 2 m v_{x}=\mathrm{A} v_{x}^{2} m n \Delta t\) ……………….. (2)

From Newton’s second law, the change in momentum in a small interval of time gives rise to force.
The force exerted by the molecules on the wall (in magnitude)

F = \(\frac{\Delta p}{\Delta t}=n m \mathrm{A} v_{x}^{2}\) ……………….. (3)
Pressure P = force divided by the area of the wall

P = \(\frac{F}{A}\) = nmv²_x …………………. (4)
Since all the molecules are moving completely in random manner, they do not have same speed. So we can replace the term v²_x by the average \(\bar{v}_{x}^{2}\) in equation (4)

P = nm\(\bar{v}_{x}^{2}\) ………………… (5)

Since the gas is assumed to move in random direction, it has no preferred direction of motion (the effect of gravity on the molecules is neglected). It implies that the molecule has same average speed in all the three direction. So, \(\bar{v}_{x}^{2}\) = \(\bar{v}_{y}^{2}\) = \(\bar{v}_{z}^{2}\). The mean square speed is written as

\(\bar{v}^{2}\) = \(\bar{v}_{x}^{2}\) + \(\bar{v}_{y}^{2}\) + \(\bar{v}_{z}^{2}\) = 3\(\bar{v}_{x}^{2}\)
\(\bar{v}_{x}^{2}\) = \(\frac{1}{3}\) \(\bar{v}^{2}\)
Using this in equation (5), we get
P = \(\frac{1}{3}\)nm \(\bar{v}^{2}\) or P = \(\frac{1}{3}\) \(\frac{N}{V}\) m\(\bar{v}^{2}\) as [n = \(\frac{N}{V}\)] ……………… (6)

Question 38 (a).
Explain with graphs the difference between work done by a constant force and by a variable force. Arrive at an expression for power and velocity. Give some examples for the same?
Answer:
Work done by a constant force: When a constant force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation,
dW = (F cos θ) dr ………………. (1)
The total Work done in producing a displacement from initial position r_i to final position r_f is,

The graphical representation of the work done by a constant force is shown in figure given below. The area under the graph shows the work done by the constant force.

Work done by a variable force:
When the component of a variable force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation.

dW = F cos θ dr [F cos θ is the component of the variable force F]
where, F and θ are variables. The total work done for a displacement from initial position r_i to final position r_f is given by the relation,
W = \(\int_{r_{i}}^{r_{f}} d \mathrm{W}=\int_{r_{i}}^{r_{f}} \mathrm{F} \cos \theta d r\) ………………. (4)

A graphical representation of the work done by a variable force is shown in figure given below. The area under the graph is the work done by the variable force.

Expression for power and velocity

The work done by a force \(\vec { F } \) for a displacement \(\bar { dr } \) is
W = ∫\(\vec { F } \).\(\vec { dr } \) ……………. (1)
Left hand side of the equation (1) can be written as
W = ∫dW = ∫\(\frac{dW}{dt}\) (multiplied and divided by dt) ………………… (2)
Since, velocity is \(\vec { v } \) = \(\frac{d \vec{r}}{d t}\); \(\vec { dr } \) = \(\vec { v } \) dt. Right hand side of the equation (I) can be written as

Substituting equation (2) and equation (3) in equation (1), we get

This relation is true for any arbitrary value of di. This implies that the term within the bracket must be equal to zero, i.e.,
\(\frac{dW}{dt}\) – \(\vec { F } \).\(\vec { v } \) = 0 Or \(\frac{dW}{dt}\) = \(\vec { F } \).\(\vec { v } \)
Hence power P = \(\vec { F } \).\(\vec { v } \)

[OR]

(b) Explain in detail Newton’s law of cooling?
Answer:
Newton’s law of cooling: Newton’s law of cooling states that the rate of loss of heat of a body is directly proportional to the difference in the temperature between that body and its surroundings.
\(\frac{dQ}{dt}\) ∝ (T – T_s)
The negative sign indicates that the quantity of heat lost by liquid goes on decreasing with time. Where,
T = Temperature of the object
T_s = Temperature of the surrounding
From the graph in figure it is clear that the rate of cooling is high initially and decreases with falling temperature.
Let us consider an object of mass m and specific heat capacity s at temperature T. Let T_s be the temperature of the surroundings. If the temperature falls by a small amount dT in
time dt, then the amount of heat lost is,
dQ = msdT ………………. (2)
Dividing both sides of equation (2) by dt

\(\frac{dQ}{dt}\) = \(\frac{msdT}{dt}\) ……………….. (3)
From Newton’s law of cooling
\(\frac{dQ}{dt}\) ∝ (T – T_s)
\(\frac{dQ}{dt}\) -a(T – T_s) …………………. (4)
Where a is a positive constant.
From equation (3) and (4)
– a(T – T_s) = ms \(\frac{dT}{dt}\)
\(\frac{d T}{T-T_{s}}\) = -a\(\frac{a}{ms}\) dt ………………. (5)
Integrating equation (5) on both sides,

Where b₁ is the constant of integration. Taking exponential both sides we get,
\(\mathrm{T}=\mathrm{T}_{s}+b_{2} e^{\frac{-a}{m s}}\) ………………… (6)
Here b₂ = e^b1 = constant

Students can download 6th Social Science Term 3 Geography Chapter 1 Asia and Europe Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science Geography Solutions Term 3 Chapter 1 Asia and Europe

Samacheer Kalvi 6th Social Science Asia and Europe Text Book Back Questions and Answers

I. Choose the correct Answer

Question 1.
Which is not the Western margin of Asia?
(a) Black Sea
(b) Mediterranean Sea
(c) Red Sea
(d) Arabian Sea
Answer:
(d) Arabian Sea

Question 2.
The Intermontane …………… plateau is found between Elbruz and Zagros.
(a) Tibet
(b) Iran
(c) Deccan
(d) The Yunnan
Answer:
(b) Iran

Question 3.
Equatorial climate:
(i) Uniform throughout the year.
(ii) The average / mean rainfall is 200 mm.
(iii) The average temperature is 10°C.
(iv) Of the statements give above.
(a) i alone is correct
(b) ii and iii are correct
(c) i and iii are correct
(d) i and ii are correct
Answer:
(a) i alone is correct

Question 4.
Match list I correctly with list II and select your answer from the codes given below.

Codes:
(a) 2, 3, 4, 1
(b) 4, 3 , 2, 1
(c) 4, 3, 1, 2
(d) 2, 3, 1, 4
Answer:
(a) 2, 3, 4, 1

Question 5.
India is the leading producer of ______
(a) Zinc
(b) Mica
(c) Manganese
(d) Coal
Answer:
(b) Mica

Question 6.
The natural boundary between Spain and France is ……………
(a) The Alps
(b) The Pyrenees
(c) The Carpathian
(d) The Caucasus
Answer:
(b) The Pyrenees

Question 7.
The western and north-western Europe enjoys mild and humid climate.
Choose the correct option:
(a) These regions are found near the equator
(b) It is influenced by the North Atlantic Drift
(c) It is surrounded by mountains
(d) All of the above
Answer:
(b) It is influenced by the North Atlantic Drift

Question 8.
Which of the following statements is incorrect?
(a) Europe produces electricity from hydel power.
(b) All the rivers of Europe originate in the Alps.
(c) Most of the rivers in Europe are used for inland navigation.
(d) The fivers of Europe are perennial in nature.
Answer:
(b) All the rivers of Europe originate in the Alps.

Question 9.
Choose the incorrect pair.
(a) The Meseta – Spain
(b) The Jura – France
(c) The Pennine – Italy
(d) The Black Forest – Germany
Answer:
(c) The Pennines – Italy

Question 10.
Which country in Europe has a very low density of population?
(a) Iceland
(b) The Netherlands
(c) Poland
(d) Switzerland
Answer:
(a) Iceland

II. Fill in the blanks

1. The Taurus and the Pontine ranges radiate from the …………….
2. The wettest place in the world is …………….
3. Iran is the largest producer of ……………. in the world.
4. Europe connected with south and south east Asia by …………….
5. The national dance of Philippines is …………….
6. The second highest peak in Europe is …………….
7. The type of climate that prevails in the central and eastern parts of Europe is …………….
8. The important fishing ground in North Sea is ……………..
9. The density of population in Europe is ……………..
10. The river ……………. passes through nine countries of Europe.

Answer:

1. Armenian
2. Mawsynram
3. dates
4. the Suez canal
5. Tinikling
6. the Mont Blanc
7. Continental type
8. Dogger Bank
9. 34 persons/Km²
10. Danube

III. Match the following

Answer:
1. – d
2. – a
3. – e
4. – b
5. – c

IV. Let us learn

Question 1.
Assertion (A) : Italy has dry summers and rainy winters
Reason (R) : It is located in the Mediterranean region
(a) Both A and R are individually true and R is the correct explanation for A
(b) Both A and R are individually true but R is not the correct explanation for A
(c) A is true, but R is false
(d) A is false, but R is true
Answer:
(d) A is false, but R is true

Question 2.
Places marked as 1, 2, 3 and 4 in the given map are noted for the following plains.
(a) Indo – Gangetic plain
(b) Manchurian plain
(c) Mesopotamian
(d) Great plains of China
Match the plains with the notation on the map and select the correct answer using the codes given below.
Codes:

Answer:
b) 2 1 3 4

Question 3.
In the given outline map of Asia, the shaded areas indicate the cultivation of ……………..

(a) Sugarcane
(b) Dates
(c) Rubber
(d) Jute
Answer:
(b) Dates

V. Answer in Brief

Question 1.
Name the important intermontane plateaus found in Asia.
Answer:
The plateau of Anatolia, The plateau of Iran, and the plateau of Tibet are the important intermontane plateaus found in Asia.

Question 2.
Write a short note on the monsoon climate.
Answer:

1. The south, southeast and eastern parts of Asia are strongly influenced by monsoon winds.
2. Summer is hot and humid while winter is cool and dry.
3. The summer monsoon winds bring heavy rainfall to India, Bangladesh, Indo-China, Philippines and Southern China.

Question 3.
How does physiography play a vital role in determining the population of Asia?
Answer:

1. In Asia, the population is unevenly distributed because of various physical features.
2. China and India alone cover three-fifth of Asia’s population.
3. River plains and industrial regions have a high density of population, whereas low density is found in the interior parts of Asia.

Question 4.
Name the ports found is Asia.
Answer:
Tokyo, Shanghai, Singapore, Hong Kong, Chennai, Mumbai, Karachi and Dubai are the important seaports in Asia.

Question 5.
Asia is called the ‘Land of Contrasts – Justify.
Answer:
The biggest continent Asia is called “the land of contrasts”.
Because:

1. Asia is the biggest continent has different types of land features such as mountain, plateau, plain, valley, bay, island etc.
2. It has different climatic conditions from the equator to polar region.
3. Apart from this many races, languages, religions and cultures are followed by people who live in Asia. Therefore, Asia is called ‘the land of contrasts’.

Question 6.
Name the important mountains found in the Alpine system.
Answer:
The important mountain ranges in the Alpine system are the Sierra Nevada, the Pyrenees, the Alps, the Apennines, the Dinaric Alps, the Caucasus and the Carpathian.

Question 7.
What are the important rivers of Europe?
Answer:
The important rivers of Europe are Volga, Danube, Dnieper, Rhine, Rhone, Po, and Thames.

Question 8.
Name a few countries which enjoy the Mediterranean type of climate.
Answer:
The Mediterranean and sub-mediterranean climate regions in Europe are found in much of southern Europe, mainly in southern Portugal, most of Spain, the southern coast of France, Italy, the Croatian Coast, much of Bosnia, Montenegro, Kosovo, Serbia, Albania, Macedonia, Greece and the Mediterranean Islands.

Question 9.
Give a short note on the population of Europe.
Answer:

1. Europe is the third-most populous continent, after Asia and Africa. The population density in Europe is.34 persons / km2.
2. High population density is often associated with the coalfields of Europe.
3. Other populous areas are sustained by mining, manufacturing, commerce, offering large market, labour forces and productive agriculture.
4. Monaco, Malta, San Marino, and the Netherlands are the most densely populated countries; Iceland and Norway have a very low density of population.

Question 10.
Name the important festivals celebrated in Europe.
Answer:

1. The Europeans celebrate both religious and holiday festivals.
2. Christmas, Easter, Good Friday, the Saint Day, Redentore, Tomatina and Carnival are the important festivals of Europe.

VI. Distinguish

Question 1.
Intermontane plateaus and southern plateaus.
Answer:
Intermontane plateaus:

1. Intermontane plateaus are found in the mountain ranges.
2. Eg, The plateau of Anatolia, The plateau of Iran, and the plateau of Tibet

Southern plateaus:

1. The southern plateaus are relatively lower than the northern plateaus.
2. Eg. Arabian Plateau, Deccan Plateau, Shan Plateau, and the Yunnan Plateau.

Question 2.
Cold desert and hot desert.
Answer:
Cold desert:

1. A barren or desolate area especially sandy region of little rainfall, featuring cold dry winter.
2. Cold deserts are found in the antarctic, Green land, Western China, Turkartan the Gopi crodi desert in Mongolia.

Hot desert:

1. A barren or desolate area often the sandy region of little rainfall.
2. The largest hot desert is the Sahara desert.

Question 3.
Tundra and Taiga.
Answer:

Thunder:

1. The Arctic and northern Scandinavian highland have Tundra type of vegetation.
2. The winters are very long and severe summers are very short and warm.
3. It is the land with few animals like polar bear, reindeer and walrus
4. No trees. Lowest form of vegetation like Mosses and Lichen only available.

Taiga:

1. They are found in the south of the Tundra region in Norway, Sweden, Finland, Germany, Poland and Austria.
2. The winters are long and cold. Summers are short and warm.
3. It is the land of fur bearing animals. Eg. Mink, silver fox, squirrel etc.
4. Pine, fir, spruce and larch are the important tree varieties.

Question 4.
The North-Western highlands and Alpine mountain range
Answer:
The North-Western Highlands:

1. This region includes the mountains and plateaus of Norway, Sweden, Finland, Scotland, and Iceland.
2. This region has a fjord coast. It was created by glaciations.
3. A lot of lakes here serve as reservoirs for producing hydroelectricity.

The Alpine mountain range:

1. The Alpine mountain system consists of a chain of young fold mountains found in the southern part of Europe.
2. The Sierra Nevada, the Pyrenees, the Alps, the Apennines, the Dinaric Alps, the Caucasus and the
3. Carpathian is the important mountain ranges.
4. The Pyrenees is a natural boundary between Spain and France.

VII. Give Reasons

Question 1.
Asia is the leading producer of rice.
Answer:
Because:

1. In Asia, India has the largest area of arable lands.
2. Agriculture is intensively practiced in the riverine plains of Asia
3. China and India are the leading producers of rice in the world.

Question 2.
Asia is the largest and most populous continent in the world.
Answer:
Because:

1. Most of the land of Asia in the northern hemisphere has different physical and cultural features.
2. Lofty mountains, plateaus, plains, islands and peninsulas are the major physiographic features.
3. Many perennial rivers flow through different parts. These river valleys are the cradles of ancient civilizations.
4. River plains and industrial regions have high density of population. Population density 143 persons/Km².
5. Asia covers about 30 percent of the world’s population.

Question 3.
Although Western Europe is located in the high latitudes, it has a moderate climate.
Answer:
Because:

1. The western part has a mild, generally humid climate, influenced by the North Atlantic Drift.
2. North Atlantic Drift is a Warm ocean current which brings warmth to the Western Europe.

VIII. Answer in Paragraph

Question 1.
Give an account of the drainage system in Asia.
Answer:

1. The rivers of Asia originate mostly from the central highlands.
2. The Ob, Yenise and Lena are the major rivers flow towards the north and drain into the Arctic Ocean. They remain frozen during winter.
3. Many perennial rivers like Brahmaputra, Indus, Ganga and Irrawaddy originate from the high mountains.
4. They do not freeze during winter.
5. The Euphrates and Tigris flow in west Asia.
6. The Amur, Huang He, Yangtze and Mekong flow in the south and southeastern parts. The Yangtze is the longest river in Asia.

Question 2.
Describe the mineral sources found in Asia.
Answer:

1. Asia has a variety of mineral deposits like Iron, Coal, Manganese, Bauxite, Zinc, Tungsten, Petroleum, Tin etc. Oil and Natural Gas found in the west Asian countries.
2. Iron Ore: Asia has the largest deposits of iron ore in the world. China and India are the important iron ore deposit countries of Asia.
3. Coal: Coal is a fossil fuel. China and India are the largest producers of coal in Asia.
4. Petroleum: Petroleum is a mineral oil. The largest petroleum reserves are found in South West Asia. The important petroleum-producing countries are Saudi Arabia, Kuwait, Iran, Bahrain, Qatar and UAE.
5. Bauxite is found in India and Indonesia.
6. Mica: India is the largest producer in the world.
7. Tin is found in Myanmar, Thailand, Malaysia, and Indonesia.

Question 3.
What are fjords? How do they protect harbours from bad weather conditions?
Answer:

1. A fjord is a narrow and deep-sea inlet between steep clifts.
2. Fjords reduce the speed of wind irrespective of their direction.
3. The force of sea waves is also controlled.
4. Fjord coast was created by glaciations in the past.
5. Areas with fjords are best suited for natural harbours. Example : Norway.

Question 4.
Describe the climatic divisions of Europe.
Answer:

1. The climate of Europe varies from the subtropical to the polar climate.
2. The Mediterranean climate of the south has warm summer and rainy winter.
3. The western and northwestern parts have a mild, generally humid climate, influenced by the North Atlantic Drift.
4. In central and eastern Europe, the climate is humid continental-type.
5. In the northeast, subarctic and tundra climates are found.
6. The whole of Europe is subject to the moderating influence of prevailing westerly winds from the Atlantic Ocean.
7. North Atlantic Drift is a warm ocean current which brings warmth to Western Europe.
8. The westerly wind further transports warmth across Europe.

X. Activity

Question 1.
Complete the following
I belong to ………… district. My district is famous for the following : …………, ………… and ………… . The boundaries of my districts are in the north, in the east, in the south and in the west. It spreads for an area of km². There are ………… taluks and ………… villages in my district. …………, …………, ………… are the important mountain / plain / plateaus (If all, mention all features). The rivers …………, ………… ………… criss – cross my district. …………, …………, ………… are common trees and wildlife such as, are found here. …………, …………, ………… are important minerals available in my district. Based on this …………, ………… industries are located here. The major crops are …………, …………, ………… . (Coastal districts may write the variety of fish). The total population is …………. We celebrate …………, …………, ………… festivals.
Answer:
Tirunelveli, Nellaiyappar Temple, Courttalam, Halwa, Virudhunagar, Tuticorin, Kanyakumari, Western Ghats, 6823sq.kms, 16 taluks, 559 Villages, Thamirabarani, Chittar, Manimuthar, Palm, Neem, Cocount, Monkeys, Tigers, Elephants, Bluemetal, Lime stone, Thorium, Cement, Ginning, Vessels, Paddy, Cotton, Sugarcane, 33, 22, 644, Pongal, Deepavali, Christmas.

Question 2.
If you get a chance to settle in Europe, which country would you choose? List out the reasons why?

Question 3.
Choose any region is Asia. In the map of Asia, mark its distribution of natural vegetation and wildlife. Paste related pictures.

Samacheer Kalvi 6th Social Science Asia and Europe Additional Important Questions and Answers

I. Choose the Correct Answer

Question 1.
……………. separates Asia from Africa
(a) Suez Canal
(b) Bering Strait
(c) Mediterranean Sea
(d) Palk Striat
Answer:
(a) Suez Canal

Question 2.
Shan plateau is located in ______
(a) Saudi Arabia
(b) Myanmar
(c) India
(d) China

Question 3.
The South Asian rivers
(i) remain frozen during winter
(ii) flow towards the north
(iii) are perennial
Of the statements given above
(a) i alone is correct
(b) iii alone is correct
(c) All the three are correct
(d) All the three are wrong
Answer:
(b) iii alone is correct

Question 4.
Find out the wrong pair.
(a) Coal – China
(b) Iron ore – India
(c) Bauxite – Iran
(d) Tin – Myanmar
Answer:
(c) Bauxite – Iran

Question 5.
River yangtze flows in ……………
(a) Inida
(b) Japan
(c) Myanmar
(d) China
Answer:
(d) China

Question 6.
The light house of the Mediterranean is ______
(a) Mt. Stromboli
(b) Mt. Etana
(c) Mt. Vesuvius
(d) None of the above

Question 7.
Choose the incorrect pair:
(a) Siberian Plain – Ob, Yenisey
(b) Manchurian Plain – Amur
(c) Greet plain of China – Yangtze, Sikiang
(d) Mesopotamian Plain – Irrawaddy
Answer:
(d) Mesopotamian Plain – Irrawaddy

II. Match the following

Answer:
1. – c
2. – e
3. – d
4. – b
5. – a

III. True/False

1. There are two knots found in Asia.
2. Ob, Yensie, Lena remain frozen during winter
3. Teak, Sandal wood are coniferous trees
4. The fjord region has a lot of lakes
5. Wheat is the dominant crop throughout Europe.

Answer:

1. True
2. True
3. False
4. True
5. True

IV. Answer in Brief

Question 1.
What are the cradles of ancient civilization? Why?
Answer:

1. The river valleys are the cradles of civilizations.
2. Because the ancient civilizations Indus valley, Mesopotamian and Chinese civilizations were born in Asian river valleys.

Question 2.
Mention the Physical divisions of Asia.
Answer:
The physical divisions of Asia are

1. The Northern lowlands
2. The Central High Mountains
3. The Southern Plateaus
4. The Great Plains and
5. The Island Groups.

Question 3.
What are the rare species found in Asia?
Answer:

1. Orang – Utan
2. Komodo Dragon
3. Giant Panda

Question 4.
Mention the Great Plains of Asia.
Answer:
The great plains of Asia are

1. West Siberian plain (Ob and Yenisey)
2. Manchurian Plain (Amur)
3. Great Plain of China (Yangtze and Sikiang)
4. Indo-Gangetic Plain (Indus and Ganga)
5. Mesopotamian plain (Tigris and Euphrates) and
6. The Irrawaddy plain (Irrawaddy)

Question 5.
Name the countries where fishing is a large industry.
Answer:

1. Norway
2. Iceland
3. Russia
4. Denmark
5. The United Kingdom
6. The Netherlands

V. Give Reasons

Question 1.
Europe is a modern and economically developed continent.
Answer:
Avilability of sources, efficient educated work force, research, contact with other nations and innovations are the factors that transformed like this.

Question 2.
Varied patterns of agricultural activities are in use in Europe.
Answer:

1. Europe is an industrially developed continent. It has great diversity in its topography, climate and soil.
2. These interact to produce varied patterns of agriculture activities.

[The varied patterns of agriculture activities in use: Mediterranean agriculture, Dairy farming, mixed livestock, crop farming, horticulture]

Question 3.
There is no winter in the equatorial region.
Answer:
The areas found in and around the equator of Asia have uniform climate throughout the year. There is no winter. Average temperature 27°c. The mean rainfall 1270 mm.

VI. Answer in Paragraph

Question 1.
Describe Industries in Europe.
Answer:

1. Large scale Industries : Steel and Iron are, Ship building, Motor vehicle, Aircraft construction, Pharmaceutical drugs.
2. Small scale Industries that produce nondurable goods are found throughout Europe.
3. Some countries have a reputation for speciality goods.
   • Bicycles – English, Italian and Dutch
   • Glass – Swedish and Finnish
   • Perfumes and fashion goods – Parisian
   • Precision instruments – Swiss

VII. Mind map

Students can download 6th Social Science Term 3 History Chapter 4 South Indian Kingdoms Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science History Solutions Term 3 Chapter 4 South Indian Kingdoms

Samacheer Kalvi 6th Social Science South Indian Kingdoms Text Book Back Questions and Answers

I. Choose the correct Answer

Question 1.
Who among the following built the Vaikundaperumal temple?
(a) Narasimhavarma II
(b) Nandivarma II
(c) Dantivarman
(d) Parameshvaravarma
Answer:
(b) Nandivarma II

Question 2.
Which of the following titles were the titles of Mahendra Varma I?
(a) Mattavilasa
(b) Vichitra Chitta
(c) Gunabara
(d) all the three
Answer:
(d) all the three

Question 3.
Which of the following inscriptions describes the victories of Pulakesin II?
(a) Aihole
(b) Saranath
(c) Sanchi
(d) Junagath
Answer:
(a) Aihole

II. Read the statement and tick the appropriate answer

Question 1.
Statement I : Pallava art shows transition from rock – cut – monolithic structure to stone built temple.
Statement II : Kailasanatha temple at Kanchipuram is an example of Pallava art and architecture.
(a) Statement I is wrong
(b) Statement II is wrong
(c) Both the statements are correct
(d) Both the statements are wrong.
Answer:
(c) Both the statements are correct

Question 2.
Consider the following statement(s) about Pallava Kingdom.
Statement I : Tamil literature flourished under Pallava rule, with the rise in popularity of Thevaram composed by Appar.
Statement II : Pallava King Mahendravarman was the author of the play MattavilasaPrahasana.
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
Answer:
(c) Both I and II

Question 3.
Consider the following statements about the Rashtrakuta dynasty and find out which of the following statements are correct.
(1) It was founded by Dantidurga
(2) Amogavarsha wrote Kavirajmarga
(3) Krishna I built the Kailasanatha temple at Ellora.
(a) 1 only
(b) 2 and 3
(c) 1 and 3
(d) all the three
Answer:
(d) all the three

Question 4.
Which of the following is not a correct pair?
Answer:
(a) Ellora caves – Rashtrakutas
(b) Mamallapuram – Narasimhavarma I
(c) Elephanta caves – Ashoka
(d) Pattadakal – Chalukyas
Answer:
(c) Elephanta caves – Ashoka

Question 5.
Find out the wrong pair.
(a) Dandin – Dasakumara Charitam
(b) Vatsyaya – Bharathavenba
(c) Bharavi – Kiratarjuneeyam
(d) Amogavarsha – Kavirajamarga
Answer:
(b) Vatsyaya – Bharathavenba

III. Fill in the blanks

1. ……………….. defeated Harsha Vardhana on the banks of the river Narmada.
2. ……………….. destroyed Vatapi and assumed the title VatapiKondan.
3. ……………….. was the author of Aihole Inscription.
4. ……………….. was the army general of Narasimhavarma I
5. The music inscriptions in ……………….. and ……………….. show Pallavas ‘interest in music.

Answer:

1. Pulakesin II
2. Narasimhavarma
3. Ravikirti
4. Paranjothi
5. Kudumianmalai, Thiruamayam

IV. Match the following

Answer:
1. – c
2. – d
3. – a
4. – b

V. State True or False

1. The famous musician Rudracharya lived during Mahendravarma I.
2. The greatest king of the Rashtrakuta dynasty was Pulakesin II.
3. Mamallapuram is one of the UNESCO World Heritage Sites.
4. Thevaram was composed by Azhwars.
5. The Virupaksha temple was built on the model of Kanchi Kailasanatha Temple.

Answer:

1. True
2. False
3. True
4. False
5. False

VI. Answer in one or two sentences

Question 1.
Name the three gems of Kannada literature.
Answer:
The three gems of Kannada literature were Pampa, Sri Ponna, and Raima.

Question 2.
How can we classify the Pallava architecture?
Answer:
Pallava architecture can be classified as

1. Rock-cut temples – Mahendravarman style.
2. Monolithic Rathas and Sculptural Mandapas Mamallan style.
3. Structural Temples – Rajasimhan style and Nandivarman style.

Question 3.
What do you know of Gatika?
Answer:

1. Gatika means monastery or Centre of learning.
2. It was popular during the Pallava times at Kanchi.
3. It attracted students from all parts of India and abroad.
4. Vatsyayana who wrote Nyaya Bhashya was a teacher at Kanchi (Gatika). Panchapandavar rathas are monolithic rathas. Explain.

Question 4.
Panchapandavar rathas are monolithic rathas. Explain
Answer:

1. Under Mamalla style, the five rathas (chariots), popularly called Panchapandavar rathas, signify the different style of temple architecture.
2. Each ratha has been carved out of a single rock.
3. So they are called monolithic.
4. The popular mandapams here are Mahishasuramardhini mandapam, Thirumoorthi mandapam and Varaha mandapam.

Question 5.
Make a note on Battle of Takkolam.
Answer:

1. Krishna III was the last able ruler of the Rashtrakuta dynasty,
2. He defeated the Cholas in the battle of Takkolam (presently in Vellore Dt) and captured Thanjavur.

VII. Answer the following

Question 1.
Examine Pallavas’ contributions to architecture.
Answer:
Pallava period is known for architectural splendour. In 1984 Mamallapuram was added to the list of UNESCO World Heritage Sites. The illustrious examples of Pallava architecture are the Shore Temple, other temples and the Varaha cave.

Mahendra style : (Rock – cut temples)
Mahendravarma style of cave temples are seen at Mandagapattu, Mahendra vadi, Mamandur, Dalavanur, Trichirapalli, Vallam, Tirukazhukkundram and Siyamangalam.

Mamalla Style : (Monolithic Rathas and Sculptural Mandapas)

1. The last example for Mamalla style monolithic is Panchapandavar rathas. Mahishasuramardhini mandapam, Thirumoorthi mandapam and Varaha mandapam are the popular mandapams.
2. The most important is the open art gallery. The fall of the Ganges from the head of Lord Shiva and the Arjun’s penance are notable sculptures.

Rajasimha Style : (Structural Temples)
Rajasimha (Narasimhavarma II) Style was a structural temple. The best example is the Kailasanatha temple at Kanchipuram. This temple is called Rajasimheswaram.

Nandivarma Style : (Structural Temples)
Nandivarma style was the last stage of pallava architecture. The best example is Vaikunda Perumal temple at Kanchipuram.

Question 2.
Write a note on Elephanta island and Kailasanatha temple at Ellora.
Answer:
Elephanta island:

1. Elephanta is an island near Mumbai. It is originally known as Sripuri and the local people called Gharapuri.
2. The Portuguese named it as Elephanta after seeing the image.
3. The Trimurthi Siva icon and the images of dwarapalakas are seen in the cave temple.

Kailasanatha temple at Ellora:

1. Krishna I built the Kailasanatha temple. It was one of the 30 temples carved out at Ellora.
2. The temple covers an area of over 60,000 sq. feet and vimanam rises to a height of 90 feet.
3. It portrays typical Dravidian features and has a resemblance to the shore temple at Mamallapuram.

VIII. HOTS

Question 1.
Give an account of the Western Chalukyas of Kalyani.
Answer:
Western Chalukyas of Kalyani:

1. They were the descendants of Badami Chalukyas ruled from Kalyani (modem day Basavakalyan).
2. In 973, Tailapa II, a feudatory of the Rashtrakuta mling from the Bijapur region, defeated Parmara of Malwa.
3. Tailapa II occupied Kalyani and his dynasty quickly grew into an empire under Someswara I.
4. Someswara I moved the capital from Manyakheta to Kalyani.
5. For over a century, both the Chalukyas and the Cholas fought many fierce battles to control the fertile region of Vengi.
6. In the late 11th century, under Vikramaditya VI, vast areas between the Narmada river in the north and Kaveri river in the South came under Chalukya control.
7. The Kasi Vishwesvara Temple at Lakkundi, the Mallikaijuna temple at Kuruvatti, the Kalleshwara temple at Bagali and the Mahadeva temple at Itagi represent well-known examples of the architecture of Western Chalukyas of Kalyani.

IX. Life Skills (For Students)

1. Collect temple architecture pictures of Pallavas, Chalukyas and Rashtrakutas and identify the distinguishing features of each period.
2. Field Trip : Plan a trip to any place of historical importance.

X. Activity

Question 1.
(a) Sketch the biography of Mahendravarma I and Pulakesin II.
(b) See the picture and write a few sentences on it.
Answer:
Arjuna is fasting in one leg At the centre there is a naga Siva is attended by devaganas Hunters, animals, birds and trees are seen. There is also a herd of elephants.

XI. Answer Grid

Question 1.
Give examples for the structural temples of Pallava period.
Answer:
Kailasanatha temple, Vaikunda Perumal temple

Question 2.
Name the new style of architecture developed during Chalukya period.
Answer:
Vesara

Question 3.
What does Aihole inscription mention?
Answer:
Defeat of Harsha Vardhana by Pulakesan II

Question 4.
Who built the Kailasanatha temple at Ellora?
Answer:
Krishna I

Question 5.
Name the sculptural mandapas of Mamallan style of architecture.
Answer:
Monolithic

Question 6.
Where do structural temples of Chalukya exist?
Answer:
Aihole, Badami, Pattadakal

Question 7.
Name two Saivite saints and Vaishnavite saints who practised bhakticult during Pallava period?
Answer:
Appar, Manikkavasakar. Nammazhvar, Andal

Question 8.
Who was the founder of Rashtrakuta dynasty?
Answer:
Dantidurga

Question 9.
What were the titles adopted by Narasimhavarma I?
Answer:
Mamallan, Vatapi kondan

Samacheer Kalvi 6th Social Science South Indian Kingdoms Additional Important Questions and Answers

I. Choose the Correct Answer:

Question 1.
Who was Avanisimha?
(a) Simhavishnu
(b) Pulakesin II
(c) Mahendravarman
(d) Aparajita
Answer:
(a) Simhavishnu

Question 2.
Cave temples of the Pallavas are found at ________
(a) Vallam
(b) Vengi
(c) Badami
(d) Pattadakal
Answer:
(a) Vallam

Question 3.
Mangalesa belonged to Dynasty.
(a) Chalukya
(b) Pallava
(c) Rashtrakuta
(d) Gupta
Answer:
(a) Chalukya

Question 4.
The new style of architecture Vesara was introduced by
(a) Chalukyas
(b) Pallavas
(c) Rastrakutadas Vakataka
(d) Cave
Answer:
(a) Chalukyas

II. Read the statement and tick the appropriate answer

Question 1.
Statement I : The life of Rishabadeva, the first Jain Tirthankara is depicted in Adipurana
Statement II : The Rashtrakutas followed Jainism
(a) Statement I is wrong
(b) Statement II is wrong
(c) Both the statements are correct
(d) Both the statements are wrong.
Answer:
(b) Statement II is wrong

Question 2.
Statement I : Appar and Manikkavasakar were Vaishnavites.
Statement II : Nammazhvar and Andal were saivites
(a) Statement I is correct
(b) Statement II is correct
(c) Both the statements are wrong
(d) Both the statements are correct.
Answer:
(c) Both the statements are wrong

III. Fill in the blanks

1. The last Pallava ruler …………..
2. The poet who was patronized by Nandivarman II was …………..
3. The style adopted by Chalukyas in paintings is ……………
4. The last ruler to hold the empire intact was ……………

Answer:

1. Aprajita
2. Perundevanar
3. Vakataka
4. Govinda III

IV. State True or False

1. Rudracharya was a famous musician during Pallava Period
2. Varaha, Narasimha, Vamana are the Avatar of Siva
3. The Rashtrakutas were of Telugu origin
4. The Chalukyas perfected the art of stone building without mortar.

Answer:

1. True
2. False
3. False
4. True

V. Answer in one or two sentences

Question 1.
Write about ‘Siruthondar’
Answer:

1. The army general of Narasimhavarman I, Paranjothi, led the army during the invasion of Vatapi.
2. After the victory devoted himself to Lord Siva, he was known as Siruthondar (one of the 63 Nayanmars)

Question 2.
Write a note on Simhavishnu.
Answer:

1. Simhavishnu, son of Simhavarman-II, created a strong Pallava kingdom after destroying the Kalabhras.
2. He defeated many kings in the south including the Cholas and Pandyas.
3. His able son was Mahendravarman I.

Question 3.
Name the distinct but closely related and independent Chalukya dynasties.
Answer:

1. Chalukyas of Badami
2. Chalukyas of Vengi (Eastern chalukyas)
3. Chalukyas of Kalyani (Western chalukyas)

Question 4.
Who were Chalukyas?
Answer:

1. There were three distinct but closely related and independent Chalukya dynasties,
2. They were:
   • Chalukyas of Badami
   • Chalukyas of Vengi (Eastern Chalukyas)
   • Chalukyas of Kalyani (Western Chalukyas).
3. These Chalukyas held Harsha in the north, the Pallavas in the south and Kalinga (Odisha) in the east.

VII. Answer the following

Question 1.
Explain – ’Pattatakal’
Answer:

1. Pattatakal is a small village in Bagalkot district of Karnataka.
2. Here are 10 temples. Out of them 4 were in Nagara style and 6 were in Dravida style.
3. Dravida style – Virupaksha Temple, Sangameshwara Temple.
4. Nagara style – Papanatha Temple.
5. Pattatakal is one of the UNESCO World Heritage sites.

Question 2.
What do you know about ‘Rashtrakutas?
Answer:

1. Rashtrakutas were of Kannada origin. They ruled not only the Deccan but parts of the far south and the Ganges plain during 8 – 10 centuries.
2. Dantidurga was the founder of the Rashtrakuta dynasty. He was an official of high rank under the Chalukyas of Badami.
3. Krishna I was the successor of Dantidurga and he built the Kailasanatha temple at Ellora.
4. The greatest king of Amogavarsha. Krishna III was the last able ruler of the Rashtrakuta dynasty.
5. Capital: Malkhed (Manyakheta). Port: Broach.

VIII. Mind map

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TN State Board 11th Maths Model Question Paper 5 English Medium

General Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in above three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in detail Draw diagrams wherever necessary.

Time: 2:30 Hours
Maximum Marks: 90

PART – I

I. Choose the correct answer. Answer all the questions. [20 × 1 = 20]

Question 1.
If n((A × B) ∩ (A × C)) = 8 and n(B ∩ C) = 2 then n(A) = …………………
(a) 6
(b) 4
(c) 8
(d) 16
Answer:
(b) 4

Question 2.
The value of log₃ \(\frac{1}{81}\) is ……………….
(a) -2
(b) -8
(c) -4
(d) -9
Answer:
(c) -4

Question 3.
The value of log₃ 11 log₁₁ 13 log₁₃ 15 log₁₅ 27 log₂₇ 81 is ……………………
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 4.
The value of sin(45° + θ) – cos (45° – θ) is …………………..
(a) 2 cos θ
(b) 1
(c) 0
(d) 2 sin θ
Answer:
(c) 0

Question 5.
If tanα and tan β are the roots of x² + ax + b = 0 then \(\frac{\sin (\alpha+\beta)}{\sin \alpha \sin \beta}\) is equal to ……………………..
(a) \(\frac{b}{a}\)
(b) \(\frac{a}{b}\)
(c) –\(\frac{a}{b}\)
(d) –\(\frac{b}{a}\)
Answer:
(c) –\(\frac{a}{b}\)

Question 6.
If a² – aC₂ = a² – aC₄ then the value of a is …………………….
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(b) 3

Question 7.
If ⁿP_r = 840, ⁿC_r= 35 then n = …………………..
(a) 1
(b) 6
(c) 5
(d) 4
Answer:
(a) 1

Question 8.
If 2x² + 3xy – cy² = 0 represents a pair of perpendicular lines then c = …………………….
(a) -2
(b) \(\frac{1}{2}\)
(c) – \(\frac{1}{2}\)
(d) 2
Answer:
(d) 2

Question 9.
The number of terms in the expansion of [(a + b)²]¹⁸ = …………………..
(a) 19
(b) 18
(c) 36
(d) 37
Answer:
(d) 37

Question 10.
The point on the line 2x – 3y = 5 is equidistance from (1, 2) and (3, 4) is …………………..
(a) (7, 3)
(b) (4, 1)
(c) (1,-1)
(d) (3, 4)
Answer:
(b) (4, 1)

Question 11.
Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?
(a) A + B is a symmetric matrix
(b) AB is a symmetric matrix
(c) (AB) = (BA)^T
(d) A^TB = AB^T
Answer:
(d) A^TB = AB^T

Question 12.
If [3 -1 2] B = [5, 6] then the order of B is ………………….
(a) 3 × 2
(b) 2 × 3
(c) 3 × 1
(d) 1 × 1
Answer:
(a) 3 × 2

Question 13.
1f \(\underset { x\rightarrow 0 }{ lim } \) \(\frac{sin px}{tan 3x}\) = 4 then the value of p is …………………….
(a) 6
(b) 9
(c) 12
(d) 4
Answer:
(c) 12

Question 14.
For \(\vec { a } \) = \(\vec { i } \) + \(\vec { j } \) – 2\(\vec { k } \), \(\vec { b } \) = \(\vec { i } \) + 2\(\vec { j } \) + \(\vec { k } \) and \(\vec { c } \) = \(\vec { i } \) – 2\(\vec { j } \) + 2\(\vec { k } \) the unit vector parallal to is \(\vec { a } \)
+ \(\vec { b } \) + \(\vec { c } \) is ……………………….
(a) \(\frac{\vec{i}+\vec{j}-\vec{k}}{\sqrt{3}}\)
(b) \(\frac{\vec{i}+\vec{j}+\vec{k}}{\sqrt{3}}\)
(c) \(\frac{\vec{i}+\vec{j}+\vec{k}}{3}\)
(d) \(\frac{\vec{i}-\vec{j}+\vec{k}}{\sqrt{6}}\)
Answer:
(b) \(\frac{\vec{i}+\vec{j}+\vec{k}}{\sqrt{3}}\)

Question 15.
The differential co-efficient of log₁₀ x with respect to log_x 10 is …………………….
(a) 1
(b) -(log₁₀x)²
(c) (log_x10)²
(d) \(\frac { x^{ 2 } }{ 100 } \)
Answer:
(b) -(log₁₀x)²

Question 16.
\(\frac{d}{dx}\)(e^x+5logx) is …………………..
(a) e^xx⁴(x + 5)
(b) e^xx(x + 5)
(c) e^x + \(\frac{5}{x}\)
(d) e^x – \(\frac{5}{x}\)
Answer:
(a) e^xx⁴(x + 5)

Question 17.
If f(x) = x tan^-1x thenf'(1) = ……………………..
(a) 1 + \(\frac { \pi }{ 4 } \)
(b) \(\frac{1}{2}\) + \(\frac { \pi }{ 4 } \)
(c) \(\frac{1}{2}\) – \(\frac { \pi }{ 4 } \)
(d) 2
Answer:
(b) \(\frac{1}{2}\) + \(\frac { \pi }{ 4 } \)

Question 18.
∫cosec xdx = …………………….
(a) log tan \(\frac{x}{2}\) + c
(b) -log (cosec x + cot x) + c
(c) log (cosecx – cot x) + c
(d) all of them
Answer:
(d) all of them

Question 19.
Ten coins are tossed; The probability of getting atleast 8 heads is …………………..
(a) \(\frac{7}{64}\)
(b) \(\frac{7}{32}\)
(c) \(\frac{7}{128}\)
(d) \(\frac{7}{16}\)
Answer:
(c) \(\frac{7}{128}\)

Question 20.
Two items are chosen from a lot containing twelve items of which four are defective. Then the probability that atleast one of the item is defective is …………………..
(a) \(\frac{19}{33}\)
(b) \(\frac{17}{33}\)
(c) \(\frac{23}{33}\)
(d) \(\frac{13}{34}\)
Answer:
(a) \(\frac{19}{33}\)

PART – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
For a set A, A × A contains 16 elements and two of its elements are (1, 3) and (0, 2). Find the elements of A?
Answer:
A × A = 16 elements = 4 × 4
⇒ A has 4 elements
∴ A = {0, 1, 2, 3}

Question 22.
Prove that \(\frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}\) = \(\frac{1+sinθ}{cosθ}\)
Answer:

Question 23.
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
Answer:
No. of non-collincar points = 15
To draw a Triangle we need 3 points
∴ Selecting 3 from 15 points can be done in ¹⁵C₃ ways.
∴ No. of Tnangle formed ¹⁵C₃
= \(\frac{15 \times 14 \times 13}{3 \times 2 \times 1}\) = 455

Question 24.
Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1?
Answer:
Givc sum of the intercepts = 1
⇒ when x intercept a then y intercept = 1 – a
Equation of the line is \(\frac{x}{a}\) + \(\frac{y}{1-a}\) = 1
The line passes through (8, 3) ⇒ \(\frac{8}{a}\) + \(\frac{3}{1-a}\) = 1
(i.e) 8 (1 – a) + 3a = a(1 – a)
8 – 8a + 3a = a – a²
a² – 6a + 8 =0
(a – 2)(a – 4) = 0 ⇒a = 2 or 4
1. When a = 2 equation of the line is \(\frac{x}{2}\) + \(\frac{y}{-2}\) = 1 (i.e) \(\frac{x}{2}\) – y = 1 ⇒ x – 2y = 2
2.When a = 4 equation of the line is \(\frac{x}{4}\) + \(\frac{y}{1-4}\) = 1 (i.e) \(\frac{x}{4}\) – \(\frac{y}{3}\) = 1 ⇒ 3x – 4y = 12

Question 25.
Find the values of p, q, r, & s if \(\left[\begin{array}{ccc}
p^{2}-1 & 0 & -31-q^{3} \\
7 & r+1 & 9 \\
-2 & 8 & s-1
\end{array}\right]=\left[\begin{array}{rrr}
1 & 0 & -4 \\
7 & \frac{3}{2} & 9 \\
-2 & 8 & -\pi
\end{array}\right]\)
Answer:
When two matrices (of some order) are equal then their correspondings entries are equal.

Question 26.
Find |\(\vec { a } \) × \(\vec { b } \)| where \(\vec { a } \) = 3\(\vec { i } \) + 4\(\vec { j } \) and \(\vec { b } \) = \(\vec { i } \) + \(\vec { j } \) + \(\vec { k } \)
Answer:

Question 27.
At the given point x₀ discover whether the given function is continous or discontinous citing the reasons for your answer?
Answer:

Question 28.
Evaluate y = xe^-x2
Answer:

Question 29.
Evaluate ∫\(\frac{1}{x logx}\) dx?
Answer:

Question 30.
Evaluate [((256)^-1/2)^-1/4]³
Answer:

PART – III

III. Answer any seven questions. Question No. 40 Is compulsory. [7 × 3 = 21]

Question 31.
Find the largest possible domain for the real valued functionsf defined by f(x) = \(\sqrt { x^{ 2 }-5x+6 } \)

Question 32.
Show that tan 75° + cot 75° = 4?

Question 33.
There are 10 bulbs in a room. Each one of them can be operated independently. Find the number of ways in which the room can be illuminated?

Question 34.
Find the \(\sqrt [ 3 ]{ 126 } \) approximately to two decimal places?

Question 35.
Find the equation of the line passing through the point of intersection 2x + y = 5 and x + 3y + 8 = O and parallel to the line 3x + 4y = 7?

Question 36.
If \(\left|\begin{array}{ccc}
a & b & a \alpha+b \\
b & c & b \alpha+c \\
a \alpha+b & b \alpha+c & 0
\end{array}\right|\) = 0 prove that a, b, c are in G.P. or a is a root of ax² + 2bx + c =0

Question 37.
Evaluate \(\underset { x\rightarrow 3 }{ lim } \)\(\frac { x^{ 2 }-9 }{ x-3 } \) ¡f it exists by finding f(3^–) and f(3⁺)

Question 38.
Find the derivative of tan^-1 (1 + x²) with respect x² + x + 1?

Question 39.
Evaluate: ∫x⁵e^{x2 dx}

Question 40.
Prove that the line segment joining the mid points of the adjacent sides of a quadrilateral from parllelogram?

PART – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41.
(a) Graph the functions f(x) = x³ and g(x) = \(\sqrt [ 3 ]{ x } \) on the same coordinate plane. Find fog and graph it on the plane as well. Explain your results.

[OR]

(b) 1f x = -2 is one root of x³ – x² – 17x = 22 then find the other roots of the equation?

Question 42.
(a) lf A + B + C= it prove that cosA + cos B + cosC = 1 + 4 sin (\(\frac{A}{2}\)) sin (\(\frac{B}{2}\) sin (\(\frac{C}{2}\))

[OR]

(b) If A = \(\left[\begin{array}{lll}
1 & 2 & 2 \\
2 & 1 & 2 \\
2 & 2 & 1
\end{array}\right]\) show that A² – 4A – 5I = O

Question 43.
(a) If ⁿ⁺¹C₈ : ^(n-3)P₄ = 57 : 16, find the value of n?

[OR]

(b) If the letters of the word IITJEE arc permuted in all possible ways and the strings thus formed are arranged in the lexicographic order, find the rank of the word IITJEE?

Question 44.
(a) The line \(\frac{x}{a}\) + \(\frac{y}{b}\)= 1 moves in such a way that \(\frac { 1 }{ a^{ 2 } } \) + \(\frac { 1 }{ b^{ 2 } } \) = \(\frac { 1 }{ c^{ 2 } } \) where c is a constant. Find the locus of the foot of the perpendicular from the origin on the given line?

[OR]

(b) Show that the equation 4x² + 4xy + y² – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them?

Question 45 (a).
Prove that \(\left|\begin{array}{lll}
1 & x^{2} & x^{3} \\
1 & y^{2} & y^{3} \\
1 & z^{2} & z^{3}
\end{array}\right|\) = (x – y) (y – z) (z – x) (xy + yz + zx)

(b) Evaluate \(\underset { x\rightarrow \infty }{ lim } \) \(\frac{3}{x-2}\) – \(\frac{2 x+11}{x^{2}+x-6}\)

Question 46.
(a) Evaluate \(\frac{1}{6 x-7-x^{2}}\)

(b) Evaluate ∫e^tan-1x (\(\frac { 1+x+x^{ 2 } }{ 1+x^{ 2 } } \)) dx

Question 47 (a).
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?

[OR]

(b) Firm manufactures PVC pipes in three plants viz. X, Y and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,

1. find the probability that the selected pipe is a defective one.
2. if the selected pipe ¡s a defective, then what is the probability that it was produced by plant Y?

Students can download 6th Social Science Term 3 History Chapter 3 The Age of Empires: Guptas and Vardhanas Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science History Solutions Term 3 Chapter 3 The Age of Empires: Guptas and Vardhanas

Samacheer Kalvi 6th Social Science The Age of Empires: Guptas and Vardhanas Text Book Back Questions and Answers

I. Choose the correct Answer

Question 1.
………………. was the founder of Gupta dynasty.
(a) Chandragupta I
(b) Sri Gupta
(c) Vishnu Gopa
(d) Vishnugupta
Answer:
(b) Sri Gupta

Question 2.
Prayog Prashasti was composed by ________
(a) Kalidasa
(b) Amarasimha
(c) Harisena
(d) Dhanvantri
Answer:
(c) Harisena

Question 3.
The monolithic iron pillar of Chandragupta is at ………………
(a) Mehrauli
(b) Bhitari
(c) Gadhva
(d) Mathura
Answer:
(a) Mehrauli

Question 4.
________ was the first Indian to explain the process Of surgery.
(a) Charaka
(b) Sushruta
(c) Dhanvantri
(d) Agnivasa
Answer:
(b) Sushrutal

Question 5.
……………… was the Gauda ruler of Bengal.
(a) Sasanka
(b) Maitraka
(c) Rajavardhana
(d) Pulikesin II
Answer:
(a) Sasanka

II. Match the statement with the reason and tick the appropriate answer

Question 1.
Assertion (A) : Chandragupta I crowned himself as a monarch of a large kingdom after eliminating various small states in Northern India.
Reason (R) : Chandragupta I married Kumaradevi of Lichchavi family.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are correct but R is not correct explanation of A.
(c) A is correct but R is not correct.
(d) A is not correct but R is correct.
Answer:
(a) Both A and R are true and R is the correct explanation of A

Question 2.
Statement I : Chandragupta II did not have cordial relationship with the rules of South India.
Statement II : The divine theory of kingship was practised by the Gupta rulers.
(a) Statement I is wrong but statement II is correct.
(b) Statement II is wrong but statement I is correct.
(c) Both the statements are correct.
(d) Both the statements are wrong.
Answer:
(a) Statement I is wrong but statement II is correct.

Question 3.
Which of the following is arranged in chronological order?
(a) Srigupta – Chandragupta I – Samudragupta – Vikramaditya
(b) Chandragupta I – Vikramaditya – Srigupta – Samudragupta
(c) Srigupta – Samudragupta – Vikramaditya – Chandragupta I
(d) Vikramaditya – Srigupta – Samudragupta – Chandragupta I
Answer:
(a) Srigupta – Chandragupta I – Samudragupta -Vikramaditya

Question 4.
Consider the following statements and find out which of the following statements (s) is/are correct.
(1) Lending money at high rate of interest was practised.
(2) Pottery and mining were the most flourishing industries,
(a) 1. is correct
(b) 2. is correct
(c) Both 1 and 2 are correct
(d) Both 1 and 2 are wrong
Answer:
(a) 1. is correct

Question 5.
Circle the odd one

Answer:
Samudragupta.

Answer:
Harshacharita.

III. Fill in the blanks Answer

1. ……………., the king of Ceylon, was a contemporary of Samudragupta.
2. A Buddhist monk from China ……………., visited India during the reign of Chandragupta II.
3. ……………. invasion led to the downfall of the Gupta Empire.
4. ……………. was the main revenue to the Government.
5. The official language of the Guptas was …………….
6. ……………., the Pallava king was defeated by Samudragupta.
7. ……………. was the popular king of the Vardhana dynasty.
8. Harsha shifted his capital from ……………. to Kanauj.

Answer:

1. Reign of
2. Fahien
3. Huns
4. Land tax
5. Sanskrit
6. Vishnugopa
7. Harsha Vardhana
8. Thaneswar

IV. State whether True or False

1. Dhanvantri was a famous scholar in the field of medicine.
2. The structural temples built during the Gupta period resemble the Indo – Aryan style.
3. Sati was not in practice in the Gupta Empire.
4. Harsha belonged to the Hinayana school of thought.
5. Harsha was noted for his religious intolerance.

Answer:

1. True
2. False
3. False
4. False
5. False

V. Match the following

Question 1.

Answer:
b) 2, 4, 1, 3, 5

Question 2.

Answer:
c) 3, 5, 1, 2, 4

VI. Answer in one or two sentences

Question 1.
Who was given the title Kaviraja? Why?
Answer:

1. The title Kaviraja was given to Samudragupta.
2. He was a great lover of poetry and music.
3. In one of the gold coins, he is portrayed playing the harp (Veenai)

Question 2.
What were the subjects taught at Nalanda University?
Answer:

1. At Nalanda University Buddhism was the main subject of study.
2. Other subjects like Yoga, Vedic literature, and medicine were also taught.

Question 3.
Explain the Divine Theory of Kingship.
Answer:

1. The divine theory of Kingship meant that the king is the representative of God on earth.
2. He is answerable only to God and not to anyone else.

Question 4.
Highlight the achievements of Guptas in metallurgy.
Answer:

1. Mining and metallurgy were the most flourishing industries during the Gupta period.
2. The most important evidence of development in metallurgy was the Mehrauli Iron Pillar installed by King Chandragupta in Delhi.
3. This monolithic iron pillar has lasted through the centuries without rusting.

Question 5.
Who were the Huns?
Answer:

1. Huns were the nomadic tribe, who under their great Attila were terrorizing Rome and Constantinople.
2. They came to India through Central Asia, defeated Skandagupta, and spread across central India.
3. Their chief Toromana crowned himself asking.
4. After him, his son Mihirakula ruled and got finally defeated by Yasodharman, ruler of Malwa.

Question 6.
Name the three kinds of tax collected during Harsha’s reign.
Answer:
A Bhaga, Hiranya, and Bali were three kinds of tax collected during Harsha’s reign.

Question 7.
Name the books authored by Harsha.
Answer:
The books authored by Harsha were Ratnavali, Nagananda, and Priyadharshika.

VII. Answer the following briefly

Question 1.
Write a note on Prashasti.
Answer:

1. Prashasti is a Sanskrit word, meaning communication or in praise of.
2. Court poets flattered their kings listing out their achievements.
3. These accounts were later engraved on pillars so that the people could read them.

Question 2.
Give an account of Samudragupta’s military conquests.
Answer:

1. Samudragupta was a great general and he carried on a vigorous campaign all over the country.
2. He defeated the Pallava king Vishnugopa.
3. He conquered nine kingdoms in northern India.
4. He reduced 12 rulers of southern India to the status of feudatories and to pay tribute.
5. He received homage from the rulers of East Bengal, Assam, Nepal, the eastern part of Punjab, and various tribes of Rajasthan.

Question 3.
Describe the land classification during the Gupta period.
Answer:
Classification of land during the Gupta period.

1. Kshetra – Cultivable land
2. Khila – Wasteland
3. Aprahata – Jungle (or) Forest land
4. Vasti – Habitable land
5. Gapata saraha – Pastoral and

Question 4.
Write about Sresti and Sarthavaha traders.
Answer:

1. Sresti: Sresti traders were usually settled at a standard place.
2. Sarthavaha: Sarthavaha traders caravan traders who carried their goods to different places.

Question 5.
Highlight the contribution of Guptas to architecture.
Answer:

1. From the earlier tradition of rock – out shrines, the Guptas were the first to construct temples.
2. These temples, adorned with towers and elaborate carvings, were dedicated to all Hindu deities.
3. The most notable rock-cut caves are found at Ajanta and Ellora, Bagh, and Udaygiri.
4. The structural temples built during this period resemble the Dravidian style.

Question 6.
Name the works of Kalidasa.
Answer:

1. Kalidasa’s famous dramas were Sakunthala, Malavikagnimitra and Vikramaoorvashiyam.
2. Other significant works were Meghaduta, Raghuvamsa, Kumarasambava and Ritusamhara

Question 7.
Estimate Harshvardhana as a poet and a dramatist.
Answer:

1. Harsha himself was a poet and dramatist.
2. Around him gathered the best of poets and artists.
3. His popular works are Ratnavali, Nagananda and Priyadharshika
4. is royal court was adorned by Banabhatta, Mayura, Hardatta, and Jayasena.

VIII. HOTs

Question 1.
The gold coins issued by Gupta kings indicate ………………
Answer:
(a) the availability of gold mines in the kingdom
(b) the ability of the people to work with gold
(c) the prosperity of the kingdom
(d) the extravagant nature of kings.
Answer:
(c) the prosperity of the kingdom

Question 2.
The famous ancient paintings at Ajanta were painted on __________
a. walls of caves
b. ceilings of temples
c. Rocks
d. papyrus
Answer:
a. walls of caves

Question 3.
Gupta period is remembered for ……………….
(a) renaissance in literature and art
(b) expeditions to southern India
(c) invasion of Huns
(d) religious tolerance
Answer:
(a) renaissance in literature and art

Question 4.
What did Indian scientists achieve in astronomy and mathematics during the Gupta period?
Answer:

1. The invention of zero and the consequent evolution of the decimal system was the legacy of Guptas to the modem world.
2. Aryabhatta, Varahamihira, and Brahmagupta were the foremost astronomers and mathematicians of the time.
3. Aryabhatta, in his book ‘ Surya Siddhanta’, explained the true causes of solar and lunar eclipses.
4. He was the first Indian astronomer to declare that the earth revolves around its own axis.
5. Dhanvantri was a famous scholar in the field of medicine.
6. He was a specialist in Ayurveda.
7. Charaka was a medical scientist.
8. Susruta was the first Indian to explain the process of surgery.

IX. Student activity (For Students)

1. Stage any one of the dramas of Kalidasa in the classroom.
2. Compare and contrast the society of Guptas with that of Mauryas.

X. Life Skills (For Students)

1. Collect information about the contribution of Aryabhatta, Varahamihira and Brahmagupta to astronomy.
2. Visit a nearby ISRO centre to know more about satellite launching.

XI. Answer Grid

Question 1.
Who was Toromana?
Answer:
Toromana was the chief of White Huns.

Question 2.
Name the high-ranking officials of the Gupta Empire.
Answer:
Dandanayakas and Maha dandanayakas.

Question 3.
Name the Gupta kings who performed AsVamedha yagna.
Answer:
Samudragupta and Kumaragupta I

Question 4.
Name the book which explained the causes for the lunar and solar eclipses,
Answer:
Surya Siddhanta

Question 5.
Name the first Gupta king to find a place on coins.
Answer:
Samudragupta

Question 6.
Which was the main source of information to know about the Samudragupta’s reign?
Answer:
Allahabad Pillar

Question 7.
Harsha was the worshipper in the beginning.
Answer:
Shiva

Question 8.
University reached its fame during the Harsha period.
Answer:
The Nalanda

Samacheer Kalvi 6th Social Science The Post-Mauryan India Additional Important Questions and Answers

I. Choose the Correct Answer:

Question 1.
The successor of Sri Gupta ……………
(a) Kumaragupta I
(b) Skandagupta
(c) Vishnugupta
(d) Ghatotkacha
Answer:
(d) Ghatotkacha

Question 2.
Sri Gupta was succeeded by _______
(a) Chandra Gupta
(b) Samundra Gupta
(c) Ghatotkacha
(d) Skanda Gupta
Answer:
(c) Ghatotkacha

Question 3.
The Huhs chief crowned himself as king.
(a) Yasodharman
(b) Attila
(c) Mihirakula
(d) Toromana
Answer:
(d) Toromana

Question 4.
Srimeghavarman was the ruler of _______
(a) Singapore
(b) Ceylon
(c) Malaysia
(b) Hansena
Answer:
(b) Ceylon

Question 5.
The place Harsha went to participate in the great Kumbhamela held.
(a) Allahabad
(b) Kasi
(c) Ayodhya
(d) Prayag
Answer:
(d) Prayag

II. Match the statement with the reason and tick the appropriate answer

Question 1.
Assertion (A) : The last of the great Guptas Narasimha Gupta I was paying tribute to Mihirakula.
Reason (R) : He stopped paying tribute to Mihirakula’s hostility towards Buddhism.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are correct but R is not the correct explanation of A.
(c) A is correct but R is not correct
(d) A is not correct but R is correct
Answer:
(b) Both A and R are correct but R is not the correct explanation of A

Question 2.
Statement I : Criminal law was not more severe than that of the Gupta age.
Statement II : Death punishment was the punishment for violation of the laws and for plotting against the king.
(a) Statement I is wrong but statement II is correct
(b) Statement II is wrong but statement I is correct.
(c) Both the statements are correct.
(d) Both the statements are wrong.
Answer:
d) Both the statements are wrong

III. Fill in the blanks

1. In the assembly at ……………. Harsha distributed his wealth.
2. The capital of China ……………. was a great center of art and learning.
3. ……………. was the wife of Chandragupta I.
4. The military campaigns of kings were financed through revenue ……………..
5. The peasants were required to pay various taxes and were reduced to the position of ……………..

Answer:

1. Prayag
2. Xian
3. Kumaradevi
4. Surpluses
5. serfs

IV. Match the following

Answer:
b) 4, 5, 2, 1, 3

V. Answer in one or two sentences

Question 1.
Write a note on ‘Lichchhavi’.
Answer:

1. Lichchhavi was an old gana – Sanga and its territory lay between the Ganges and the Nepal Terai.
2. Chandragupta, I married Kumaradevi of the famous and powerful lichchhavi family.

Question 2.
How did Chandragupta I crown himself the monarch of a larger kingdom?
Answer:

1. Chandragupta, I married Kumaradevi of the famous and powerful Lichchhavi family.
2. With the support of this family, Chandragupta eliminated various small states and| crowned himself the monarch of a larger kingdom.

Question 3.
What did the travel accounts of Fahien provide information about the condi¬tions of the people of Magadha?
Answer:

1. According to Fahien the people of Magadha were happy and prosperous.
2. Gaya was desolated. Kapilvasthu had become a jungle, but at Pataliputra people were rich and prosperous.

VII. Answer the following briefly

Question 1.
Name the officials employed by the Gupta rulers.
Answer:

1. High – ranking officials were called dandanayakas and mahadandnayakas.
2. The provinces known as deshas or bhuktis were administered by the governors designated as Uparikas. The districts such as vaishyas, were controlled by vishyapatis. At the village level, gramika and gramadhyaksha were the functionaries.
3. The military designations.
4. Baladhikrita (Commander of infantry)
5. Mahabaladhikrita (Commander of the cavalry)
6. Dutakas (spies)

Question 2.
Mention the importance of Fahien’s travel accounts.
Answer:

1. During the reign of Chandragupta II, the Buddhist monk Fahien visited India.
2. His travel accounts provided us information about the socio-economic, religious and moral conditions of the people of the Gupta age.
3. According to Fahien, the people of Magadha were happy and prosperous.
4. Justice was mildly administered and there was no death penalty.
5. Gaya was desolated, Kapilavasthu had become a jungle, but at Pataliputra, people were rich and prosperous.

VIII. Mind map

Students can Download Tamil Nadu 11th Maths Model Question Paper 4 English Medium Pdf, Tamil Nadu 11th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 11th Maths Model Question Paper 4 English Medium

General Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in above three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in detail Draw diagrams wherever necessary.

Time: 2:30 Hours
Maximum Marks: 90

PART – I

I. Choose the correct answer. Answer all the questions: [20 × 1 = 20]

Question 1.
If n(A) = 2 and n(B∪C) = 3 then n[(A × B) ∪ (A × C)] is ………………..
(a) 2³
(b) 3²
(c) 6
(d) 5
Answer:
(c) 6

Question 2.
For any two sets A and B, A∩(A∪B) = …………………….
(a) B
(b) ∅
(c) A
(d) none of these
Answer:
(c) A

Question 3.
cos 1° + cos 2° + cos 3° + cos 4° + cos 179° = …………………
(a) 0
(b) 1
(c) -1
(d) 89
Answer:
(a) 0

Question 4.
The value of log₉ 27 is ……………………
(a) \(\frac{2}{3}\)
(b) \(\frac{3}{2}\)
(c) \(\frac{3}{4}\)
(d) \(\frac{4}{3}\)
Answer:
(b) \(\frac{3}{2}\)

Question 5.
The value of \(\frac{\sin 3 \theta+\sin 5 \theta+\sin 7 \theta+\sin 9 \theta}{\cos 3 \theta+\cos 5 \theta+\cos 7 \theta+\cos 9 \theta}\) = ………………..
(a) tan3θ
(b) tan6θ
(c) cot3θ
(d) cot6θ
Answer:
(b) tan6θ

Question 6.
In 3 fingers the number of ways 4 rings can be worn in ……………………. ways.
(a) 43 – 1
(b) 34
(c) 68
(d) 64
Answer:
(d) 64

Question 7.
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ……………….
(a) 11
(b) 12
(c) 10
(d) 6
Answer:
(b) 12

Question 8.
The H.M of two positive number whose AM and G.M. are 16, 8 respectively is ………………..
(a) 10
(b) 6
(c) 5
(d) 4
Answer:
(d) 4

Question 9.
The co-efficient of the term independent of x in the expansion of (2x+\(\frac{1}{3x}\))⁶ is …………………
(a) \(\frac{160}{27}\)
(b) \(\frac{160}{27}\)
(c) \(\frac{80}{3}\)
(d) \(\frac{80}{9}\)
Answer:
(a) \(\frac{160}{27}\)

Question 10.
The value of \(\left|\begin{array}{lll}
a & 0 & 0 \\
0 & b & 0 \\
0 & 0 & c
\end{array}\right|^{2}\) is ………………..
(a) abc
(b) -abc
(c) 0
(d) a²b²c²
Answer:
(d) a²b²c²

Question 11.
The value of x for which the matrix A = \(\left[\begin{array}{cc}
e^{x-2} & e^{7+x} \\
e^{2+x} & e^{2 x+3}
\end{array}\right]\) is singular is …………………..
(a) 9
(b) 8
(c) 7
(d) 6
Answer:
(b) 8

Question 12.
If |\(\vec { a } \) + \(\vec { b } \)| = 60, |\(\vec { a } \) – \(\vec { b } \)| = 40 and |\(\vec { b } \)| = 46 then |\(\vec { a } \)| is …………………
(a) 42
(b) 12
(c) 22
(d) 32
Answer:
(c) 22

Question 13.
Given \(\vec { a } \) = 2\(\vec { i } \) + \(\vec { j } \) – 8\(\vec { k } \) and \(\vec { b } \) = \(\vec { i } \) + 3\(\vec { j } \) – 4\(\vec { k } \) then |\(\vec { a } \) + \(\vec { b } \)| = ………………….
(a) 13
(b) \(\frac{13}{3}\)
(c) \(\frac{4}{13}\)
(d) \(\frac{3}{13}\)
Answer:
(a) 13

Question 14.
If f(x) = \(\left\{\begin{array}{ccc}
k x & \text { for } & x \leq 2 \\
3 & \text { for } & 2
\end{array}\right.\) is continous at x = 2 then the value of k is ……………………
(a) \(\frac{3}{4}\)
(b) 0
(c) 1
(d) \(\frac{4}{3}\)
Answer:
(c) 1

Question 15.
If f: R→R is defined by f(x) = |x – 3| + |x – 4| for x∈R then \(\lim _{x \rightarrow 3^{-}}\) f(x) is equal to ………………..
(a) -2
(b) -1
(c) 0
(d) 1
Answer:
(c) 0

Question 16.
\(\lim _{x \rightarrow \infty}\left(\frac{x^{2}+5 x+3}{x^{2}+x+3}\right)^{x}\) is ………………..
(a) e⁴
(b) e²
(c) e³
(d) 1
Answer:
(a) e⁴

Question 17.
\(\int \frac{e^{x}\left(x^{2} \tan ^{-1} x+\tan ^{-1} x+1\right)}{x^{2}+1}\) dx is ………………..
(a) e tan^-1(x + 1)
(b) tan^-1(e^x) + c
(c) e^x \(\frac{\left(\tan ^{-1} x\right)^{2}}{2}\) + c
(d) e^xtan^-1x + c
Answer:
(d) e^xtan^-1x + c

Question 18.
∫ \(\frac { secx }{ \sqrt { cos2x } } \) dx = …………………..
(a) tan^-1(sin x) + c
(b) 2 sin^-1(tan x) + c
(c) tan^-1(cos x) + c
(d) sin^-1 (tan x) + c
Answer:
(d) sin^-1 (tan x) + c

Question 19.
\(\int \frac{e^{6 \log x}-e^{5 \log x}}{e^{4 \log x}-e^{3 \log x}}\) dx = ………………..
(a) x + c
(b) \(\frac { x^{ 3 } }{ 3 } \) + c
(c) \(\frac { 3 }{ x^{ 3 } } \) + c
(d) \(\frac { 1 }{ x^{ 2 } } \) + c
Answer:
(b) \(\frac { x^{ 3 } }{ 3 } \) + c

Question 20.
It is given that the events A and B are such that P(A) = \(\frac{1}{4}\), P(A/B) = \(\frac{1}{2}\), P(B/A) = \(\frac{2}{3}\) then P(B) = …………………
(a) \(\frac{1}{6}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{2}\)
Answer:
(b) \(\frac{1}{3}\)

PART – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
In the set Z of integers, define mRn if m – n is a multiple of 12. Prove that R is an equivalence relation?
Answer:
As m – m = 0 and 0 = 0 × 12, we have 0 is a multiple of 12; hence mRm proving that R is reflexive.
Let mRn. Then m – n = 12k for some integer k; thus n – m = 12(-k) and hence nRm.
This shows that R is symmetric.
Let mRn and nRp: then m – n = 12k and n – p = 12l for some integers k and l.
So m – p = 12(k + l) and hence mRp. This shows that R is transitive.
Thus R is an equivalence relation.

Question 22.
Simplify:
\(\frac { 1 }{ 2+\sqrt { 3 } } \) + \(\frac { 3 }{ 4-\sqrt { 5 } } \) + \(\frac { 6 }{ 7-\sqrt { 8 } } \)
Answer:

Question 23.
Find the value of sin 22 \(\frac{1}{2}\)°?
Answer:
We know that cos θ = 1 – 2 sin² \(\frac{θ}{2}\) ⇒ sin \(\frac{θ}{2}\) = ±\(\sqrt { \frac { 1-cos2\theta }{ 2 } } \)
Take θ = 45°, we get sin \(\frac{45°}{2}\) = ±\(\sqrt { \frac { 1-cos45°}{ 2 } } \), (taking positive sign only, since 22\(\frac{1}{2}\)° lies in the first quadrant)
Thus, sin 22\(\frac{1}{2}\)° = \(\sqrt{\frac{1-\frac{1}{\sqrt{2}}}{2}}=\frac{\sqrt{2-\sqrt{2}}}{2}\).

Question 24.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th
hour and wth hour?
Answer:
No. of bacteria at the beginning = 30
No. of bacteria after 1 hour = 30 × 2 = 60
No. of bactena after 2 hours = 30 × 2² = 30 × 4 = 120
No. of bacteria after 4 hours = 30 × 2⁴ = 30 × 16 = 480
No. of bacteria after n^th hour = 30 × 2ⁿ

Question 25.
If the sum of the distance of a moving point in a plane from the axis is 1, then find the locus of the point?
Answer:
Let coordinates of a moving point P be (x, y).
Given that the sum of the distances from the axis to the point is always 1.
∴|x| + |y| = 1 ⇒ x + y = 1
⇒- x- y = 1 ⇒ x + y = 1
⇒ x – y = 1
Hence, these equations give us the locus of the point P which is a square.

Question 26.
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0) then find a set of values of a, b, c?
Answer:
Let A be the point (1, 0, 0) and B be the point (0, 1, 0) (i.e.,) \(\overline { OA } \) = \(\hat { i } \) and \(\overline { OB } \) = \(\hat { j } \).
Then \(\overline { AB } \) = \(\overline { OB } \) – \(\overline { OA } \) = \(\hat { j } \) – \(\hat { i } \) = –\(\hat { i } \) + \(\hat { j } \)
= (-1, 1, 0)
= (a, a + b, a + b + c)
⇒ a = -1, a + b = 1 and a + b + c = 0
⇒ a = -1, ⇒ -1 + b = 1; a + b + c = 0
⇒ b = 2; -1 + 2 + c = 0 ⇒ c + 1 = 0
⇒ c = -1
∴ a = -1, b = 2, c = -1.
Note: if we taken \(\overline { BA } \) then we get a = 1, b = -2 and c = 1.

Question 27.
Find \(\frac{dy}{dx}\) for y = (x² + 4x + 6)⁵
Answer:
Let u = x² + 4x + 6
⇒ \(\frac{du}{dx}\) = 2x + 4
Now y = u⁵ = \(\frac{dy}{du}\) = 5u⁴
∴ \(\frac{dy}{dx}\) = \(\frac{dy}{du}\) × \(\frac{du}{dx}\) = 5u⁴ (2x + 4)
= 5(x² + 4x + 6)⁴ (2x + 4)
= 5(2x + 4) (x² + 4x + 6)⁴

Question 28.
Evaluate ∫\(\sqrt { 25x^{ 2 }-9 } \) dx?
Answer:

Question 29.
A bag contains 5 white and 7 black balls. 3 balls are drawn at random. Find the probability that

1. all are white
2. one white and 2 black.

Answer:
Number of white balls = 5
Number of black balls = 7
Total number of balls = 12
Selecting 3 from 12 balls can be done in
¹²C₃ = \(\frac{12 \times 11 \times 10}{3 \times 2 \times 1}\) = 220 ways
∴n(S) = 220

1. Let A be the selecting 3 white balls.
∴n(A) = ⁵C₃ = ⁵C₂ = \(\frac{5×3}{2×1}\) = 10
∴P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{10}{220}\) = \(\frac{1}{22}\)

2. Let B be the event of selecting one white and 2 black balls.
∴n(B) = ⁵C₁ × ⁷C₂ = (5) (\(\frac{7×6}{2×1}\)) = 5(21) = 105
∴P(B) = \(\frac{n(B)}{n(S)}\) = \(\frac{105}{220}\) = \(\frac{21}{44}\).

Question 30.
If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k?
Answer:
Area of ∆ with vertices (k, 2) (2, 4) and (3, 2) = \(\frac{1}{2}\) \(\left|\begin{array}{lll}
k & 2 & 1 \\
2 & 4 & 1 \\
3 & 2 & 1
\end{array}\right|\) = 4 given
⇒ \(\left|\begin{array}{lll}
k & 2 & 1 \\
2 & 4 & 1 \\
3 & 2 & 1
\end{array}\right|\) = 2(4) = 8
(i.e.,) k(4 – 2) – 2(2 – 3) + 1(4 – 12) ± 8
(i.e.,) 2k – 2(-1) + 1(-8) = ± 8
(i.e.,) 2k + 2 – 8 = 8
(i.e.,) 2k = 8 + 8 – 2 = 14
k = 14/2 = 7
∴k = 7
So k = 7 (or) k = -1.

2k + 2 – 8 = -8
⇒2k = – 8 + 8 – 2
2k = – 2
k = -1

PART – III

III. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
In the set Z of integers define mRn if m – n is a multiple of 12. Prove that R is an equivalence relation?

Question 32.
Prove that \(\frac{sin4x+sin2x}{cos4x+cos2x}\) = tan 3x?

Question 33.
A polygon has 90 diagonals. Find the number of its sides?

Question 34.
If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x + y)ⁿ are equal?

Question 35.
Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3 : 10?

Question 36.
Prove that \(\left|\begin{array}{ccc}
1 & x & x \\
x & 1 & x \\
x & x & 1
\end{array}\right|^{2}=\left|\begin{array}{ccc}
1-2 x^{2} & -x^{2} & -x^{2} \\
-x^{2} & -1 & x^{2}-2 x \\
-x^{2} & x^{2}-2 x & -1
\end{array}\right|\)

Question 37.
If G is the centroid of a traiangle ABC prove that \(\overline { GA } \) + \(\overline { GB } \) + \(\overline { GC } \) = 0

Question 38.
Find \(\frac{dy}{dx}\) for y = \(\sqrt { 1+tan2x } \)?

Question 39.
Evaluate \(\frac { \sqrt { x } }{ 1+\sqrt { x } } \) dx?

Question 40.
Find the relation between a and b if \(\underset { x\rightarrow 3 }{ lim } \) f(x) exists where f(x) = \(\left\{\begin{array}{cc}
a x+b & \text { if } x>3 \\
3 a x-4 b+1 \text { if } x<3
\end{array}\right.\)

PART – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41 (a).
From the curve y = |x|, draw(i) y = |x-1| + 1

1. y = |x + 1| + 1
2. y = |x + 2| – 3

[OR]

(b) Resolve into partial fraction \(\frac { x+4 }{ (x^{ 2 }-4)(x+1) } \)

Question 42 (a).
Find the number of positive integers greater than 6000 and less than 7000 which arc divisible by 5, provided that no digit is to be repeated?

[OR]

(b) If ⁿP_r = ⁿP_r+1 and ⁿC_r = ⁿC_r-1, find the values of n and r?

Question 43 (a).
In a ∆ABC, prove that b² sin 2C + c² sin 2B = 2bc sin A?

[OR]

(b) Differentiate the following s(t) = \(\sqrt[4]{\frac{t^{3}+1}{t^{3}-1}}\)?

Question 44 (a).
Find the equation of the lines make an angle 60° with the positive x axis and at a distance 5\(\sqrt{2}\) units measured from the point (4, 7) along the line x – y + 3 = 0

[OR]

(b) If y = A cos4x + B sin 4x, A and B are constants then Show that y₂ + 16y = 0

Question 45 (a).
Find the sum up to the 17^th term of the series \(\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}\) + …………..

[OR]

(b) A shopkeeper in a Nuts and Spices shop makes gifi packs of cashew nuts, raisins and almonds?

1. Pack I contains 100 gm of cashew nuts, 100 gm of raisins and 50 gm of almonds.
2. Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds.
3. Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds.
4. The cost of 50 gm of cashew nuts is ₹50, 50 gm of raisins is ₹10. and 50gm of almonds is ₹60. What is the cost of each gift pack?

Question 46 (a).
Find matrix C if A = \(\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}\), B = \(\begin{bmatrix} -3 & 2 \\ 4 & -1 \end{bmatrix}\) and 5C + 28= A?

[OR]

(b) The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that

1. it will get at least one of the two awards
2. it will get only one of the awards.

Question 47 (a).
\(\underset { \alpha \rightarrow 0 }{ lim } \) \(\frac { sin(\alpha ^{ n }) }{ (sin\alpha )^{ m } } \)

[OR]

(b) Evaluate I = sin^-1 (\(\frac { 2x }{ (1+x)^{ 2 } } \)) dx?

Students can download 6th Social Science Term 3 History Chapter 2 The Post-Mauryan India Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science History Solutions Term 3 Chapter 2 The Post-Mauryan India

Samacheer Kalvi 6th Social Science The Post-Mauryan India Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
The last Mauryan emperor was killed by ……………
(a) Pushyamitra
(b) Agnimitra
(c) Vasudeva
(d) Narayana
Answer:
(a) Pushyamitra

Question 2.
___________ was the founder Of Satavahana dynasty.
(a) Simuka
(b) Satakarani
(c) Kanha
(d) Sivasvati
Answer:
(a) Simuka

Question 3.
…………… was the greatest of all the Kushana emperors.
(a) Kanishka
b) Kadphises I
(c) Kadphises II
(d) Pan – Chiang
Answer:
(a) Kanishka

Question 4.
The Kantara School of Sanskrit flourished in the
(a) Deccan
(b) North-west India
(c) Punjab
(d) Gangetic valley
Answer:
(a) Deccan

Question 5.
Sakas ruled over Gandhara region …………… as their capital.
(a) Sirkap
(b) Taxila
(c) Mathura
(d) Purushpura
Answer:
(a) Sirkap

II. Match the statement with the reason and tick the appropriate answer

Question 1.
Assertion (A) : Colonies of Indo – Greeks and Indo – Parthians were established along the north-western part of India.
Reason (R) : The Bactrian and Parthian settlers gradually intermarried and intermixed with the indigenous population.
(a) Both A and R are correct and R is the correct explanation of A.
(b) Both A and R are correct but R is not the correct explanation of A.
(c) A is correct but R is not correct.
(d) A is not correct but R is correct
Answer:
(a) Both A and R are correct and R is the correct explanation of A

Question 2.
Statement I : Indo – Greek rulers introduced die system and produced coins with inscription and symbols, engraving figures on them.
Statement II : Indo – Greek rule was ended by the Kushanas.
(a) Statement I is wrong, but statement II is correct.
(b) Statement II is wrong, but statement I is correct
(c) Both the statements are correct.
(d) Both the statements are wrong.
Answer:
(b) Statement II is wrong, but statement I is correct

Question 3.
Circle the odd one

Answer:
Kanishka

Question 4.
Answer the following in a word:

Question 1.
Who was the last Sunga ruler?
Answer:
Devabhuti

Question 2.
Who was the most important and famous king of Sakas?
Answer:
Rudradaman

Question 3.
Who established Kanva dynasty in Magadha?
Answer:
Vasudeva

Question 4.
Who converted Gondophemes into Christianity?
Answer:
St.Thomas

III. Fill in the blanks

1. …………… was the founder of Indo – Parthian Kingdom.
2. In the South, Satavahanas became independent after …………… death.
3. Hala is famous as the author of ……………
4. …………… was the last ruler of Kanva dynasty.
5. Kushana’s later capital was ……………

Answer:

1. Arsaces
2. Susarman
3. Sattasai (Saptasati)
4. Susarman
5. Peshawar(Purushpura)

IV. State whether True or False Answer

1. Magadha continued to be a great centre of Buddhist culture True even after the fall of the Mauryan Empire.
2. We get much information about Kharavela from Hathigumba True inscription.
3. Simuka waged a successful war against Magadha.
4. Buddhacharita was written by Asvaghosha.

Answer:

1. True
2. True
3. False
4. True

V. Match the following

Answer:
b) 3451 2

VI. Find out the wrong statement from the following

(1) The Kushanas formed a section of the yueh-chi tribes who inhabited north-western China.
(2) Kanishka made Jainism the state religion and built many monasteries.
(3) The Great Stupa of Sanchi and the railings which enclose it belog to the Sunga period.
(4) Pan – Chiang was the Chinese general defeated by Kanishka.
Answer:
2) Kanishka made Jainism the state religion and built many monasteries.

VII. Answer in one or two sentences

Question 1.
What happened to the last Mauryan emperor?
Answer:

1. The last Mauryan emperor was Brihadratha.
2. He was assassinated by his own general, Pushyamitra Sunga.

Question 2.
Write a note on Kalidasa’s Malavikagnimitra.
Answer:

1. Pushyamitra’s son Agnimitra is said to be the hero of Kalidasa’s Malavikagnimitra.
2. This drama also refers to the victory of Vasumitra, Agnimitra’s son, over the
   Greeks on the banks of the Sindhu river.

Question 3.
Name the ruler of Kanva dynasty.
Answer:

1. Vasudeva
2. Bhumi Mitra
3. Narayana
4. Susarman.

Question 4.
Highlight the literary achievements of Satavahanas.
Answer:

1. The Satavahana king Hala was himself a great scholar of Sanskrit.
2. The Kantara school of Sanskrit flourished in the Deccan in Second Century B.C.
3. Hala is famous as the author of Sattasai (Saptasati), 700 stanzas in Prakrit.

Question 5.
Name the places where Satavahana’smounments are situated.
Answer:

1. Gandhara
2. Madhura
3. Amaravati
4. BodhGaya
5. Sanchi
6. Bharhut

Question 6.
Give an account of the achievements of Kadphises
Answer:

1. Kadphises I was the first famous military and political leader of the Kushanas.
2. He overthrew the Indo-Greek and Indo-Parthian rulers.
3. He established himself as a sovereign ruler of Bactria.
4. He extended his power in Kabul, Gandhara and up to the Indus.

Question 7.
Name the Buddhist saints and scholars who adorned the court of Kanishka
Answer:

1. Asvaghosha
2. Vasumitra
3. Nagarjuna

VIII. Answer the following

Question 1.
Who invaded India after the decline of the Mauryan empire.
Answer:

1. The break-up of the Mauryan empire resulted in the invasions of Sakas, Scythians, Parthians, Indo-Greeks or Bactria Greeks, and Kushanas from the north-west.
2. In the South, Satavahanas became independent after Asoka’s death.
3. There were Sunga and Kanvas in the north before the emergence of the Gupta dynasty.
4. Chedis (Kalinga) declared their independence.
5. Though Magadha ceased to be the premier state of India, it continued to be a great center of Buddhist culture.

Question 2.
Give an account of the conquests of Pushyamitra Sunga.
Answer:

1. The last Mauryan emperor, Brihadratha, was assassinated by his own general, Pushyamitra Sunga.
2. He established his Sunga dynasty in Magadha. His capital was Pataliputra.
3. Pushyamitra successfully repulsed the invasion of Bactria king Menander. He also conquered Vidarbha.
4. He was a staunch follower of Vedic religion. He performed two Asvamedbayagnas (horse sacrifices) to assert his imperial authority.

Question 3.
Write a note on GautamiputraSatakarni
Answer:

1. GautamiputraSatakarni was the greatest ruler of the family.
2. In the Nasik prashasti, published by his mother GautamiBalasri, Gautamiputra Satakami is described as the destroyer of Sakas, Yavanas (Greeks), and Pahlavis (Parthians).
3. The extent of the empire is also mentioned in the record.
4. Their domain included Maharashtra, north Konkan, Berar, Gujarat, Kathiawar, and Malwa.
5. His ship coins are suggestive of Andhras’ skill in seafaring and their naval power.
6. The Bogor inscriptions suggest that South India played an important role in the process of early state formation in Southeast Asia.

Question 4.
What do you know of the Gondopharid dynasty?
Answer:

1. Indo-Parthians came after the Indo-Greeks and the Indo-Scythians who were, in turn, defeated by the Kushanas in the second half of the first century A.D.
2. Indo-Parthian kingdom or Gondopharid dynasty was founded by Gondophemes.
3. The domain of Indo-Parthians comprised Kabul and Gandhara.
4. The name of Gonodophemes is associated with the Christian apostle St. Thomas.
5. According to Christian tradition, St.Thomas visited the court of Gondophemes and converted him to Christianity.

Question 5.
Who was considered the best known Indo-Greek king? Why?
Answer:

1. Menander was one of the best known Indo-Greek kings.
2. He is said to have ruled a large kingdom in the north-west of the country.
3. His coins were found over an extensive area ranging from Kabul valley and Indus river to western Uttar Pradesh.
4. MilindaPanha, a Buddhist text, is a discourse between Bactrian king Milinda and the learned Buddhist scholar Nagasena.
5. This Milinda is identified with Menander.
6. Menander is believed to have become a Buddhist and promoted Buddhism.

Question 6.
Who was Sakas?
Answer:

1. The Indo-Greek rule in India was ended by the Sakas. Sakas as nomads came in huge number and spread all over northern and western India.
2. The Sakas were against the tribe of Turki nomads.
3. Sakas were Scythians, nomadic ancient Iranians, and known as Sakas in Sanskrit.
4. Saka rule was founded by Maos or Mogain in the Gandhara region and his capital was ‘Sirkap’. His name is mentioned in Mora inscription. His coins bear images of Buddha and Siva.
5. Rudradaman was the most important and famous king of Sakas. His Junagadh/ Gimar inscription was the first inscription in chaste Sanskrit.
6. In India, the Sakas were assimilated into Indian society. They began to adopt Indian names and practice Indian religious beliefs.
7. The Sakas appointed kshetras or satraps as provincial governors to administer their territories.

Question 7.
Give an account of the religious policy of Kanishka.
Answer:

1. Kanishka was an ardent Buddhist.
2. His empire was a Buddhist empire.
3. He adopted Buddhism under the influence of Asvaghosha, a celebrated monk from Pataliputra.
4. He was as equal as the exponent and champion of Mahayanism.
5. He made Buddhism the state religion.
6. He built many stupas and monasteries in Mathura, Taxila, and many other parts of his kingdom.
7. He sent Buddhist missionaries to Tibet, China, and many countries of Central Asia for the propagation of Buddha’s gospel.
8. He organised the fourth Buddhist Council at Kundalavana near Srinagar to sort out the differences between the various schools of Buddhism. It was only in this council that Buddhism was split into Hinayanism and Mahayanism.

IX. HOTS

Question 1.
The importance of the Gandhara School of Art.
Answer:

1. The Gandhara School of Indian Art is heavily indebted to Greek influence.
2. The Greeks were good cave builders.
3. The Mahay ana Buddhists learnt the art of carving out caves from them.
4. They became skilled in rock-cut architecture.
5. This Gandhara art flourished during Kanishka time. The most favourite subject was the carving of Sculptures of Buddha.

Question 2.
Provide an account of trade and commerce during the Post-Mauryan period in South India.
Answer:

1. Kadphises II maintained a friendly relationship with the emperors of China and Rome.
2. He encouraged trade and commerce with foreign countries.
3. His coins contained the inscribed figures of Lord Siva and his imperial titles.
4. The inscriptions in the coins were in the Kharosthi language.

X. Activity (For Students)

1. Prepare an album with centres of archaeological monuments of Satavahanas and Kushanas.
2. Arrange a debate in the classroom on the cultural contribution of Indo-Greeks, Sakas, and Kushanas.

XI. Answer Grid

Question 1.
Who wrote Brihastkatha?
Answer:
Gunadhya

Question 2.
Name the Satavahana ruler who performed two Asvamedha sacrifices.
Answer:
Satakarni

Question 3.
How many years did the Satavahanas rule the Deccan?
Answer:
450 years

Question 4.
Who laid the foundation of the Saka era?
Answer:
Mao’s (or) Mogain

Question 5.
What was the favourite subject of Gandhara artists?
Answer:
Carving of Sculptures of Buddha

Question 6.
Where did Kanishka organise the fourth Buddhist Council?
Answer:
Kundalavana (near Srinagar)

Samacheer Kalvi 6th Social Science The Post-Mauryan India Additional Important Questions and Answers

I. Choose the Correct Answer:

Question 1.
The Chinese Buddhist monk and traveller who wrote si-yu-ki …………….
(a) Fahien
(b) Hiuen Tsang
(c) Yuch – Chi
(d) Pan – Chiang
Answer:
(b) Hiuen Tsang

Question 2.
Asvahosha wrote
(a) Brihastkatha
(b) Mahabhasya
(c) Buddhacharita
(d) Harshacharita
Answer:
(c) Buddhacharita

Question 3.
During the Sunga period stone was replaced by railings.
(a) wood
(b) iron
(c) copper
(d) brick
Answer:
(a) wood

Question 4.
MilindaPanha is a Buddhist
(a) Statue
(b) Cave
(c) Text
(d) Monastry
Answer:
(c) Text

Question 5.
……………. gradually gained ascendancy and became the court language.
(a) Sanskrit
(b) Kharasthi
(c) Kannada
(d) Prakrit
Answer:
(a) Sanskrit

II. Match the statement with the reason and tick the appropriate answer

Question 1.
Assertion (A): The Greek rulers of Bactria and Parthia started encroaching into the northwestern borderlands of India.
Reason (R): There was a decline in the Mauryan empire.
(a) Both A and R are correct and R is the correct explanation of A.
(b) Both A and R are correct and R is not the correct explanation of A.
(c) A is correct but R is not correct.
(d) Both the statements are wrong.
Answer:
(a) Both A and R are correct and R is the correct explanation of A

Question 2.
Statement I: The Mahayana Buddhists learned the art of carving out caves from the Greeks.
Statement II: The Greeks were good cave builders.
(a) Statement I is wrong, but statement II is correct.
(b) Statement II is wrong, but the statement I is correct.
(c) Both the statements are correct.
(d) Both the statements are wrong.
Answer:
(c) Both the statements are correct.

III. Fill in the blanks

1. Simuka’s successor was his brother …………….
2. A bronze statue of the standing Buddha was discovered in …………….
3. The Indo – Greek rule in India was ended by the ……………..
4. The Saka ruler Mogain’s capital was ……………..
5. Rudradaman’s ……………. inscription was the first inscription in chaste Sanskrit.

Answer:

1. Krishna
2. OC – EO
3. Sakas
4. Sirkap
5. Junagadh / Girnar

IV. True or False

1. Satakarni was Simuka’s nephew.
2. A stone seal discovered in Nakhon Pathom was in Thailand.
3. Mao’s name is mentioned in the Mora inscription.
4. The Kushanas appointed satraps as provincial governors.
5. Kushana rulers were Buddhists.

Answer:

1. True
2. True
3. True
4. False
5. True

V. Answer in one or two sentences

Question 1.
Write a short note on king Kharavela of Kalinga
Answer:

1. King Kharavela was a contemporary of the Sungas.
2. Hathigumba Inscription gave information about Kharavela.

Question 2.
Who laid the foundation of the Satavahana dynasty?
Answer:

1. The last Kanva ruler Susarman was assassinated by his powerful feudatory chief of Andhra named Simuka.
2. Simuka laid the foundation of the Satavahana dynasty.

Question 3.
How did the Sakas assimilate into Indian Society?
Answer:

1. The Sakas began to adopt Indian names.
2. They practiced Indian religious beliefs.

Question 4.
Under whom did the satrapies Bactria and Parthia become independent,
Answer:
Satrapies Bactria became independent under the leadership of Diodotus I and Parthia under Arsaces.

VII. Answer the following

Question 1.
Write a note on the Conquests of Kanishka.
Answer:

1. Kanishka conquered and annexed Kashmir.
2. He waged a successful war against Magadha.
3. He also waged a war against a ruler of Parthia to maintain safety and integrity in his vast empire on the western and south-western border.
4. After the conquest of Kashmir and Gandhara, he turned his attention towards China.
5. He defeated the Chinese general Pan-Chiang and safeguarded the northern borders of India from Chinese intrusion.
6. His empire extended from Kashmir down to Benaras, and the Vindhya mountain in the south. It included Kashgar, Yarkand touching the borders of Persia and Parthia.

VIII. Mind map

Students can download 6th Social Science Term 3 History Chapter 1 Society and Culture in Ancient Tamizhagam: The Sangam Age Questions and Answers, Notes, Samacheer Kalvi 6th Social Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Social Science History Solutions Term 3 Chapter 1 Society and Culture in Ancient Tamizhagam: The Sangam Age

Samacheer Kalvi 6th Social Science Society and Culture in Ancient Tamizhagam: The Sangam Age Text Book Back Questions and Answers

I. Choose the correct answer

Question 1.
Pattini cult in Tamil Nadu was introduced by …………….
(a) PandyanNeduncheliyan
(b) CheranSenguttuvan
(c) IlangoAdigal
(d) Mudathirumaran
Answer:
(b) CheranSenguttuvan

Question 2.
Which dynasty was not in power during the Sangam Age?
(a) Pandyas
(b) Cholas
(c) Pallavas
(d) Cheras
Answer:
(c) Paliavas

Question 3.
The rule of Pandyas was followed by ……………..
(a) Satavahanas
(b) Cholas
(c) Kalabhras
(d) Pallavas
Answer:
(c) Kalabhras

Question 4.
The lowest unit of administration during the Sangam Age was
(a) Mandalam
(b) Nadu
(c) Ur
(d) Pattinam
Answer:
(c) Ur

Question 5.
What was the occupation of the inhabitants of the Kurinji region?
(a) Plundering
(b) Cattle rearing
(c) Hunting and gathering
(d) Agriculture
Answer:
(c) Hunting and gathering

II. Read the statement and tick the appropriate answer

Question 1.
Assertion (A) : The assembly of the poets was known as Sangam.
Reason (R) : Tamil was the language of Sangam literature.
(a) Both A and R are true. R is the correct explanation of A.
(b) Both A and R are true. R is not the correct explanation of A.
(c) A is true but R is false.
(d) Both A and R is not true.
Answer:
(a) Both A and R are true. R is the correct explanation of A

Question 2.
Which of the following statements are not true?
a. Karikala won the battle of Talayalanganam.
b. The Pathitrupathu provides information about Chera Kings.
c. The earliest literature of the Sangam age was written mostly in the form of prose
a. 1 only
b. 1 and 3 only
c. 2 only
Answer:
(b) 1 and 3 only

Question 3.
The ascending order of the administrative division in the ancient Tamizhagam was
(a) Ur < Nadu < Kurram < Mandalam
(b) Ur < Kurram < Nadu < Mandalam
(c) Ur < Mandalam < Kurram < Nadu
(d) Nadu < Kurram < Mandalam < Ur
Answer:
(b) Ur < Kurram < Nadu < Mandalam

Question 4.
Match the following dynasties with the Royal Insignia

Answer:
A) 3 2 1

III. Fill in the blanks

1. The battle of Venni was won by ………………
2. The earliest Tamil grammar work of the Sangam period was ………………
3. ……………… built Kallanai across the river Kaveri.
4. The chief of the army was known as ……………….
5. Land revenue was called ………………

Answer:

1. Karikal Valavan
2. Tholkappiyam
3. Karikalan
4. Thanai thalaivan
5. Irai

IV. True or False

1. Caste system developed during the Sangam period.
2. Kizhar was the village chief.
3. Puhar was the general term for city.
4. Coastal region was called Marudham.

Answer:

1. False
2. True
3. False
4. False

V. Match

Answer:
1. – d
2. – a
3. – b
4. – c

VI. Answer in one or two sentences

Question 1.
Name any two literary sources to reconstruct the history of ancient Tamizhagam?
Answer:
Tholkappiyam, Ettuthogai, and Patthupattu are some of the literary sources to reconstruct the history of ancient Tamizhagam.

Question 2.
What was Natukkal or Virakkal?
Answer:

1. The ancient Tamils had great respect for the heroes who died on the battlefield.
2. The hero stones were created to commemorate heroes who sacrificed their lives in war. These hero stones were known as Natukkal or Virakkal.

Question 3.
Name five things mentioned in the Sangam literature.
Answer:

1. Kurinji.
2. Mullai.
3. Marutham.
4. Neithal.
5. Palai.

Question 4.
Name any two archaeological sites related to Sangam period.
Answer:
The excavated materials from Adichanallur, Arikamedu, Kodumanal, Puhar, Korkai, Alankulam, Urariyur etc.

Question 5.
Name the seven patrons (KadaiyeluVallalgal).
Answer:
The seven patrons were

1. Pari
2. Kari
3. Ori
4. Pegan
5. Ay
6. Adiyaman
7. Nalli

Question 6.
Name any three Tamil poetic works of Kalahhra period.
Answer:
Periapuranam, Seevakachinthamani, and Kundalakesi were written during the Kalabhra

VII. Answer the following

Question 1.
Discuss the status of women in the Sangam Society.
Answer:

1. In the Sangam Society, there were learned and wise women.
2. Forty women poets had lived
3. Marriage was a matter of choice.
4. Chastity (Karpu) was considered the highest virtue.
5. In their Parents’ property sons and daughters had equal shares.

VIII. HOTS

Question 1.
KarikalValavan is regarded as the greatest Chola king. Justify.
Answer:

1. KarikalValavan or Karikalan was the most famous of the Chola kings.
2. He defeated the combined army of the Cheras, Pandyas and the eleven Velir Chieftains who supported them at Venni, a small village in the Thanjavur region.
3. He converted forests into cultivable lands.
4. He built Kallanai across the river Kaveri to develop agriculture.
5. Their port Puhar attracted merchants from various regions of the Indian Ocean.
6. The Pattinapaalai a poetic work in the pathinenkeezhkanakku gives elaborate information of the trading activity during the rule of Karikalan.

Question 2.
The period ilabhra is not a dark age. Give reasons.
Answer:

1. Following the Sangam period, the Kalabhras had occupied Tamil Country for about two and half centuries.
2. There is evidence of their rule in literary texts.
3. The literary sources for this period include Tamil Navalar Charithai, Yapemkalam and Periapuranam.
4. Seevakachinthamani and Kundalakesi were also written during this period.
5. In Tamizhagam, Jainism and Buddhism became prominent during this period
6. Introduction of Sanskrit and Prakrit languages had resulted in the development of a new script called Vattezhuththu.
7. Many works under Pathinenkeezhkanakku were composed.
8. Trade and commerce continued to flourish during this period.
9. So the Kalabhra period is not a dark age, as it is portrayed.

X. Life skill (For Students)

Collect and paste the pictures of landscape and find out the eco – region to which belongs. Write the important crops grown and occupation of the people there.

XI. Answer Grid

Question 1.
Mention two epics of the Sangam period.
Answer:

1. Silapathikaram
2. Manimegalai

Question 2.
Name the two groups of officials who assisted the king.
Answer:

1. Aimperunguzhu
2. Enberayam

Question 3.
Name any two women poets of the Sangam period.
Answer:

1. Awaiyar, Velli
2. Veethiyar

Question 4.
Name any three major ports of Sangam age.
Answer:

1. Musiri
2. Tondi
3. Korkai

Question 5.
What constituted Muthamizh?
Answer:

1. Iyal
2. Isai
3. Naatakam

Question 6.
Silapathikaram was written by ……………
Answer:
Ilango Adigal

Question 7.
Talayalanganam is related to whish Pandya king?
Answer:
Nedunchezhiyan

Question 8.
Which ecoregion was called menpulam?
Answer:
Marutham

Question 9.
The lighthouses in the ports are called ……………
Answer:

1. Kalangari
2. flangu Sudar

Samacheer Kalvi 6th Social Science Society and Culture in Ancient Tamizhagam: The Sangam Age Additional Important Questions and Answers

I. Choose the Correct Answer:

Question 1.
According to Prof.George L.Hart Tanial is as old as ……………
(a) Chinese
(b) Greek
(c) Latin
(d) English
Answer:
(c) Latin

Question 2.
The epic character from Silappathikaram
(a) Pallavas
(b) Cheras
(c) Pandyas
(d) Cholas
Answer:
(d) Cholas

Question 3.
…………… is the port of Pandvas.
(a) Puhar
(b) Korgai
(c) Muziri
(d) Tondi
Answer:
(b) Korgai

Question 4.
Bow and arrow as the symbol of
(a) Kalabhras
(b) Cholas
(c) Cheras
(d) Pandyas
Answer:
(c) Cheras

II. Read the statement and tick the appropriate answer

Question 1.
Assertion (A) : The Kalabhra period is not a dark age.
Reason (R) : It is known about the literary sources, new script and flourishing of trade and commerce.
(a) Both A and R are true. R is not the correct explanation of A.
(b) Both A and R are true. R is the correct explanation of A
(c) A is true but R is false.
(d) Both A and R is not true.
Answer:
(b) Both A and R are true. R is the correct explanation of A.

Question 2.
Which of the following statements are not true?
(1) Pandyas garlanded Fig (Athi) flower.
(2) The deity of the kurinji people is Indiran.
(3) The author of ‘Natural History’ is Pliny the younger
(a) 1, 2 and 3
(b) 2 and 3
Answer:
(b) 2 and 3

III. Answer the following

Question 1.
What were the ornaments made of?
Answer:

1. Gold
2. Silver
3. Pearls
4. Precious stones
5. Conch shells
6. Beads

Question 2.
What were the main imports?
Answer:

1. Topaz
2. Tin
3. Wine
4. Glass
5. Horses

Question 3.
What do you know about Indian silk?
Answer:

1. The silk supplied by Indians, merchants to the Roman Empire was very important. .
2. The Roman emperor Aurelian declared it to be worth its weight in gold.

Question 4.
What is the Royal Insignia?
Answer:

1. Sceptre
2. Drum
3. White umbrella

VII. Answer the following

Question 1.
Explain the Religious Beliefs and Social Divisions in the Sangam Society. The primary deity of the Tamils was Seyon or Murugan.
Answer:

1. The other worshipped gods were Sivan, Mayon (Vishnu), Indiran, Varunan and Kotravai.
2. The Hero stone (natukkal) worship was in practice
3. Buddhism and Jainism also co-existed.
4. As it did in northern India caste did not develop in Tamizhagam.
5. Varuna system came to the Dravidian south comparatively late.

Question 2.
What was said by George L Hart about the Tamil language?
Answer:

1. George L. Hart, Professor of Tamil language at the University of California, has said that Tamil is as old as Latin.
2. The language arose as an entirely independent tradition with no influence of other languages.

VII. Mind map

Students can Download Tamil Nadu 11th Maths Model Question Paper 3 English Medium Pdf, Tamil Nadu 11th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 11th Maths Model Question Paper 3 English Medium

General Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about one or two sentences.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in above three to five short sentences.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in detail Draw diagrams wherever necessary.

Time: 2:30 Hours
Maximum Marks: 90

PART – 1

I. Choose the correct answer. Answer all the questions: [20 × 1 = 20]

Question 1.
Let R be the universal relation on a set X with more than one element then R is ………………
(a) Not reflexive
(b) Not symmetric
(c) Transitive
(d) None of the above
Answer:
(c) Transitive

Question 2.
The value of log_ab log_bc log_ca is …………………..
(a) 2
(b) 1
(c) 3
(d) 4
Answer:
(b) 1

Question 3.
If log \(\log _{\sqrt{ }}\) 0.25 = 4 then the value of x is ………………..
(a) 0.5
(b) 2.5
(c) 1.5
(d) 1.25
Answer:
(a) 0.5

Question 4.
The product of r consecutive positive integers is divisible by ………………..
(a) r!
(b) (r-1)!
(c) (r+l)!
(d) r^r
Answer:
(a) r!

Question 5.
The value of tan75° – cot 75° is ……………….
(a) 1
(b) 2 + \(\sqrt{3}\)
(c) 2 – \(\sqrt{3}\)
(d) 2\(\sqrt{3}\)
Answer:
(d) 2\(\sqrt{3}\)

Question 6.
If (1 +x²)²(1 + x)² = a₀ + a₁ x + a₂x² …. + xⁿ⁺⁴ and if a₀, a₁, a₂, are in AP, then n is …………………..
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(c) 3

Question 7.
If _nC₁₂ = _nC₅ then _nC₂ = …………………
(a) 72
(b) 306
(c) 152
(d) 153
Answer:
(d) 153

Question 8.
The line (p + 2q)x + (p- 3q)y =p – q for different values of p and q passes through the point …………………
(a) (\(\frac{3}{5}\), \(\frac{2}{5}\))
(b) (\(\frac{2}{5}\), \(\frac{2}{5}\))
(c) (\(\frac{3}{5}\), \(\frac{3}{5}\))
(d) (\(\frac{2}{5}\), \(\frac{3}{5}\))
Answer:
(d) (\(\frac{2}{5}\), \(\frac{3}{5}\))

Question 9.
The number of terms in the expansion of [(a + b)²]¹⁸ = ………………..
(a) 19
(b) 18
(c) 36
(d) 37
Answer:
(d) 37

Question 10.
A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 5 then its y intercept is …………………
Answer:
(a) \(\frac{3}{4}\)
(b) \(\frac{4}{3}\)
(c) 5
(d) \(\frac{1}{3}\)

Question 11.
If a and b are the roots of the equation x² – kx + 16 = 0 satisfy a² + b² = 32, then the value of k is ………………..
(a) 10
(b) -8
(c) -8, 8
(d) 6
Answer:
(c) -8, 8

Question 12.
If A is a square matrix of order 3 then |kA| = ………………….
(a) k |A|
(b) k²|A|
(c) k³|A|
(d) k|A³|
Answer:
(c) k³|A|

Question 13.
If ABCD is a parallelogram then \(\bar { AB } \) + \(\bar { AD } \) + \(\bar { CD } \) + \(\bar { CD } \) = ………………..
(a) 2(\(\bar { AB } \) + \(\bar { AD } \))
(b) 4\(\bar { AC } \)
(c) 4\(\bar { BD } \)
(d) \(\bar { o } \)
Answer:
(d) \(\bar { o } \)

Question 14.
\(\lim _{x \rightarrow 0}\) x cot x = ………………….
(a) 0
(b) 1
(c) -1
(d) ∞
Answer:
(b) 1

Question 15.
If x = \(\frac { 1-t^{ 2 } }{ 1+t^{ 2 } } \) and y = \(\frac { 2t }{ 1+t^{ 2 } } \) then \(\frac{dy}{dx}\) = ………………..
(a) \(\frac{y}{x}\)
(b) \(\frac{-y}{x}\)
(c) –\(\frac{x}{y}\)
(d) \(\frac{x}{y}\)
Answer:
(c) –\(\frac{x}{y}\)

Question 16.
If y = \(\frac { (1-x)^{ 2 } }{ x^{ 2 } } \) then \(\frac{dy}{dx}\) is …………………..
(a) \(\frac { 2 }{ x^{ 2 } } \) + \(\frac { 2 }{ x^{ 3 } } \)
(b) –\(\frac { 2 }{ x^{ 2 } } \) + \(\frac { 2 }{ x^{ 3 } } \)
(c) –\(\frac { 2 }{ x^{ 2 } } \) – \(\frac { 2 }{ x^{ 3 } } \)
(d) –\(\frac { 2 }{ x^{ 3 } } \) + \(\frac { 2 }{ x^{ 2 } } \)
Answer:
(d) –\(\frac { 2 }{ x^{ 3 } } \) + \(\frac { 2 }{ x^{ 2 } } \)

Question 17.
If y = \(\frac{sinx+cosx}{sinx-cosx}\) then \(\frac{dy}{dx}\) at x = \(\frac { \pi }{ 2 } \) is ………………….
(a) 1
(b) 0
(c) -2
(d) 2
Answer:
(c) -2

Question 18.
\(\int \frac{\sin ^{8} x-\cos ^{8} x}{1-2 \sin ^{2} x \cos ^{2} x}\) dx is ……………………
(a) \(\frac{1}{2}\) sin2x + c
(b) –\(\frac{1}{2}\) sin2x + c
(c) \(\frac{1}{2}\) cos 2x + c
(d) – \(\frac{1}{2}\) cos 2x + c
Answer:
(b) –\(\frac{1}{2}\) sin2x + c

Question 19.
An urn contains 5 red and 5 black balls. A balls is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be ………………
(a) \(\frac{5}{12}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{7}{12}\)
(d) \(\frac{1}{4}\)
Answer:
(b) \(\frac{1}{2}\)

Question 20.
Let A and B be two events such that P(\(\bar { AUB } \)) = \(\frac{1}{6}\) , Then the events A and B are P(A∩B) = 1/4 and P(\(\bar { A } \)) = 1/4 is ………………
(a) Equally likely but not independent
(b) Independent but not equally likely
(c) Independent and equally likely
(d) Mutually inclusive and dependent
Answer:
(b) Independent but not equally likely

PART – II

II. Answer any seven questions. Question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
Let A and B are two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2) and (z, 1) are in A × B, find A and B where x, y, z are distinct elements?
Answer:
n(A) = 3 ⇒ set A contains 3 elements
n(B) = 2 ⇒ set B contains 2 elements
we are given (x, 1), (y, 2), (z, 1) are elements in A × B
⇒ A = {x, y, z} and B = {1, 2}

Question 22.
Solve |5x — 12| ← 2
Answer:
5x – 12 > -2 (or) 5x – 12 < 2 ⇒ 5x > -2 + 12 (= 10)
⇒ x > \(\frac{10}{5}\) = 2
x > 2
(or)
5x < 2 + 12 (= 14)
⇒ x < \(\frac{14}{5}\)
so 2 < x < \(\frac{14}{5}\)

Question 23.
If ¹⁰P_r-1 = 2 × 6 P_r, find r?
Answer:
¹⁰P_r-1 = 2 × 6P_r

⇒ (11 – r) (10 – r) (9 – r) (8 – r) (7 – r) = 10 × 9 × 4 × 7
= 5 × 2 × 3 × 3 × 2 × 2 × 7
= 7 × 6 × 5 × 4 × 3
⇒ 11 – r = 7
11 – 7 = r
r = 4

Question 24.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^nd hour, 4^th hour and n^th hour?
Answer:
No. of bacteria at the beginning = 30
No. of bacteria after 1 hour = 30 × 2 = 60
No. of bacteria after 2 hours = 30 × 2² = 30 × 4 = 120
No. of bacteria after 4 hours = 30 × 2⁴ = 30 × 16 = 480
No. of bacteria after n^th hour = 30 × 2ⁿ

Question 25.
Find |A| if A = \(\left[\begin{array}{ccc}
0 & \sin \alpha & \cos \alpha \\
\sin \alpha & 0 & \sin \beta \\
\cos \alpha & -\sin \beta & 0
\end{array}\right]\)
Answer:
\(\left[\begin{array}{ccc}
0 & \sin \alpha & \cos \alpha \\
\sin \alpha & 0 & \sin \beta \\
\cos \alpha & -\sin \beta & 0
\end{array}\right]\)
= 0M₁₁ – sin αM₁₂ + cos αM₁₃
= 0 – sin α(0 – cos α sin β) + cos α(- sin α sin β – 0) = 0

Question 26.
Find the value of λ for which the vectors \(\vec { a } \) = 3\(\hat { i } \) + 2\(\hat { j } \) + 9\(\hat { k } \) and \(\vec { a } \) = \(\hat { i } \) + λ\(\hat { j } \) +3\(\hat { k } \) are parallel?
Answer:
Given \(\vec { a } \) and \(\vec { b } \) are parallel ⇒\(\vec { a } \) = t\(\vec { b } \) (where t is a scalar)
(i.e.,) 3\(\hat { i } \) + 2\(\hat { j } \) + 9\(\hat { k } \) = t\(\hat { i } \) + λ\(\hat { j } \) + 3\(\hat { k } \))
equating \(\hat { i } \) components we get 3 = t
equating \(\hat { j } \) components
(i.e); 2 = tλ
2 = 3λ ⇒λ = 2/3

Question 27.
Evaluate \(\underset { x\rightarrow \pi }{ lim } \) \(\frac{sin 3x}{sin 2x}\)
Answer:

Question 28.
Find the derivative of sinx² with respect to x²?
Answer:

Question 29.
Let the matrix M = \(\begin{bmatrix} x & y \\ z & 1 \end{bmatrix}\) if x, y and z are chosen at random from the set {1, 2, 3}, and repetition is allowed (i.e., x = y = z), what is the probability that the given matrix M is a singular matrix?
Answer:
If the given matnx M is singular, then = \(\begin{vmatrix} x & y \\ z & 1 \end{vmatrix}\) = 0
That is, x – yz = 0
Hence the possible ways of selecting (x, y, z) are
{(1, 1, 1), (2, 1, 2), (2, 2, 1), (3, 1, 3), (3, 3, 1)} = A (say)
The number of favourable cases n(A) = 5
The total number of cases are n(S) = 3³ = 27
The probability of the given matrix is a singular matrix is
P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{5}{27}\)

Question 30.
Evaluate \(\frac { x^{ 2 } }{ 1+x^{ 6 } } \)
Answer:

PART – III

III. Answer any seven questions. Question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
If f, g, h are real valued functions defined on R, then prove that (f + g) o h = f o h + g o h. What can you say about fo(g + h)? Justify your answer?

Question 32.
Solve \(\frac{4}{x+1}\) ≤ 3 ≤ \(\frac{6}{x+1}\), x > 0?

Question 33.
Prove that cos^-1 \(\frac{4}{5}\) + tan^-1 \(\frac{3}{5}\) = tan^-1 \(\frac{27}{11}\)?

Question 34.
There are 15 candidates for an examination. 7 candidates are appearing for mathematics examination while the remaining 8 are appearing for different subjects. In how many ways
can they be seated in a row so that no two mathematics candidates are together?

Question 35.
Prove that if a, b, c are in H.P. if and only if \(\frac{a}{c}\) = \(\frac{a-b}{b-c}\)?

Question 36.
If (-4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x – y + 7 = 0, then find the equation of another diagonal?

Question 37.
Verify the existence of \(\underset { x\rightarrow 1 }{ lim } \) f(x), where f(x) = \(\left\{\begin{aligned}
\frac{|x-1|}{x-1}, & \text { for } x \neq 1 \\
0, & \text { for } x=1
\end{aligned}\right.\)

Question 38.
If y = sin^-1 x then find y?

Question 39.
Evaluate cot² x + tan² x?

Question 40.
Show that
\(\left|\begin{array}{ccc}
2 b c-a^{2} & c^{2} & b^{2} \\
c^{2} & 2 c a-b^{2} & a^{2} \\
b^{2} & a^{2} & 2 a b-c^{2}
\end{array}\right|=\left|\begin{array}{ccc}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right|^{2}\)

PART – IV

IV. Answer all the questions. [7 × 5 = 35]

Question 41 (a).
The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S are functions of the mileage m; C(m) = 0.4m + 50 and S(m) = 0.03m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying ¡600 miles?

[OR]

(b) Evaluate \(\sqrt { x^{ 2 }+x+1 } \)?

Question 42 (a).
Determine the region in the plane determined by the inequalities y ≥ 2x and -2x + 3y ≤ 6?

[OR]

(b) If y(cos^-1 x)², prove that (1-x²) \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) – x \(\frac{dy}{dx}\) – 2 = 0. Hence find y₂ when x = 0?

Question 43(a).
Prove that ⁿC_r + ⁿC_r-1 = ⁿ⁺¹C_r

[OR]

(b) If the binomial coefficients of three consecutive terms in the expansion of (a + x)ⁿ are in the ratio 1 : 7 : 42, then find n?

Question 44 (a).
(a) Prove that

1. sin A + sin( 120° + A) + sin (240° + A) = O
2. cos A+ cos (120° + A) + cos (120° – A) = O

[OR]

(b) A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

Question 45 (a).
Show that \(\left|\begin{array}{ccc}
a^{2}+x^{2} & a b & a c \\
a b & b^{2}+x^{2} & b c \\
a c & b c & c^{2}+x^{2}
\end{array}\right|\) is divisible by x⁴?

[OR]

(b) \(\left[\begin{array}{ccc}
0 & p & 3 \\
2 & q^{2} & -1 \\
r & 1 & 0
\end{array}\right]\) is skew-symmetric, find the values of p, q and r?

Question 46 (a).
In a shopping mall there is a hail of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find

1. The minimum total length of the escalator
2. The heights at which the escalator changes its direction
3. The slopes of the escalator at the turning points.

[OR]

(b) Evaluate \(\lim _{x \rightarrow a} \frac{\sqrt{x-b}-\sqrt{a-b}}{x^{2}-a^{2}}(a>b)\)

Question 47 (a).
Evaluate ∫\(\frac { 3x+5 }{ x^{ 2 }+4x+7 } \) dx

[OR]

(b) A factory has two Machines – I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an itci is drawn at random what is the probability that it is defective?