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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?

Students can download 6th Social Science Term 2 Economics Chapter 1 Economics-An Introduction 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 Economics Solutions Term 2 Chapter 1 Economics-An Introduction

Samacheer Kalvi 6th Social Science Economics-An Introduction Text Book Back Questions and Answers

I. Fill in the blanks

1. The producers of food grains are ……………..
2. Collection of honey is a …………….. occupation.
3. The conversion of raw materials into finished goods is called ……………..
4. According to Gandhiji the villages are …………….. of the nation.
5. The percentage of population in the cities of Tamil Nadu is ……………..

Answer:

1. Farmers
2. Primary
3. Secondary activities
4. backbone
5. 47%

II. Match the following

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

III. Match and find the odd pair

Answer:
1. – d
2. – c
3. – b
4. – a

IV. Choose the correct answer

1. Agriculture is a (primary / Secondary) occupation.
2. Economic activities are divided on the basis of (ownership / use)
3. Sugar Industries are (Primary / Secondary) activity.
4. Agro based industry (Cotton / Furniture)
5. Dairy farming is a (Public sector/Co-operative sector)

Answer:

1. Primary
2. use
3. Secondary
4. Cotton
5. Co-operative sector

V. Answer the following questions

Question 1.
Sandhai – Define
Answer:
In villages once in a week or month, all things are sold in a particular place at a specific time to meet the needs of the people. That is called Sandai.

Question 2.
What is called the barter system?
Answer:
A system of exchanging goods for other goods is called a barter system. Example: Exchange a bag or rice for enough clothes.

Question 3.
What is trade?
Answer:
Trade involves the transfer of goods or services from one person to another often in exchange of money.

Question 4.
What is Savings?
Answer:
The amount from the income which is left for future needs after consumption is called sayings.

Question 5.
What was the necessity for the invention of money?
Answer:

1. When traders exchange commodities there arises a difference in the value of the commodity.
2. To solve this problem people invented money.

Question 6.
What was the reason for the development of settlements near water bodies?
Answer:

1. Rivers act as the main source for the cultivation of crops.
2. So early man settled permanently near the rivers.

Question 7.
What are called secondary occupation?
Answer:
The raw materials obtained from the primary activities are converted into finished products is called a secondary occupation.

Question 8.
Name the city-centered industries.
Answer:
Cement, iron, and Aluminium industries, seafood processing are some of the city centered industries.

VI. Answer the following in detail

Question 1.
List out the important primary occupations of your district.
Answer:

1. Agriculture
2. Cattle rearing
3. Collection of fruits, nuts, honey, and medicinal herbs.

Question 2.
Mention the manufacturing industries found in your district.
Answer:

1. Cotton textiles
2. Spinning and weaving
3. Food processing industries
4. Beedi production
5. Wind power generations

Question 3.
How are the industries classified on the basis of raw materials?
Answer:
On the basis of raw materials industries are classified as

1. Agro-Based Industries – Cotton textiles, Sugar mills, and Food processing.
2. Forest-Based Industries – Paper mills, Furniture making, Building materials.
3. Mineral Based Industries – Cement, Iron, Aluminium Industries.
4. Marine Based Industries – Seafood processing.

Question 4.
Write down the occupations in the service sector.
Answer:
The service sector serves the people to fulfill their daily needs like:

1. Transport – Roadways, Railways, Waterways, Airways.
2. Communication – Post, Telephone, Information Technology.
3. Trade – Procurement of goods, selling.
4. Banking – Money Transaction, Banking Services.

Question 5.
What do you know about the features of cities?
Answer:

1. A city is a large human settlement.
2. The high density of population.
3. Four-way roads, flyovers, skyscrapers, parks.
4. Educational institution, hospital, Government offices.
5. Private and public industries and technological institutions.
6. Employment opportunities permanent monthly income, basic requirements are

VII. Fill in the tabular column given below

Activity:
Write the lyrics of Bharathiyar’s Analyze the lyrics and write down the commodities which were exchanged in yesteryears with the help of the teacher.

(1) Wheat
(2) Betel
(3) Tusk

VIII. Stick picture

Samacheer Kalvi 6th Social Science Economics-An Introduction Additional Important Questions and Answers

I. Fill in the blanks Answer

1. The permanent settlements near the rivers were called ……………
2. More than …………… percentage of the world’s population live in cities.
3. The …………… sector serves the people to fulfill their daily needs.
4. One who uses the products is called ……………
5. …………… are the real shadow of cities.

Answer:

1. Villages
2. 50
3. Service
4. Consumer
5. Villages

II. Choose the correct answer

Question 1.
Tertiary activities are also called as sector ……………
(a) Private
(b) Service
(c) Public
Answer:
(b) Service

Question 2.
Secondary and tertiary activities are …………… centred activities.
(a) City
(b) Town
(c) Village
Answer:
(a) City

Question 3.
…………… is the main occupation in villages.
(a) Mining
(b) Fishing
(c) Farming
Answer:
(c) Farming

III. Answer the following questions

Question 1.
Sandhai – Define
Answer:
In villages, once in a week or month, things are sold in a particular place at a specific time to meet the needs of the people. That is called Sandhai.

Question 2.
What is called the barter system?
Answer:

1. A system of exchanging goods for other goods is called a barter system.
2. Example: Exchange a bag or rice for enough clothes.

Question 3.
What are consumer goods?
Answer:
The finished goods which are brought from the market to fulfill the daily needs of the consumers are called consumer goods.

Question 4.
Who are cultivators?
Answer:
Persons who are involved in farming and grazing are called cultivators or farmers.

Question 5.
How are industries classified?
Answer:
Industries are classified on the basis of the:

1. Availability of raw materials
2. Capital
3. Ownership

Question 6.
Name the sectors that are helpful in the economic development of our country.
Answer:
Agriculture and Industries are helpful in the economic development of our country.

IV. Mind map

Students can Download Tamil Nadu 11th Maths Model Question Paper 2 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 2 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 set of all real numbers. Consider the following subsets of the plane R × R:
S= {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y): x – y is an integer}
Then which of the following is true?
(a) T is an equivalence relation but S is not an equivalence relation.
(b) Neither S nor T is an equivalence relation
(c) Both S and T are equivalence relation
(d) S is an equivalence relation but T is not an equivalence relation.
Answer:
(a) T is an equivalence relation but S is not an equivalence relation.

Question 2.
If the set A has m elements the set B has n elements and the number of elements in A × B is …………………
(a) m + n
(b) mn
(c) \(\frac{m}{n}\)
(d) m²
Answer:
(b) mn

Question 3.
If \(\frac{ax}{(x+2)(2x-3)}\) = \(\frac{2}{x+2}\) + \(\frac{3}{2x-3}\) then a = ……………….
(a) 8
(b) 7
(c) 5
(d) 4
Answer:
(b) 7

Question 4.
The number of solutions of x² + |x – 1| = 1 is ………………….
(a) 1
(b) 0
(c) 2
(d) 3
Answer:
(c) 2

Question 5.
If a, 8, b are in A.P. a, 4, b are in G.P. and a, x, b are in H.P then x = ………………..
(a) 2
(b) 1
(c) 4
(d) 16
Answer:
(a) 2

Question 6.
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are ……………….
(a) 45
(b) 40
(c) 10!
(d) 2¹⁰
Answer:
(a) 45

Question 7.
The value of e^2logx = …………………..
(a) 2x
(b) x²
(c) \(\sqrt{x}\)
(d) \(\frac{x}{2}\)
Answer:
(b) x²

Question 8.
The n^th term of the sequence 1, 2, 4, 7, 11 …. is …………………
(a) n³ + 3n² + 2n
(b) n³ – 3n² + 3n
(c) n\(\frac{(n+1)(n+2)}{3}\)
(d) \(\frac { n^{ 2 }-n+2 }{ 2 } \)
Answer:
(d) \(\frac { n^{ 2 }-n+2 }{ 2 } \)

Question 9.
The last term in the expansion (2+\(\sqrt{3}\))⁸ is ………………
(a) 81
(b) 27
(c) 9
(d) 3
Answer:
(a) 81

Question 10.
A line perpendicular to the line 5x -y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5sq.units, then its equation is …………………..
(a) x + 5y ± 5\(\sqrt{2}\) = 0
(b) x – 5y ± 5\(\sqrt{2}\) = 0
(c) 5x + y ± 5\(\sqrt{2}\) = 0
(d) 5x – y ± 5\(\sqrt{2}\) = 0
Answer:
(a) x + 5y ± 5\(\sqrt{2}\) = 0

Question 11.
A factor of the determinant \(\left|\begin{array}{ccc}
x & -6 & -1 \\
2 & -3 x & x-3 \\
-3 & 2 x & x+2
\end{array}\right|\) is ……………….
(a) x + 3
(b) 2x – 1
(c) x – 2
(d) x – 3
Answer:
(a) x + 3

Question 12.
If λ\(\vec { a } \) + 2λ\(\vec { j } \) + 2λ\(\vec { k } \) is a unit vector then the value of λ is ………………
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{9}\)
(d) \(\frac{1}{2}\)
Answer:
(a) \(\frac{1}{3}\)

Question 13.
One of the diagonals of parallelogram ABCD with \(\vec { a } \) and \(\vec { b } \) are adjacent sides is \(\vec { a } \) + \(\vec { b } \). The other diagonal BD is ………………….
(a) \(\vec { a } \) – \(\vec { b } \)
(b) \(\vec { a } \) – \(\vec { b } \)
(c) \(\vec { a } \) + \(\vec { b } \)
(d) \(\frac{\vec{a}+\vec{b}}{2}\)
Answer:
(b) \(\vec { a } \) – \(\vec { b } \)

Question 14.
If (1, 2, 4) and (2, -3λ, -3) are the initial and terminal points of the vector \(\vec { i } \) + 5\(\vec { j } \) – 7\(\vec { k } \) then the value of λ …………………..
(a) \(\frac{7}{3}\)
(b) –\(\frac{7}{3}\)
(c) \(\frac{5}{3}\)
(d) \(\frac{-5}{3}\)
Answer:
(b) –\(\frac{7}{3}\)

Question 15.
If y = mx + c and f(0) =f'(0) = 1 then f(2) = …………………..
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(c) 3

Question 16.
The derivative of (x + \(\frac{1}{x}\))² w.r.to. x is ………………..
(a) 2x – \(\frac { 2 }{ x^{ 3 } } \)
(b) 2x + \(\frac { 2 }{ x^{ 3 } } \)
(c) 2(x + \(\frac{1}{x}\))
(d) 0
Answer:
(a) 2x – \(\frac { 2 }{ x^{ 3 } } \)

Question 17.
If f(x) is \(\left\{\begin{array}{cc}
a x^{2}-b, & -1<x<1 \\
\frac{1}{|x|}, & \text { elsewhere }
\end{array}\right.\) is differentiable at x = 1, then …………………
(a) a = \(\frac{1}{2}\), b = \(\frac{-3}{2}\)
(b) a = \(\frac{-1}{2}\), b = \(\frac{3}{2}\)
(c) a = \(\frac{-1}{2}\), b = \(\frac{-3}{2}\)
(d) a = \(\frac{1}{2}\), b = \(\frac{3}{2}\)
Answer:
(c) a = \(\frac{-1}{2}\), b = \(\frac{-3}{2}\)

Question 18.
∫\(\frac { \sqrt { tanx } }{ sin2x } \) dx is ………………
(a) \(\sqrt{tanx}\) + c
(b) 2\(\sqrt{tanx}\) + c
(c) \(\frac{1}{2}\) \(\sqrt{tanx}\) + c
(d) \(\frac{1}{4}\) \(\sqrt{tanx}\) + c
Answer:
(a) \(\sqrt{tanx}\) + 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.
It is given that the events A and B are such that P(A) = \(\frac{1}{4}\), P(A/B) = \(\frac{1}{2}\), and 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.
If n(P(A)) = 1024, n(A∪B) = 15 and n(P(B)) = 32 then find n(A∩B)
Answer:
n(P(A)) = 1024 = 2¹⁰ ⇒ n(A) = 10
n(A∪B) = 15
n(P(B)) = 32 = 2⁵ ⇒ n(B) = 5
We know n(A∪B) = n(A) + n(B) – n(A∩B)
(i.e) 15 = 10 + 5 – n(A∩B)
⇒ n(A∩B) = 15 – 15 = 0

Question 22.
Simplify (343)^2/3
Answer:
(343)^2/3 = (7³)^2/3 = 7^3×2/3 = 7² = 49

Question 23.
Show that cos36° cos 72° cos 108° cos 144° = \(\frac{1}{16}\)
Answer:
LHS = cos36° cos(90° – 18°) cos(90° – 18°) cos(90° + 18°) cos(180° – 36°)
= sin² 18° cos² 36°
= (\(\frac { \sqrt { 5-1 } }{ 4 } \))² (\(\frac { \sqrt { 5+1 } }{ 4 } \))² = \(\frac{1}{16}\) = RHS

Question 24.
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour?
Answer:
There are 6 red balls, 5 white balls and 5 blue balls.
We have to select 3 balls of each colour.
∴Number of ways of selection = ⁶C₃ × ⁵C₃ × ⁵C₃
= \(\frac { 6! }{ 3!3! } \) × \(\frac { 5! }{ 3!2! } \) × \(\frac { 5! }{ 3!2! } \)
= 20 × 10 × 10 = 2000

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.
For any vector prove that \(\vec { r } \) = [\(\vec { r } \).\(\vec { i } \)) + (\(\vec { r } \).\(\vec { j } \))j + [\(\vec { r } \).\(\vec { k } \)}k
Answer:
Let \(\vec { r } \) = x\(\hat { i } \) + y\(\hat { j } \) + z\(\hat { k } \)

Question 27.
Calculate \(\lim _{x \rightarrow-2}\) (x³ – 3x + 6) (-x² + 15)
Answer:

Question 28.
Evaluate y = e^x sin x
Answer:

Question 29.
Integrate the following with respect to x
\(\frac{4}{3+4x}\) + (10x + 3)⁹ – 3 cosec(2x + 3) cot (2x + 3)
Answer:

Question 30.
P(A) = 0.6, P (B) = 0.5 and P(A∩B) = 0.2 find P(A/B)
Answer:
Given that P(A) = 0.6, P(B) = 0.5, and P(A∩B) = 0.2
P(A/B) = \(\frac { p(A∩B) }{ p(B) } \) = \(\frac{0.2}{0.5}\) = \(\frac{2}{5}\)

PART – III

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

Question 31.
A quadratic polynomial has one of its zeros 1 + \(\sqrt{5}\) and it satisfies p(1) = 2. Find the quadratic polynomial?

Question 32.
Prove that

1. tan^-1 (\(\frac{1}{7}\)) + tan^-1(\(\frac{1}{13}\)) = tan^-1(\(\frac{2}{9}\))
2. cos^-1\(\frac{4}{5}\) + tan^-1\(\frac{3}{5}\) = tan^-1\(\frac{27}{11}\)

Question 33.
The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP?

Question 34.
Find the equation of the line passing through the point (5, 2) and perpendiular to the line joining the points (2, 3) and (3, -1)?

Question 35.
Find the area of the triangle whose vertices are (0,0), (1,2) and (4,3)?

Question 36.
If \(\vec { a } \), \(\vec { b } \), \(\vec { c } \) are three vectors such that \(\vec { a } \) + 2\(\vec { b } \) + \(\vec { c } \) = 0 and |\(\vec { a } \)| = 3, |\(\vec { b } \)| = 4, |\(\vec { c } \)| = 7 fimd the angle between \(\vec { a } \) and \(\vec { b } \)

Question 37.
Evaluate: \({ \underset { x\rightarrow 0 }{ lim } }\) \(\frac { 3^{ x }-1 }{ \sqrt { 1+x-1 } } \)

Question 38.
Find \(\frac{dy}{dx}\) for y = tan^-1 \((\frac { cosx+sinx }{ cosx-sinx } )\)

Question 39.
Evaluate: ∫x⁵ e^x2

Question 40.
How many automobile license plates can be made, if each plate contains two different letters followed by three different digits?

PART – IV

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

Question 41.
(a) If f : R – {-1, 1} → R is defined by f(x) = \(\frac { x }{ x^{ 2 }-1 } \), verify whether f is one-to-one or not?

[OR]

(b) Solve: log₂ x + log₄ x + log₈ x = 11

Question 42.
(a) Prove that \(\frac{\sin x+\sin 3 x+\sin 5 x+\sin 7 x}{\cos x+\cos 3 x+\cos 5 x+\cos 7 x}\) = tan 4x

[OR]

(b) If x + y + z = xyz, then prove that \(\frac { 2x }{ 1-x^{ 2 } } \) + \(\frac { 2y }{ 1-y^{ 2 } } \) + \(\frac { 2z }{ 1-z^{ 2 } } \) = \(\frac { 2x }{ 1-x^{ 2 } } \) \(\frac { 2y }{ 1-y^{ 2 } } \) \(\frac { 2z }{ 1-z^{ 2 } } \)

Question 43.
(a) If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then and the ranks of the words

1. GARDEN
2. DANGER

[OR]

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

Question 44.
(a) 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?

[OR]

(b) Evalute \(\sqrt { x^{ 2 }+y^{ 2 } } \) = tan^-1(\(\frac{y}{x}\))

Question 45.
Let \(\vec { a } \), \(\vec { b } \), \(\vec { c } \) be three vectors such that |\(\vec { a } \)| = 3, |\(\vec { b } \)| = 4, |\(\vec { c } \)| = 5 and each one of them being perpendicular to the sum of the other two, find |\(\vec { a } \) + \(\vec { b } \) + \(\vec { c } \)|.

[OR]

(b) Evaluate ∫sec³ 2xdx

Question 46.
(a) Find all the equations of the straight lines in the family of the lines y = mx – 3, for which m and the x-coordinate of the point of intersection of the lines with x – y = 6 are integers?

[OR]

(b) There are two identical boxes containing respectively 5 white and 3 red balls, 4 white and 6 red balls. A box is chosen at random and a ball is drawn from it

1. Find the probability that the ball is white
2. If the ball is white, what is the probability that it from the first box?

Question 47 (a).
If A_i B_i, C_i are the cofactors of a_i, b_i, c_i, respectively, i = 1 to 3 in

[OR]

(b) Express the matrix \(\left(\begin{array}{ccc}
3 & 3 & -1 \\
-2 & -2 & 1 \\
-4 & -5 & 2
\end{array}\right)\) as the sum of symmetric martix and a skew-symmetric martix?

Students can Download Tamil Nadu 11th Maths Model Question Paper 1 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 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 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.
For non empty sets A and B if A ⊂ B then (A × B) n (B × A) is equal to ………………….
(a) A ∩ B
(b) A × A
(c) B × B
(d) none of these
Answer:
(b) A × A

Question 2.
The solution set of the inequality |x – 1| ≥ |x – 3| is ………………..
(a) [0, 2]
(b) [2, ∞)
(c) (0, 2)
(d) (-∞, 2)
Answer:
(b) [2, ∞)

Question 3.
The numer of solutions of x² + |x – 1| = 1 is …………………
(a) 1
(b) 0
(c) 2
(d) 3
Answer:
(c) 2

Question 4.
Which of the following is not true?
(a) sin θ = – \(\frac{3}{4}\)
(b) cos θ = -1
(c) tan θ = 25
(d) sec θ = \(\frac{1}{4}\)
Answer:
(d) sec θ = \(\frac{1}{4}\)

Question 5.
Let f_k(x) = \(\frac{1}{k}\) [sin^k x + cos² x] where x ∈ R and k ≥ 1. Then f₄(x) – f₆(x) = …………………
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{12}\)
(c) \(\frac{1}{6}\)
(d) \(\frac{1}{3}\)
Answer:
(b) \(\frac{1}{12}\)

Question 6.
If A and B are coefficients of xⁿ in the expansion of (1 + x)²ⁿ and (1 + x)^2n-1 respectively then \(\frac{A}{B}\) =
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{n}\)
(c) 1
(d) 2
Answer:
(d) 2

Question 7.
The value of 15C₈ + 15C₉ – 15C₆ – 15C₇ is …………………
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Question 8.
The slope of the line which makes an angle 45° with the line 3x -y = – 5 are …………………
(a) 1, -1
(b) \(\frac{1}{2}\), -2
(c) 1, \(\frac{1}{2}\)
(d) 2, \(\frac{-1}{2}\)
Answer:
(b) \(\frac{1}{2}\), -2

Question 9.
The sum of the binomial co-efficients is ………………….
(a) 2n
(b) 2ⁿ
(c) n²
(d) 1
Answer:
(b) 2ⁿ

Question 10.
If the square of the matrix \(\begin{pmatrix} \alpha & \beta \\ \gamma & -\alpha \end{pmatrix}\) satisfy the relation
(a) 1 + α² + βγ = 0
(b) 1 – α² – βγ = 0
(c) 1 – α² + βγ = 0
(d) 1 + α² – βγ = 0
Answer:
(b) 1 – α² – βγ = 0

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

Question 12.
If A = \(\begin{pmatrix} \lambda & 1 \\ -1 & -\lambda \end{pmatrix}\) then for what value of λ, A² = 0?
(a) 0
(b) ±1
(c) -1
(d) 1
Answer:
(b) ±1

Question 13.
lim_x→1 \(\frac { xe^{ x }-sinx }{ x } \) is ……………….
(a) 1
(b) 2
(c) 3
(d) 0
Answer:
(d) 0

Question 14.
If the points whose position vectors 10\({ \vec { i } }\) + 3\({ \vec { j } }\) + 12\({ \vec { i } }\) – 5\({ \vec { j } }\) and a\({ \vec { i } }\) + 11\({ \vec { j } }\) are collinear then the value of a is ……………….
(a) 3
(b) 5
(c) 6
(d) 8
Answer:
(d) 8

Question 15.
If y = mx + c and f(0) = f'(0) = 1 then f(2) = ………………..
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(c) 3

Question 16.
lim_x→1 \(\frac { e^{ x }-e }{ x-1 } \) = ……………….
(a) 1
(b) e
(c) ∞
(d) 0
Answer:
(b) e

Question 17.
∫2^3x+5 dx is ………………..
(a) \(\frac { 3(2^{ 3x+5 }) }{ log2 } \) + c
(b) \(\frac { 2^{ 3x+5 } }{ 2log(3x+5) } \) + c
(c) \(\frac { 2^{ 3x+5 } }{ 2log3 } \) + c
(d) \(\frac { 2^{ 3x+5 } }{ 3log2 } \) + c
Answer:
(d) \(\frac { 2^{ 3x+5 } }{ 3log2 } \) + c

Question 18.
∫x² cos xdx is ………………..
(a) x²sinx + 2xcosx – 2 sinx + c
(b) x² – 2xcosx – 2sinx + c
(c) -x² + 2xcosx + 2sinx + c
(d) -x² – 2xcosx + 2 sinx + c
Answer:
(a) x²sinx + 2xcosx – 2 sinx + c

Question 19.
∫\(\frac { x }{ 1+x^{ 2 } } \) dx = ………………
(a) tan^-1 x + c
(b) log (1 + x²) + c
(c) log x + c
(d) \(\frac{1}{2}\) log (1 + x²) + c
Answer:
(d) \(\frac{1}{2}\) log (1 + x²) + c

Question 20.
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) \(\frac{7}{128}\)

PART – II

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

Question 21.
To secure an A grade one must obtain an average of 90 marks or more in 5 subjects each of maximum 100 marks. If A scored 84, 87, 95, 91 in first four subjects, what is the minimum mark be scored in the fifth subject to get an A grade in the course?
Answer:
Required marks = 5 × 90 = 450
Total marks obtained in 4 subjects = 84 + 87 + 95 + 91 = 357
So required marks in the fifth subject = 450 – 357 = 93.

Question 22.
Prove that (1 + tan1°) (1 + tan2°) (1 + tan 3°) …. (1 + tan 44°) is a multiple of 4?
Answer:
45°= 1 + 44 (or) 2 + 43 (or) 3 + 42 (or) 22 + 23
So we have 22 possible pairs
sa the product is (2) (22) = 44
which is ÷ by 4

Question 23.
Find the distinct permutations of the letters of the word MISSISSIPPI?
Answer:
MISSISSIPPI
Number of letters = 11
Here M-1 time, I-4timcs, S-4times, P-2timcs
So total number of arrangement is of this word = \(\frac { 11! }{ 4!4!2! } \)
\(\frac { 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4! }{ 4\times 3\times 2\times 1\times 2\times 1\times 4! } \) = 34650

Question 24.
Compare |A| using Sarrus rule if A = \(\left[\begin{array}{ccc}
3 & 4 & 1 \\
0 & -1 & 2 \\
5 & -2 & 6
\end{array}\right]\)
Answer:

|A| = [3(-1) (6) + 4(2)(5) + 1(0)(-2)] -[5(-1)(1) + (-2)(2)3 + 6(0)(4)] = [-18 + 40 + 0] – [-5 – 12 + 0] = 22 + 17 = 39.

Question 25.
If |\({ \vec { a } }\)|, |\({ \vec { b } }\)| = 6, |\({ \vec { c } }\)| =7 and \({ \vec { a } }\) + \({ \vec { b } }\) + \({ \vec { c } }\) = 0 find \({ \vec { a } }\).\({ \vec { b } }\) + \({ \vec { b } }.\) \({ \vec { c } }\) + \({ \vec { c } }\).\({ \vec { a } }\)
Answer:
Given \(\bar { a } \)+\(\bar { b } \)+\(\bar { c } \) = 0
⇒ (\(\bar { a } \)+\(\bar { b } \)+\(\bar { c } \))² = 0
(i.e;) |\(\bar { a } \)|² + |\(\bar { b } \)|² + |\(\bar { c } \)|² + 2 [\(\bar { a } \).\(\bar { b } \)+\(\bar { b } \).\(\bar { c } \)+\(\bar { c } \).\(\bar { a } \)) = 0
⇒ 5²+6²+7²+2(\(\bar { a } \).\(\bar { b } \)+\(\bar { b } \).\(\bar { c } \)+\(\bar { c } \).\(\bar { a } \)) = 0
⇒2(\(\bar { a } \).\(\bar { b } \)+\(\bar { b } \).\(\bar { c } \)+\(\bar { c } \).\(\bar { a } \)) = – 25 – 36 – 49 = -110
⇒\(\bar { a } \).\(\bar { b } \)+\(\bar { b } \).\(\bar { c } \)+\(\bar { c } \).\(\bar { a } \) = \(\frac{-110}{2}\) = -55

Question 26.
Find \(\lim _{ t\rightarrow 0 }{ \frac { \sqrt { t^{ 2 }+9-3 } }{ t^{ 2 } } } \)
Answer:
We can’t apply the quotient Iieorem it.:iiediatcly. Use the algebra technique of rationalising the numerator.

Question 27.
Evaluate y = e^-x.log x?
Answer:
y = e^-x log x = uv(say)
Here u = e^-x and v = log x
⇒ u’ = -e^-x and v’ = uv’ + vu’
Now y = uv ⇒y’ = uv’ + vu’
(i.e). \(\frac{dy}{dx}\) = e^-x(\(\frac{1}{x}\)) + log x(- e^-x)
= e^-x(\(\frac{1}{x}\) – log x)

Question 28.
Evaluate ∫\(\frac { 1 }{ \sqrt { 1+(4x)^{ 2 } } } \) dx
Answer:
Let I = ∫\(\frac { 1 }{ \sqrt { 1+4x^{ 2 } } } \)dx = ∫\(\frac { 1 }{ \sqrt { 1+(2x^{ 2 }) } } \) dx
Putting 2x = t ⇒ 2 dx = dt ⇒ dx = \(\frac{1}{2}\) dt
Thus, I = \(\frac{1}{2}\)∫\({ \frac { 1 }{ \sqrt { 1^{ 2 }+t^{ 2 } } } }\) dt
I = \(\frac{1}{2}\) log |t+\(\sqrt { t^{ 2 }+1 } \) + c = \(\frac{1}{2}\) log |2x + \(\sqrt { (2x)^{ 2 }+1 } \)| + c
I = \(\frac{1}{2}\) log |2x+\(\sqrt { 4^{ 2 }+1 } \)| + c.

Question 29.
Nine coins are tossed once. Find the probablity to get atleast 2 heads?
Answer:
Let S be the sample and A be the event of getting at least two heads.
Therefore, the event \(\bar { A } \) denotes, getting at most one head.
n(S) = 2⁹ = 521, n(\(\bar { A } \)) = 9C₀ + 9C₁ = 1 + 9 = 10
P(\(\bar { A } \)) = \(\frac{10}{512}\) = \(\frac{5}{256}\)
P(A) = 1- P(\(\bar { A } \)) = 1 – \(\frac{5}{256}\) = \(\frac{251}{256}\)

Question 30.
If P(A) denotes the power set of A, then find n(P(P(ϕ))))?
Answer:
Since P(∅) contains 1 element, P(P(∅)) contains 2¹ elements and hence P(P(P(∅))) contains 2² elements. That is, 4 elements.

PART – III

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

Question 31.
A simple cipher takes a number and codes it, using the function f(x) = 3x – 4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x (by drawing the lines)?

Question 32.
Show that 4 sin A sin (60° + A). sin(60° – A) = sin 3A?

Question 33.
How many strings of length 6 can be formed using letters of the word FLOWER if (i) either starts with F or ends with R?

Question 34.
Find the distance of the line 4x – y = 0 from the point P(4, 1) measured along the line making an angle 135° with the positive x- axis?

Question 35.
Using factor theorem prove that \(\left|\begin{array}{lll}
x+1 & 3 & 5 \\
2 & x+2 & 5 \\
2 & 3 & x+4
\end{array}\right|\) = (x – 1)² + ( x+ 9)

Question 36.
Find the unit vectors perpendicular to each of the vectors \({ \vec { a } }\) + \({ \vec { b } }\) and \({ \vec { a } }\) – \({ \vec { b } }\). Where \({ \vec { a } }\) = \({ \vec { i } }\) + \({ \vec { j } }\) + \({ \vec { k } }\) and b = \({ \vec { i } }\) + 2\({ \vec { j } }\) + 3\({ \vec { k } }\)?

Question 37.
If y = tan^-1 \(\left(\frac{1+x}{1-x}\right)\), find y’?

Question 38.
Evaluate ∫\(\frac { x }{ \sqrt { 1+x^{ 2 } } } \) dx?

Question 39.
If A and B are two events such that P(A∪B) = 0.7, P(A∩B) = 0.2 and P(B) = 0.5 then show that A and B are independent?

Question 40.
Resolve into partial fractions \(\frac { 2x^{ 2 }+5x-11 }{ x^{ 2 }+2x-3 } \)

PART – IV

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

Question 41.
(a) A photocopy store charges Rs. 1.50 per copy for the first 10 copies and Rs. 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying.
(a) Draw graph of the cost as x goes from 0 to 50 copies?
(b) Find the cost of making 40 copies

[OR]

(b) If the difference of the roots of the equation 2x² – (a + 1)x + a – 1 = 0 is equal to their product then prove that a =2?

Question 42.
(a) Prove that tan 70° – tan 20° – 2 tan 40° = 4 tan 10°?

[OR]

(b) In a ∆ABC, if a = 2\(\sqrt{3}\), b = 2\(\sqrt{2}\) and C = 75° find the other side and the angles?

Question 43.
(a) Use induction to prove that n³ – 7n + 3, is divisible by 3, for all natural numbers n?

[OR]

(b) Evaluate y = (x² + 1) \(\sqrt [ 3 ]{ x^{ 2 }+2 } \)?

Question 44.
(a) Show that f(x) f(y) = f(x + y), where f(x) = \(\left[\begin{array}{ccc}
\cos x & -\sin x & 0 \\
\sin x & \cos x & 0 \\
0 & 0 & 1
\end{array}\right]\)

[OR]

(b) The chances of X, Y and Z becoming managers of a certain company are 4 : 2 : 3. The probabilities that bonus scheme will be introduced if X, Y and Z become managers are 0.3, 0.5 and 0.4 respectively. 1f the bonus scheme has been introduced, what is the probability that Z was appointed as the manager?

Question 45.
(a) If the equation λx² – 10xy + 12y² + 5x – 16y – 3 = O represents a pair of straight lines, find

1. The value of λ and the separate equations of the lines
2. Angle between the lines

[OR]

(b) Show that

1. \(\lim _{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{3 n^{2}+7 n+2}=\frac{1}{6}\)
2. \(\lim _{n \rightarrow \infty} \frac{1^{2}+2^{2}+\ldots+(3 n)^{2}}{(1+2+\ldots+5 n)(2 n+3)}=\frac{9}{25}\)
3. \(\lim _{n \rightarrow \infty} \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\ldots .+\frac{1}{n(n+1)}=1\)

Question 46.
(a) A man repays an amount of ₹3250 by paying ₹20 in the first month and then increases the payment by ₹15 per month. How long will it take him to clear the amount?

[OR]

(b) Find the area of the triangle whose vertices are A (3, -1, 2), B (1, -1, -3) and C (4, -3, 1)?

Question 47.
(a) Evaluate (x + 1) \(\sqrt { 2x+3 } \)?
[OR]

(b) Evaluate ∫cosec²x dx?

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Tamilnadu Samacheer Kalvi 6th Social Science Civics Solutions Term 2 Chapter 2 The Constitution of India

Samacheer Kalvi 6th Social Science The Constitution of India Text Book Back Questions and Answers

I. Choose the correct Answer

Question 1.
The Constitution Day is celebrated on ……………..
(a) January 26
(b) August 15
(c) November 26
(d) December 9
Answer:
(c) November 26

Question 2.
The Constituent Assembly accepted the Constitution of India in the year
(a) 1946
(b) 1950
(c) 1947
(d) 1949
Answer:
(d) 1950

Question 3.
There are …………….. amendments made in the Constitution of India till 2016.
(a) 101
(b) 100
(c) 78
(d) 46
Answer:
(a) 101

Question 4.
Which of the following is not a fundamental right?
(a) Right to freedom
(b) Right to equality
(c) Right to vote
(d) Right to education
Answer:
(c) Right to vote

Question 5.
An Indian citizen has the right to vote at ……………..
(a) 14 years
(b) 18 years
(c) 16 years
(d) 21 years
Answer:
(b) 18 years

II. Fill in the blanks

1. …………….. was selected as the chairman of the Constituent Assembly.
2. The farther of the Constitution of India is ……………..
3. …………….. protects our fundamental rights.
4. The Constitution of India came into existence on ……………..

Answer:

1. Mr. Rajendra Prasad
2. Dr. B. R. Ambedkar
3. Law of the country
4. 26th January 1950

III. Match the following

Answer:
b) c d a b

IV. Answer the question given under the caption (Constituent Assembly)

Question 1.
In which year was the Constituent Assembly formed?
Answer:
Constituent Assembly was formed in the year 1946.

Question 2.
How many members were in the Drafting Committee?
Answer:
There are eight members in the Drafting Committee.

Question 3.
How many women were part of the Constituent Assembly?
Answer:
There were fifteen women participants in the constituent Assembly.

Question 4.
When was the Constitution of India completed?
Answer:
The Constitution of India was completed on 26th November 1949.

V. Answer the following questions

Question 1.
Why was January 26 adopted as Republic day?
Answer:

1. When the Congress met at Lahore in 1929, the members of the Congress unofficially declared the same day as the Day of Pooma Swaraj or the Day of complete self-governance.
2. The next year, 26th January 1930 was celebrated as Independence Day. That day has been observed as our Republic Day.

Question 2.
What is the Constitution of India?
Answer:

1. The constitution of India is the ultimate law.
2. We have to abide by it.
3. It explains the fundamental concepts of structure, methods, powers, and duties of Government bodies.
4. It also lists the fundamental rights and duties of the citizens.
5. Directive Principles are also mentioned in the constitution.
6. So it is holistic in nature.

Question 3.
List out the special features of the Constitution of India.
Answer:

1. The preface of the constitution is the Preamble.
2. According to it, India is a Sovereign, Socialist, Secular democratic republic.
3. The constitution has granted people the right to rule. Sovereignty refers to the ultimate power of the country.
4. The term secular refers to the freedom of worship.
5. The Constitution provides a Parliamentary form of Government, both at the center

Question 4.
What are the fundamental rights?
Answer:
Fundamental rights are the basic human rights of all citizens. They are

• Right to Equality
• Right to Freedom
• Right against exploitation
• Right to freedom of Religion
• Cultural and Educational Rights
• Right to Constitutional Remedies.

Question 5.
List out the fundamental duties that you would like to fulfill.
Answer:

1. Respecting the National flag and National Anthem.
2. Respect and protect the Constitution.
3. Readiness to serve our country if the need arises.
4. Treating everyone as brothers and sister
5. Avoid violence.
6. Protect government property etc.

Question 6.
What is Preamble?
Answer:

1. The Preamble of our constitution stresses justice, liberty, equality, and fraternity.
2. The preface of the constitution is the preamble. According to it, India is a sovereign, socialists, secular democratic republic.

Question 7.
What do you understand by Liberty, Equality, and Fraternity?
Answer:

1. The preamble of the Indian constitution clearly says that
2. To achieve Justice-social, economic and political
3. Liberty of thought, expression, belief, faith, and worship.
4. Equality of status and opportunity.
5. Fraternity assuring the dignity of the individual and the unity and integrity of the nation.

Question 8.
Define: Sovereign
Answer:

1. The Constitution of India has granted the people the right to vote.
2. The members of the Parliament and the Legislative Assembly are elected by the people.
3. The right to decide is only in the hands of the representatives.
4. Sovereignty refers to the ultimate power of the country.
5. Sovereignty refers to India as an independent country.
6. India is not subject to any external power of influence.

VI. Projects and Activities

Question 1.
Let the students work individually or in a group to prepare rules for their class. From them discuss and form a list of rules and regulations for their class.
Answer:

1. Listen to the teacher
2. Respect each other
3. Respect other people’s property
4. Listen to others
5. Take care of our equipment

Question 2.
List your duties at
(a) School
(b) Home and
(c) Society
Answer:
(a) At School:

1. Participate in learning opportunities
2. Attend school regularly on time

(b) at Home:

1. Honour your father and mother
2. Simple hygiene – brush teeth, wash and dry hands, and brush hair.

c) At Society:

1. Teach the illiterate to read and write.
2. Take an active role in literacy campaigns

Question 3.
Discuss these topics:

1. Equality
2. Child labour
3. Right to Education

Answer:

1. Equality means equal rights for all the people and the abolition of all special rights and privileges.
2. Child labour refers to the employment of children in any work that deprives the children of their childhood.
3. The right to education is a fundamental human right. Every individual irrespective of race, gender, social origin, religion, or age are entitled to free elementary education.

Question 4.
Kailash Satyarti (India) and Malala Yusufsai (Pakistan) have been awarded the Nobel Prize for Peace (2014) Find out the reason why?
Answer:
“For their struggle against the suppression of children and young people and for the right of all children to education.

VII. Life Skill

Question 1.
Which of the fundamental rights do you like the most? Why?
Answer:
Fundamental rights and duties are guaranteed by the constitution. Look at the picture and share your opinions. Right against Exploitation. Traffic in Human beings and all forms of forced labour are prohibited.

Question 2.
Fundamental rights and duties are guaranteed by the constitution. Look at the picture and share your opinions. (For Students)
Answer:

Samacheer Kalvi 6th Social Science The Constitution of India Additional Important Questions and Answers

I. Fill in the blanks Answer

1. The Constitutions of nearly …………….. countries have been adopted by our Constitution.
2. …………….. refers to the ultimate power of the country.
3. …………….. is collectively responsible to the legislature.
4. The chief architect of the Drafting Committee was
5. The Constitution of India provides a …………….. form of government both at the centre and the state.

Answer:

1. 60
2. Sovereignty
3. Executive
4. Dr. B. R. Ambedkar
5. Parliamentary

II. Answer the following questions

Question 1.
What is the Universal Adult Franchise?
Answer:
Universal Adult Franchise is every Indian citizen’s right to vote when they attain 18 years of age.

Question 2.
What are the Directive Principles?
Answer:
Directive Principles are certain guidelines to be followed while the government frame law.

Question 3.
What is Democracy?
Answer:
Democracy is a type of government in which representatives are elected by the people of that country.

Question 4.
What is Secular?
Answer:
Secular is a state which does not discriminate against anyone on a religious ground.

III. Mind map

Students can download 6th Social Science Term 2 Civics Chapter 1 National Symbols 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 Civics Solutions Term 2 Chapter 1 National Symbols

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

I. Choose the correct Answer

Question 1.
The National Song Vande Mataram was composed by …………….
(a) Pingali Venkayya
(b) Rabindra Nath Tagore
(c) Bankim Chandra Chatterjee
(d) Gandhiji
Answer:
(c) Bankim Chandra Chatterjee

Question 2.
Which is the National Anthem of India?
(a) Jana Gana Mana
(c) Amar Sonar Bangla
(b) Vande Mataram
(d) Neerarum kaduluduththa
Answer:
(a) Jana Gana Manal

Question 3.
Who wrote the most famous novel Anand Math?
(a) Akbar
(b) Rabindra Nath Tagore
(c) Bankim Chandra Chatterjee
(d) Jawaharlal Nehru
Answer:
c) Bankim Chandra Chatterjee

Question 4.
_______ birthday is celebrated as the International Day of non violence.
(a) Mahatma Gandhi
(b) Subash Chandra Bose
(c) Sardar Vallabhai Patel
(d) Jawaharlal Nehru
Answer:
(a) Mahatma Gandhi

Question 5.
The colour of the Asoka chakra found in our National flag is ……………..
(a) sky blue
(b) navy blue
(c) blue
(d) green
Answer:
(b) navy blue

Question 6.
The first flag ever flown after the Independence is stored in _______
(a) Chennai fort Museum
(c) Saranath Museum
(b) Delhi Museum
(d) Kolkata Museum
Answer:
(a) Chennai fort Museum

Question 7.
The National Anthem was written by ……………..
(a) Devandranath Tagore
(b) Bharathiyar
(c) Rabindranath Tagore
(d) Bala Gangadhar Tilak
Answer:
(c) Rabindranath Tagore

Question 8.
The time taken to play the National Anthem is _______
(a) 50 seconds
(c) 52 seconds
(b) 52 minutes
(d) 20 seconds
Answer:
(c) 52 seconds

Question 9.
“Vande Mataram” was first sung by at the 1896 session of the National Congress.
(a) Bankim Chandra Chatterjee
(b) Rabindranath Tagore
(c) Mahatma Gandhi
(d) Sarojini Naidu
Answer:
(b) Rabindranath Tagore

Question 10.
_______ hoists the flag on Independence day in Delhi
(a) The Prime Minister
(c) Vice President
(b) The President
(d) Any Political leader
Answer:
(a) The Prime Minister

II. Fill in the blanks

1. The National emblem was adopted from the Ashoka pillar of ……………..
2. The National fruit of India is ……………..
3. The National Bird of India is ……………..
4. Our National tree is the ……………..
5. The flag which was flown in 1947 Independence day was weaved in ……………..
6. The Indian National Flag was designed by ……………..
7. …………….. Started the Saka Era.
8. The longest river in India is ……………..
9. The Indian Rupee symbol was designed by ……………..
10. The Chakra of the National Flag has …………….. spokes.

Answer:

1. Sarnath
2. Mango
3. Peacock
4. Banyan tree
5. Gudiyatham
6. Pinglivenkayya
7. Kanishka
8. The Ganges
9. D. Udhaya Kumar
10. 24

III. Choose the Correct Answer

1. The Lion Capital is now in the _______ museum (Kolkata / Sarnath)
2. The National Anthem was adopted in _______ (1950 / 1947)
3. _______ is declared as our National Microorganism (Lactobacillus / Rhizobium)

Answer:

1. Sarnath
2. 1950
3. Lactobacillus

IV. Fill in the blanks

1. Saffron – Courage; White – ……………..
2. Horse – Energy; Bull – ……………..
3. 1947 – Independence day; 1950 – ……………..

Answer:

1. Honestly
2. Hard work
3. Republic day

V. Choose the Correct Option

Answer:
c) d a b c

VI. Match and Choose the Wrong pair

Answer:
1. – c
2. – d
3. – a
4. – b

VII. Choose the wrong sentence

Question 1.
The ratio of our National Flags length and breadth is 3:2
e. The Chakra has 24 spokes
f. The Chakra is Sky Blue in colour
Answer:
f. The Chakra is Sky Blue in colour

Question 2.
The National Flag was designed by pingali Venkayya
g. The First ever flown Flag after the Independence is stored in Kolkata Museum.
h. The First National Flag was weaved in Gudiyattam.
Answer:
g. The First ever flown Flag after the Independence is stored in Kolkata Museum.

VII. Choose the Correct sentence

(a) August 15 is celebrated as the Independence day.
(b) November 26 is celebrated as the Republic day
(c) October 12 is celebrated as Gandhi Jayanti.
Answer:
(a) August 15 is celebrated as the Independence day

IX. Answer the following

Question 1.
What do the colours in our National Flag represent?
Answer:

1. The saffron at the top represents valour and sacrifice.
2. The green at the bottom represents fertility and prosperity.
3. The white band in between represents honesty, peace, and purity.
4. The Ashoka Chakra or the wheel in navy blue represents truth and peace.

Question 2.
What are the parts of our National emblem?
Answer:

1. The four lions on top of the Ashoka Pillar at Samath was chosen to be our National emblem.
2. ‘Satyameva Jayate” has been inscribed at its bottom. It means truth alone triumphs.
3. The National emblem consists of two parts the upper and lower parts.
4. The upper part has four lions facing the North, South, East and West. This is on a circular pedestal. One can see only three lions at a time.
5. The lower part has an elephant, a horse, a bull and a lion. The ‘Wheel of righteousness’ is placed between them.

Question 3.
What are the salient features of the National Anthem?
Answer:

1. ‘Jana Gana Mana’ is our National anthem.
2. It symbolizes the sovereignty and integrity of our Nation.
3. This anthem was written by Rabindranath Tagore in Bengali.

Question 4.
Draw and define the Indian Rupee symbol.
Answer:

1. The Indian currency is the Indian rupees.
2. The symbol of rupees is ?.
3. This was designed by D. Udhayakumar from Tamil Nadu in the year 2010

Question 5.
Where do we use our National emblem?
Answer:
The National emblem is found at the top of the Government Communication, Indian Currency and passport.

Question 6.
Who wrote the National pledge?
Answer:

1. “India is my country. All Indians are my brothers and sisters” is our national pledge.
2. The pledge was written by Pydimarri Venkata Subba Rao in Telugu.

Question 7.
What are the animals found at the bottom of the emblem?
Answer:
At the bottom of the emblem, we see an elephant, a horse, a bull, and a lion.

Question 8.
What are the natural national symbols?
Answer:
Tiger, Elephant, River dolphin of Ganges, Peacock, King cobra, Banyan tree, Mango, The Ganges, and Lotus are the natural national symbols.

Question 9.
Where is the peacock sanctuary located in Tamil Nadu?
Answer:
There is a peacock sanctuary at Viralimalai in the district of Pudukottai (Tamil Nadu).

X. Activities

Question 1.
Draw the natural National symbols as scenery / Frame a story. (For Students)

Question 2.
Prepare a logo for your class/school of your own. (For Students)

Question 3.
What should we do to protect endangered plants and animals? Discuss?
Answer:

1. Educate your family about endangered plants and animals in your area.
2. Recycle and buy sustainable products.
3. Reduce water consumption.
4. Do not buy plastic products.

Question 4.
Celebrate the national events in your school and prepare a news item for a local newspaper.
Answer:
A feast for the eyes:

1. Marchpastl drills and entertainment programme were part of the Independence day celebration held in
2. Angel public school R. T. Nagar.
3. Dances were choreographed to spread the message of unity in diversity and peace.

XI. Life Skill Activity

Question 1.
Why are certain organisms adopted as natural National symbols? Analyse.
Answer:

1. To cultivate a deep sense of pride in the hearts of Indian citizens.
2. To represent a quality unique to India and its citizens.

Samacheer Kalvi 6th Social Science National Symbols Additional Important Questions and Answers

I. Fill in the blanks Answer

1. Our government has released a postal stamp of Tirupur Kumaran to remember his ……………… and Sacrifice and dedication ……………… to the nation.
2. The first Indian flag was hoisted by ……………… on 15th August 1947 at Red fort (Delhi)
3. The currency released by Shershahsur in the sixteenth century was ………………
4. ……………… is known for its digestive quality and cooling capacity.
5. From August 1947 to 26th January 1950, the ……………… was the honorary head ot India.
6. ……………… a variety of mango was cultivated during the Mughal reign for the royal family.

Answer:

1. Sacrifice and dedication
2. Pandit Jawaharlal Nehru
3. Rupiya
4. Curd
5. Queen of Britain
6. Imam pasand

II. Answer the following

Question 1.
What are the rules to be observed while singing the Anthem?
Answer:

1. Everyone should stand erect while singing the national anthem.
2. One should understand the meaning while singing.

Question 2.
List out Tamil Nadu’s Natural symbols.
Answer:

1. Animal – Nilgiritahr Bird
2. Flower – Gloriosa Superba Tree

Question 3.
Who has been given the right to manufacture the National flag?
Answer:
As of 2009, the Karnataka Khadi Gramodyoga Samyukta Sangha has been the sole manufacturer of the flag.

III. Mind map

Students can Download Tamil Nadu 12th Computer Science Model Question Paper 5 English Medium Pdf, Tamil Nadu 12th Computer Science 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 12th Computer Sceince 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 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 – 1

Choose the correct answer. Answer all the questions: [15 × 1 = 15]

Question 1.
Joining of two or more strings is called ……………….
(a) Append
(b) Repeating
(c) Concatenation
(d) Strike
Answer:
(c) Concatenation

Question 2.
What is the output of the following snippet?
T=1
while T:
print(True)
break
(a) False
(b) True
(c) 0
(d) No output
Answer:
(d) No output

Question 3.
………………… is an example for dynamic programming approach.
(a) Fibonacci
(b) Prime
(c) Factorial
(d) Odd, Even
Answer:
(a) Fibonacci

Question 4.
Match the following.
1. // – (I) Modulus
2. # – (II) Floor division
3. % – (III) Strings
4. ||| ||| – (IV) Comments
(a) 1-(II), 2-(IV), 3-(I), 4-(III)
(b) 1-(I), 2-(II), 3-(III), 4-(IV)
(c) 1-(IV) 2-(II) 3-(I) 4-(III)
(d) 1-(IV), 2-(I), 3-(III), 4-(II)
Answer:
(a) 1-(II), 2-(IV), 3-(I), 4-(III)

Question 5.
Lamda functions cannot be used in combination with ……………
(a) Filter
(b) Map
(c) Print
(d) Reduce
Answer:
(c) Print

Question 6.
What is stride?
(a) Index value of slide operation
(b) First argument of slice operation
(c) Second argument of slice operation
(d) Third argument of slice operation
Answer:
(d) Third argument of slice operation

Question 7.
function returns the length of the string?
(a) Strlen ( )
(b) Len (str)
(c) Length ( )
(d) Strlength ( )
Answer:
(b) Len (str)

Question 8.
Let setA={3,6,9}, setB={l,3,9}. What will be the result of the following snippet? print(setA|setB)
(a) {3,6,9,1,3,9}
(b) {3,9}
(c) {1}
(d) {1,3,6,9}
Answer:
(d) {1,3,6,9}

Question 9.
Which function is used to delete elements of a list if its index is unknown?
(a) Del
(b) Delete
(c) Remove( )
(d) Back space
Answer:
(c) Remove( )

Question 10.
The first argument of the class method is …………………..
(a) Class
(b) Func
(c) Def
(d) Self
Answer:
(d) Self

Question 11.
The …………………… command is used to insert, delete and update rows into the table.
(a) DCL
(b) DML
(c) DTL
(d) TCL
Answer:
(b) DML

Question 12.
What will be written inside the file test.csv using the following program
import csv
D = [[‘Exam’],[‘Quarterly’],[‘Halfyearly’]]
csv.register_dialect(‘M’,lineterminator = ‘\n’)
with open(‘c:\pyprg\chl3\line2.csv’, ‘w’) as f:
wr = csv.writer(f,dialect=’M’)
wr.writerows(D) f.close( )
(a) Exam Quarterly Halfyearly
(b) Exam Quarterly Halfyearly
(c) EQH
(d) Exam,Quarterly,Halfyearly
Answer:
(d) Exam,Quarterly,Halfyearly

Question 13.
The default mode when you open a file is ……………….
(a) r
(b) w
(c) x
(d) a
Answer:
(a) r

Question 14.
Which operator is used to access the functions of a imported value?
(a) +
(b) *
(c) .
(d) /
Answer:
(c) .

Question 15.
What will be the value assigned to the empty table if it is given Integer primary key?
(a) 0
(b) 1
(c) 2
(d) -1
Answer:
(b) 1

PART – II

Answer any six questions. Question No. 21 is compulsory. [6 × 2 = 12]

Question 16.
List some aggregate functions in SQL?
Answer:

1. COUNT( )
2. SUM( )
3. MIN( )
4. AVG( )
5. MAX( )

Question 17.
How recursive function works?
Answer:

1. Recursive function is called by some external code.
2. If the base condition is met then the program gives meaningful output and exits.
3. Otherwise, function does some required processing and then calls itself to continue recursion.

Question 18.
Write a short about the followings with suitable example?

1. Capitalize( )
2. Swapcase( )

Answer:

Question 19.
What is set in Python?
Answer:
In python, a set is another type of collection data type. A Set is a mutable and an unordered collection of elements without duplicates. That means the elements within a set cannot be repeated. This feature used to include membership testing and eliminating duplicate elements.

Question 20.
Write note on self?
Answer:
The class method must have the first argument named as self. No need to pass a value for this argument when we Call the method. Python provides its value automatically.

Even if a method takes no arguments, it should be defined with the first argument called self. If a method is defined to accept only one argument it will take it as two arguments i.e. self and the defined argument.

Question 21.
Differentiate data from Information.
Answer:

Question 22.
What does data manipulation means?
Answer:
By Data Manipulation we mean:

1. Insertion of new information into the database
2. Retrieval of information stored in a database.
3. Deletion of information from the database.
4. Modification of data stored in the database.

Question 23.
How will you sort more than one column from a csv file? Give an example statement?
Answer:
To sort by more than one column you can use itemgetter with multiple indices: operator 1
itemgetter (1,2).
#using operator module for sorting multiple columns
sortedlist =sorted (data, key=operator.itemgetter(l))

Question 24.
What are the different formats to create csv files?
Answer:

1. CSV file – data with default delimiter comma (,)
2. CSV file – data with Space at the beginning
3. CSV file – data with quotes
4. CSV file – data with custom Delimiters

PART – III

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

Question 25.
Why access control is required?
Answer:

• Access control is a security technique that regulates who or what can view or use resources in a computing environment.
• It is a fundamental concept in security that minimizes risk to the object. In other words access control is a selective restriction of access to data.
• In Object oriented programming languages it is implemented through access modifies.
• Classical object-oriented languages, such as C++ and Java, control the access to class members by public, private and protected keywords.

Question 26.
How will you execute python script?
Answer:

1. If your code has any error, it will be shown in red color in the IDLE window, and Python describes the type of error occurred. To correct the errors, go back to Script editor, make corrections, save the file using Ctrl + S or File → Save and execute it again.
2. For all error free code, the output will appear in the IDLE window of Python.

Question 27.
Differentiate ceil( ) and floor( ) function?
Answer:

Question 28.
Give any 6 formatting characters with their usage?
Answer:

Question 29.
How will you access the list elements in reverse order?
Answer:

Question 30.
What are the advantages of Tuples over a list?
Answer:

1. The elements of a list are changeable (mutable) whereas the elements of a tuple are unchangeable (immutable), this is the key difference between tuples and list.
2. The elements of a list are enclosed within square brackets. But, the elements of a tuple are enclosed by paranthesis.
3. Iterating tuples is faster than list.

Question 31.
How will you create a set in python?
Answer:
A set is created by placing all the elements separated by comma within a pair of curly brackets.
The set( ) function can also used to create sets in Python.
Syntax:
Set_Variable = {E1, E2, E3 ……… En}
Example
>>> S1={ 1, 2, 3, ‘A’, 3.14}
>>>print(S1)
{1, 2, 3, 3.14, ‘A’}
>>> S2={1, 2,2, ‘A’, 3.14}
>>> print(S2)
{1, 2, ‘A’, 3.14}

Question 32.
Write a program that creates a list of numbers from 1 to 20 that are divisible by 4? Program to create a list of numbers from 1 to 20 that are divisible by 4?
Answer:
divBy4=[ ]
for i in range(21):
if (i%4= =0):
divBy4.append(i)
print(divBy4)

Output:
[0, 4, 8, 12, 16, 20]

Question 33.
Write the output for the program?
Answer:
class Sample:
def_init_(self, num):
print(“Constructor of class Sample…”)
self.num=num
print(“The value is num)
S=Sample(10)
Constructor of class sample…
The value is: 10

PART – IV

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

Question 34(a).
Explain the concept of Dynamic programming with suitable example?
Answer:
Dynamic programming:
Dynamic programming is an algorithmic design method that can be used when the solution to a problem can be viewed as the result of a sequence of decisions.

Dynamic programming approach is similar to divide and conquer. The given problem is divided into smaller and yet smaller possible sub-problems.

Dynamic programming is used whenever problems can be divided into similar sub-problems. So that their results can be re-used to complete the process.

Dynamic programming approaches are used to find the solution in optimized way. For every inner sub problem, dynamic algorithm will try to check the results of the previously solved sub-problems. The solutions of overlapped sub-problems are combined in order to get the better solution.

Steps to do Dynamic programming

• The given problem will be divided into smaller overlapping sub-problems.
• An optimum solution for the given problem can be achieved by using result of smaller sub-problem.
• Dynamic algorithms uses Memoization.

Fibonacci Series – An example:
Fibonacci series generates the subsequent number by adding two previous numbers. Fibonacci series starts from two numbers – Fib 0 & Fib 1. The initial values of fibO & fibl can be taken as 0 and 1.
Fibonacci series satisfies the following conditions:
Fibn = Fib_n-1 + Fib_n-2

Hence, a Fibonacci series for the n value 8 can look like this
Fib8 = 0 1 1 2 3 5 8 13

Fibonacci Iterative Algorithm with Dynamic programming approach

The following example shows a simple Dynamic programming approach for the generation of Fibonacci series.
Initialize f0 = 0, f1 =1

step-1: Print the initial values of Fibonacci f0 and f1
step-2: Calculate fibonacci fib ← f0 + f1
step-3: Assign f0 ← f1, f1 ← fib
step-4: Print the next consecutive value of fibanocci fib
step-5: Goto step-2 and repeat until the specified number of terms generated.

For example if we generate fibanocci series up to 10 digits, the algorithm will generate the series as shown below:
The Fibonacci series is : 0 1 1 2 3 5 8 13 21 34 55

[OR]

(b) List out the set operations supported by python?
Answer:
(I) Union:
It includes all elements from two or more sets.
In python, the operator | is used to union of two sets. The function union( ) is also used to join two sets in python.

Example: Program to Join (Union) two sets using union operator
set_A={2,4,6,8}
set_B={‘A’, ‘B’, ’C, ’D’}
U_set=set_A|set_B
print(U_set)
Output:
{2, 4, 6, 8, ‘A’, ‘D’, ‘C’, ‘B’}

(II) Intersection:
It includes the common elements in two sets
The operator & is used to intersect two sets in python. The function intersection ( ) is also used to intersect two sets in python.
Example: Program to insect two sets using intersection operator
set_A={‘A’, 2, 4, ‘D’}
set_B={‘A’, ‘B’, ‘C’, ‘D’}
print(set_A & set_B)
Output:
{A’, ‘D’}

(III) Difference:
It includes all elements that are in first set (say set A) but not in the second set (say set B)
The minus (-) operator is used to difference set operation in python.
The function difference() is also used to difference operation.
Example: Program to difference of two sets using minus operator
set_A={A’, 2, 4, ‘D’}
set_B={‘A’, ‘B’, ‘C’, ‘D’}
print(set_A – set_B)
Output:
{2,4}

(IV) Symmetric difference:
It includes all the elements that are in two sets (say sets A and B) but not the one that are common to two sets.
The caret (^) operator is used to symmetric difference set operation in python. The function symmetric_difference( ) is also used to do the same operation.
Example: Program to symmetric difference of two sets using caret operator
set_A={‘A’, 2, 4, ‘D’}
set_B={‘A’, ‘B’, ‘C’, ‘D’}
print(set_A ^ set_B)
Output:
(2, 4, ’B’, ‘C’}

Question 35(a).
Write a python program using list to read marks of six subjects and to print the marks scored in each subject and show the total marks?
Answer:
marks=[ ]
subjects=[‘Tamil’, ‘English’, ‘Physics’, ‘Chemistry’, ‘Comp. Science’, ’Maths’]
for i in range(6):
m=int(input(“Enter Mark = “))
marks.append(m)
for j in range(len(marks)):
print(“{ }. { } Mark= { } “.format(j1+,subjects[j],marks[j]))
print(“Total Marks = “, sum(marks))

Output
Enter Mark = 45
Enter Mark = 98
Enter Mark = 76
Enter Mark = 28
Enter Mark = 46
Enter Mark = 15

1. Tamil Mark = 45
2. English Mark = 98
3. Physics Mark = 76
4. Chemistry Mark = 28
5. Comp. Science Mark = 46
6. Maths Mark =15 Total Marks = 308

[OR]

(b) Write a class with two private class variables and print the sum using a method?
Answer:
class Sample:
def_init_(self, n1, n2):
self._n1=n1
self._n2=n2
def display(self):
print(“class variable 1:”, self._n1)
print(“class variable 2:”, self._n2)
print(“sum self._n1+ self._n2)
s = sample(10, 20)
s.display( )

Output:
class variable 1 : 10
class variable 2 : 20
sum : 30

Question 36 (a).
Explain the characteristics of DBMS?
Answer:
Characteristics of Database Management System?

[OR]

(b) Write any three DDL commands?
Answer:
(a) CREATE TABLE Command:
You can create a table by using the CREATE TABLE command.
CREATE TABLE Student
(Admno integer),
Name char(20), \
Gender char(1),
Age integer,
Place char(10),
);

(b) ALTER COMMAND:
The ALTER command is used to alter the table structure like adding a column, renaming the existing column, change the data type of any column or size of the column or delete the column from the table. Alter table Student add address char;

(c) DROP TABLE:
Drop table command is used to remove a table from the database.
DROP TABLE Student;

Question 37 (a).
What are the functions performed by DDL?
Answer:

1. It should identify the type of data division such as data item, segment, record and database file.
2. It gives a unique name to each data item type, record type, file type and data base.
3. It should specify the proper data type.
4. It should define the size of the data item.
5. It may define the range of values that a data item may use.
6. It may specify privacy locks for preventing unauthorized data entry.

[OR]

(b) Write the different methods to read a File in Python? Read a CSV File Using Python?
Answer:
There are two ways to read a CSV file.

1. Use the csv module’s reader function
2. Use the DictReader class.

(I) CSV Module’s Reader Function:
You can read the contents of CSV file with the help of csv.reader( ) method. The reader function is designed to take each line of the file and make a list of all columns. Then, you just choose the column you want the variable data for. Using this method one can read data from csv files of different formats like quotes (” “),pipe (|) and comma(,).

The syntax for csv.reader( ) is
csv. readert(fileobject, delimiter,fmtparams)

where:-
File object:- passes the path and the mode of the file
Delimiter:- An optional parameter containing the standard dilects like, I etc can be omitted.
Fmtparams:- Optional parameter which help to override the default values of the dialects like skipinitialspace,quoting etc can be omitted.

(II) Reading CSV File Into A Dictionary:
To read a CSV file into a dictionary can be done by using DictReader class of csv module which works similar to the reader( ) class but creates an object which maps data to a dictionary.

The keys are given by the fieldnames as parameter. DictReader works by reading the first line of the CSV and using each comma separated value in this line as a dictionary key. The columns in each subsequent row then behave like dictionary values and can be accessed with the appropriate key (i.e. fieldname).

If the first row of your CSV does not contain your column names, you can pass a fieldnames parameter into the DictReader’s constructor to assign the dictionary keys manually.

The main difference between the csv.reader( ) and DictReader( ) is in simple terms csv. reader and csv. writer work with list/tuple, while csv.DictReader and csv.DictWriter work with dictionary. csv.DictReader and csv.DictWriter take additional argument fieldnames that are used as dictionary keys.

Question 38 (a).
Write a python program to read a csv file and store it in a list? Read A CSV File And Store It In A List?
Answer:
In this topic you are going to read a CSV file and the contents of the file will be stored as a list. The syntax for storing in the List is
list = [ ]                           # Start as the empty list
list.append(element)      # Use append( ) to add elements
For example all the row values of “sample.csv” file is stored in a list using the following
program
import csv
# other way of declaring the filename
inFile= ‘c:\ \pyprg\\sample.csv’
F=open(inFile,’r’)
reader= csv.reader(F)
# declaring array array Value = [ ]
# displaying the content of the list for row in reader:
array Value.append(row)
print(row)
F.close( )

[OR]

(b) Explain OR, AND and NOT operator in SQL?
Answer:
The WHERE clause can be combined with AND, OR, and NOT operators. The AND and OR operators are used to filter records based on more than one condition. In this example you
are going to display the details of students who have scored other than ‘A’. or ‘B’ from the “student table”

Example for WHERE WITH NOT Operator
import sqlite3
connection= sqlite3 ,connect(” Academy.db”)
cursor = connection.cursor( )
cursor.execute(“SELECT *FROM student where grade< >’A’ and Grade< >’B'”)
result = cursor. fetchall( )
print(*result,sep=”\n”)

OUTPUT
(3, ’BASKAR’, ‘C, ‘M’, 75.2, ‘1998-05-17’)
(7, ‘TARUN’, ’D’, ‘M’, 62.3, ‘1999-02-01’)

Example for WHERE WITH AND Operator:-
In this example we are going to display the name, Rollno and Average of students who have scored an average between 80 to 90% (both limits are inclusive) import sqlite3
connection = sqlite3.connect(” Academy.db”)
cursor = connection.cursor( )
cursor.execute(“SELECT Rollno, Same, Average FROM student WHERE (Average>=80 AND Average<=90)”)
result = cursor. fetchall( )
print(*result,sep=”\n”)

OUTPUT
(1, ’Akshay’, 87.8)
(5, ’VARUN’, 80.6)

Example for WHERE WITH OR Operator:-
In this example we are going to display the name and Rollno of students who have not scored an average between 60 to 70% import sqlite3
connection = sqlite3.connect(” Academy.db”)
cursor = connection.cursor( )
cursor.execute(“SELECT Rollno,sname FROM student WHERE (Average<60 OR
Average> 70)”)
result = cursor. fetchall( )
print(*result,sep=”\n”)

OUTPUT
(1, ‘Akshay’)
(2, ‘Aravind’)
(3, ‘BASKAR’)
(4, ‘SAJINI’)
(5, ‘VARUN’)
(6, ‘PRIYA’)