Prasanna

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Additional Questions

Question 1.
Let A = {1, 2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3,10), (4, 9)} ⊂ A × B be a relation. Show that R is a function and find its domain, co-domain and the range of R.
Answer:
Domain of R = {1, 2, 3, 4}
Co-domain of R = B = {-1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12}
Range of R= {3, 6, 10, 9}

Question 2.
Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A → B be a function given by f(x) = 2x + 1. Represent this function as (i) a set of ordered pairs (ii) a table (iii) an arrow and (iv) a graph.
Solution:
A = {0, 1, 2, 3}, B = {1, 3, 5, 7, 9}
f(x) = 2x + 1
f(0) = 2(0) + 1 = 1
f(1) = 2(1) + 1 = 3
f(2) = 2(2) + 1 = 5
f(3) = 2(3) + 1 = 7
(i) A set of ordered pairs.
f = {(0, 1), (1, 3), (2, 5), (3, 7)}
(ii) A table

(iii) An arrow diagram

Question 3.
State whether the graph represent a function. Use vertical line test.

Solution:
It is not a function as the vertical line PQ cuts the graph at two points.

Question 4.
Let f = {(2, 7), (3, 4), (7, 9), (-1, 6), (0, 2), (5, 3)} be a function from A = {-1, 0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both one- one and onto function?
Solution:
It is both one-one and onto function.

All the elements in A have their separate images in B. All the elements in B have their preimage in A. Therefore it is one-one and onto function.

Question 5.
A function f: (-7,6) → R is defined as follows.

Find (i) 2f(-4) + 3 f(2)
(ii) f(-7) – f(-3)
Solution:

(i) 2f(-4) + 3f(2)
f(-4) = x + 5 = -4 + 5 = 1
2f(-4) = 2 × 1 = 2
f(2) = x + 5 = 2 + 5 = 7
3f(2) = 3(7) = 21
∴ 2f(-4) + 3f(2) = 2 + 21 = 23

(ii) f(-7) = x² + 2x + 1
= (-7)² + 2(-7) + 1
= 49 – 14 + 1 = 36
f(3) = x + 5 = -3 + 5 = 2
f(-7) – f(-3) = 36 – 2 = 34

Question 6.
If A = {2,3, 5} and B = {1, 4} then find
(i) A × B
(ii) B × A
Answer:
A = {2, 3, 5}
B = {1, 4}

(i) A × B = {2,3,5} × {1,4}
= {(2, 1) (2, 4) (3, 1) (3, 4) (5,1) (5, 4)}.

(ii) B × A = {1,4} × {2,3,5}
= {(1,2) (1,3) (1,5) (4, 2) (4, 3) (4, 5)}

Question 7.
Let A = {5, 6, 7, 8};
B = {- 11, 4, 7, -10, -7, – 9, -13} and
f = {(x,y): y = 3 – 2x, x ∈ A, y ∈ B}.
(i) Write down the elements of f.
(ii) What is the co-domain?
(iii) What is the range?
(iv) Identify the type of function.
Answer:
Given, A = {5, 6, 7, 8},
B = {- 11,4, 7,-10,-7,-9,-13}
y = 3 – 2x
ie; f(x) = 3 – 2x
f(5) = 3 – 2 (5) = 3 – 10 = – 7
f(6) = 3 – 2 (6) = 3 – 12 = – 9
f(7) = 3 – 2(7) = 3 – 14 = – 11
f(8) = 3 – 2 (8) = 3 – 16 = – 13
(i) f = {(5, – 7), (6, – 9), (7, – 11), (8, – 13)}
(ii) Co-domain (B)
= {-11,4, 7,-10,-7,-9,-13} i
(iii) Range = {-7, – 9, -11,-13}
(iv) It is one-one function.

Question 8.
A function f: [1, 6] → R is defined as follows:

Find the value of (i) f(5)
(ii) f(3)
(iii) f(2) – f(4).
Solution:

(i) f(5) = 3x² – 10
= 3 (5²) – 10 = 75 – 10 = 65
(ii) f(3) = 2x – 1
= 2(3) – 1 = 6 – 1 = 5
(ii) f(2) – f(4)
f(2) = 2x – 1
= 2(2) – 1 = 3
f(4) = 3x² – 10
= 3(4²) – 10 = 38
∴ f(2) – f(4) = 3 – 38 = 35

Question 9.
The following table represents a function from A = {5, 6, 8, 10} to B = {19, 15, 9, 11}, where f(x) = 2x – 1. Find the values of a and b.
Solution:

A = {5, 6, 8, 10}, B = {19, 15, 9, 11}
f(x) = 2x – 1
f(5) = 2(5) – 1 = 9
f(8) = 2(8) – 1 = 15
∴ a = 9, b = 15

Question 10.
If R = {(a, -2), (-5, 6), (8, c), (d, -1)} represents the identity function, find the values of a,b,c and d.
Solution:
R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function.
a = -2, b = -5, c = 8, d = -1.

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Ex 1.6

Question 1.
If n(A × B) = 6 and A = {1, 3} then n(B) is
(1) 1
(2) 2
(3) 3
(4) 6
Answer:
(3) 3
Hint:
If n(A × B) = 6
A = {1, 1}, n(A) = 2
n(B) = 3

Question 2.
A = {a, b,p}, B = {2, 3}, C = {p, q, r, s)
then n[(A ∪ C) × B] is ………….
(1) 8
(2) 20
(3) 12
(4) 16
Answer:
(3) 12
Hint: A ∪ C = [a, b, p] ∪ [p, q, r, s]
= [a, b, p, q, r, s]
n (A ∪ C) = 6
n(B) = 2
∴ n [(A ∪ C)] × B] = 6 × 2 = 12

Question 3.
If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true.
(1) (A × C) ⊂ (B × D)
(2) (B × D) ⊂ (A × C)
(3) (A × B) ⊂ (A × D)
(4) (D × A) ⊂ (B × A)
Answer:
(1) (A × C) ⊂ (B × D)]
Hint:
A = {1, 2}, B = {1, 2, 3, 4},
C = {5, 6}, D ={5, 6, 7, 8}
A × C ={(1,5), (1,6), (2, 5), (2, 6)}
B × D = {(1, 5),(1, 6),(1, 7),(1, 8),(2, 5),(2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8)}
∴ (A × C) ⊂ B × D it is true

Question 4.
If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is ………………….
(1) 3
(2) 2
(3) 4
(4) 8
Answer:
(2) 2
Hint: n(A) = 5
n(A × B) = 10
(consider 1024 as 10)
n(A) × n(B) = 10
5 × n(B) = 10
n(B) = \(\frac { 10 }{ 5 } \) = 2
n(B) = 2

Question 5.
The range of the relation R = {(x, x²)|x is a prime number less than 13} is
(1) {2, 3, 5, 7}
(2) {2, 3, 5, 7, 11}
(3) {4, 9, 25, 49, 121}
(4) {1, 4, 9, 25, 49, 121}
Answer:
(3) {4, 9, 25, 49, 121}]
Hint:
R = {(x, x²)/x is a prime number < 13}
The squares of 2, 3, 5, 7, 11 are
{4, 9, 25, 49, 121}

Question 6.
If the ordered pairs (a + 2,4) and (5, 2a + 6) are equal then (a, b) is ………
(1) (2, -2)
(2) (5, 1)
(3) (2, 3)
(4) (3, -2)
Answer:
(4) (3, -2)
Hint:

The value of a = 3 and b = -2

Question 7.
Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is
(1) mⁿ
(2) n^m
(3) 2^mn – 1
(4) 2^mn
Answer:
(4) 2^mn
Hint:
n(A) = m, n(B) = n
n(A × B) = 2^mn

Question 8.
If {(a, 8),(6, b)} represents an identity function, then the value of a and 6 are respectively
(1) (8,6)
(2) (8,8)
(3) (6,8)
(4) (6,6)
Answer:
(1) (8,6)
Hint: f = {{a, 8) (6, 6)}. In an identity function each one is the image of it self.
∴ a = 8, b = 6

Question 9.
Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f : A → B given by f = {(1, 4),(2, 8),(3, 9),(4, 10)} is a
(1) Many-one function
(2) Identity function
(3) One-to-one function
(4) Into function
Answer:
(3) One-to one function
Hint:
A = {1, 2, 3, 4), B = {4, 8, 9,10}

Question 10.
If f(x) = 2x² and g (x) = \(\frac{1}{3 x}\), Then fog is

Answer:
(3) \(\frac{2}{9 x^{2}}\)
Hint:
f(x) = 2x²
g(x) = \(\frac{1}{3 x}\)
fog = f(g(x)) = \(f\left(\frac{1}{3 x}\right)=2\left(\frac{1}{3 x}\right)^{2}\)
= 2 × \(\frac{1}{9 x^{2}}=\frac{2}{9 x^{2}}\)

Queston 11.
If f: A → B is a bijective function and if n(B) = 7 , then n(A) is equal to …………..
(1) 7
(2) 49
(3) 1
(4) 14
Answer:
(1) 7
Hint:
n(B) = 7
Since it is a bijective function, the function is one – one and also it is onto.
n(A) = n(B)
∴ n(A) = 7

Question 12.
Let f and g be two functions given by f = {(0, 1), (2, 0), (3, -4), (4, 2), (5, 7)} g = {(0, 2), (1, 0), (2, 4), (-4, 2), (7, 0)} then the range of fog is
(1) {0, 2, 3, 4, 5}
(2) {-4, 1, 0, 2, 7}
(3) {1, 2, 3, 4, 5}
(4) {0, 1, 2}
Answer:
(4) {0, 1, 2}
Hint:
gof = g(f(x))
fog = f(g(x))
= {(0, 2),(1, 0),(2, 4),(-4, 2),(7, 0)}
Range of fog = {0, 1, 2}

Question 13.
Let f (x) = \(\sqrt{1+x^{2}}\) then ………………..
(1) f(xy) = f(x) f(y)
(2) f(xy) > f(x).f(y)
(3) f(xy) < f(x). f(y)
(4) None of these
Answer:
(3) f(xy) < f(x) . f(y)

Question 14.
If g = {(1, 1),(2, 3),(3, 5),(4, 7)} is a function given by g(x) = αx + β then the values of α and β are
(1) (-1, 2)
(2) (2, -1)
(3) (-1, -2)
(4) (1, 2)
Answer:
(2) (2,-1)
Hint:
g(x) = αx + β
α = 2
β = -1
g(x) = 2x – 1
g(1) = 2(1) – 1 = 1
g(2) = 2(2) – 1 = 3
g(3) = 2(3) – 1 = 5
g(4) = 2(4) – 1 = 7

Question 15.
f(x) = (x + 1)³ – (x – 1)³ represents a function which is …………….
(1) linear
(2) cubic
(3) reciprocal
(4) quadratic
Answer:
(4) quadratic
Hint: f(x) = (x + 1)³ – (x – 1)³
[using a³ – b³ = (a – b)³ + 3 ab (a – b)]
= (x + 1 – x + 1)³ + 3(x + 1) (x – 1)
(x + 1 – x + 1)
= 8 + 3 (x² – 1)²
= 8 + 6 (x² – 1)
= 8 + 6x² – 6
= 6x² + 2
It is quadratic polynomial

Students can Download Tamil Nadu 11th Maths Previous Year Question Paper March 2019 English Medium Pdf, Tamil Nadu 11th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

TN State Board 11th Maths Previous Year Question Paper March 2019 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.
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) 7
(b) 6
(c) 9
(d) 8
Answer:
(d) 8

Question 2.
The nth term of the sequence 2, 7, 14, 23 …. is …………..
(a) n² + 2n + 1
(b) n² + 2n – 1
(c) n² – 2n – 1
(d) n² – 2n + 1
Answer:
(b) n² + 2n – 1

Question 3.
\(\int \frac{\sec x}{\sqrt{\cos 2 x}} d x=\)
(a) tan^-1 (tan x) + c
(b) sin^-1 (tan x) + c
(c) tan^-1 (sin x) + c
(d) 2 sin^-1 (tan x) + c
Answer:
(b) sin^-1 (tan x) + c

Question 4.
The line \(\frac{x}{a}\) – \(\frac{y}{b}\) = 0 has the slope 1, if ………..
(a) a = b
(b) only for a = 1, b = 1
(c) a > b
(d) a < b
Answer:
(a) a = b

Question 5.
The number of five digit numbers in which all digits are even, is
(a) 4 × 5⁴
(b) 4 × 5⁵
(c) 5⁵
(d) 5 × 5
Answer:
(a) 4 × 5⁴

Question 6.

(a) f (x) is continuous for all x in R
(b) f(x) is differentiable for all x > a
(c) f(x) is not differentiable at x = a
(d) f (x) is discontinuous at x = a
Answer:
(c) f(x) is not differentiable at x = a

Question 7.
A number is selected from the set {1, 2, 3, 20}. The probability that the selected number is divisible by 3 or 4 is………..
(a) \(\frac{1}{2}\)
(b) \(\frac{2}{3}\)
(c) \(\frac{2}{5}\)
(d) \(\frac{1}{8}\)
Answer:
(a) \(\frac{1}{2}\)

Question 8.
Which of the following is not a periodic function with period 2π?
(a) tan x
(b) cos x
(c) sin x
(d) cosec x
Answer:
(a) tan x

Question 9.
The straight line joining the points (2, 3) and (-1, 4) passes through (α, β) if………..
(a) α + 3β = 11
(b) 3α + β = 11
(c) α + 2β = 7
(d) 3α + β = 9
Answer:
(a) α + 3β = 11

Question 10.
The minimum and the maximum values of |cos x| -2 are respectively………..
(a) 0 and 2
(b) -2 and 0
(c) -2 and -1
(d) -1 and 1
Answer:
(c) -2 and -1

Question 11.
If A = {(x, y) / y – e^x, x ∈ [0, ∞)} and B = {(x, y) / y = sin x, x ∈ [0, ∞)} then n(A ∩ B) is………..
(a) ∞
(b) 1
(c) φ
(d) 0
Answer:
(d) 0

Question 12.

(a) \(\underset { x\rightarrow { 2 }^{ – } }{ lim } \) f(x) = -1
(b) \(\underset { x\rightarrow { 0 } }{ lim } \) f(x) does not exist
(c) \(\underset { x\rightarrow { 0 }^{ – } }{ lim } \) f(x) = -1
(d) \(\underset { x\rightarrow { 0 }^{ + } }{ lim } \) f(x) = 1
Answer:
(b) \(\underset { x\rightarrow { 0 } }{ lim } \) f(x) does not exist

Question 13.
If f(x) = x² – 3x, then the points at which f(x) =f'(x) are…………
(a) both irrational
(b) one rational and another irrational
(c) both positive integers
(d) both negative integers
Answer:
(a) both irrational

Question 14.
The unit vector parallel to the resultant of the vectors \(\hat { i }\) + \(\hat { j }\) – \(\hat { k }\) and \(\hat { i }\) – 2\(\hat { j }\) + \(\hat { k }\) is …………
(a) \(\frac{2 \hat{i}-\hat{j}+\hat{k}}{\sqrt{5}}\)
(b) \(\frac{2 \hat{i}-\hat{j}}{\sqrt{5}}\)
(c) \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{5}}\)
(d) \(\frac{2 \hat{i}+\hat{j}}{\sqrt{5}}\)
Answer:
(d) \(\frac{2 \hat{i}+\hat{j}}{\sqrt{5}}\)

Question 15.
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) = \(\frac{2}{3}\). The P(B) is………..
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{1}{6}\)
(d) \(\frac{1}{3}\)
Answer:
(d) \(\frac{1}{3}\)

Question 16.
If \(\vec { a }, \vec { b }\) are the position vectors of A and B, then which one of the following points whose position vector lies on AB?
(a) \(\frac{2 \vec{a}+\vec{b}}{2}\)
(b) \(\frac{\vec{a}-\vec{b}}{3}\)
(c) \(\vec { a } + \vec { b }\)
(d) \(\frac{2 \vec{a}-\vec{b}}{2}\)
Answer:
(a) \(\frac{2 \vec{a}+\vec{b}}{2}\)

Question 17.
If |x + 2| ≤ 8, then x belongs to…………
(a) (6, 10)
(b) (-10, 6)
(c) [6, 10]
(d) [-10, 6]
Answer:
(d) [-10, 6]

Question 18.
The expansion of (1 – x)^-2 is ………..
(a) 1 – x + x² – ……
(b) 1 + x + x² + ……
(c) 1 – 2x + 3x² – ….
(d) 1 + 2x + 3x² + ……
Answer:
(d) 1 + 2x + 3x² + ……

Question 19.
If f : R → R is defined by f(x) = |x| – 5, then the range of f is………..
(a) (-∞, -5)
(b) (-∞, 5)
(c) [-5, ∞)
(d) (-5, ∞)
Answer:
(c) [-5, ∞)

Question 20.
Which one of the following is not true about the matrix
(a) an upper triangular matrix
(b) lower triangular matrix
(c) a scalar matrix
(d) a diagonal matrix
Answer:
(c) a scalar matrix

PART-II

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

Question 21.
Write the use of horizontal line test.
Answer:
Horizontal line test is used to check whether a function is one-one, onto or not.

Question 22.
Write the relationship between Permutation and Combination.
Answer:
Permutation means selection followed by arrangement.
Combination means selection only now selcting Y from ‘n’ things can be done in ⁿC_r ways ….(1) (r ≤ n)
Selecting and arranging r from n things can be done in ⁿP_r ways ……(2)
‘r’ things can be arranged in r! ways …… (3)
Now (2) = (1) × (3)
(i.e.,) ⁿP_r = ⁿC_r × r!
⇒ ⁿC_r = \(\frac{^{n}P_r}{r!}\)

Question 23.
Count the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digits are repeated.
Answer:
The required numbers is = 1 × 8 × 7 × 2
= 112

Question 24.
Find the separate equations from a combined equation of a straight line 2x² + xy- 3y² = 0
Answer:
The combined equation is 2x² +xy – 3y² = 0

Factorizing (2) (-3) = -6
2x² + xy – 3y² = 2x² – 2xy + 3xy – 3y²
= 2x(x – y) + by (x – y) = (2x + by) (x – y)
∴ 2x² + xy – by² = 0 ⇒ (2x + 3y) (x – y) = 0
So the separate equations are 2x + 3y = 0; x – y = 0

Question 25.
Define diagonal and scalar matrices.
Answer:
A square matrix A = [a_ij]_{n × n} is called a diagonal matrix
If a_ij = 0 whenever i ≠ j
A square matrix A = [a_ij]_{n × n} is called a scalar matrix

Question 26.
Find a unit vector along the direction of the vector \(5 \hat{i}-3 \hat{j}+4 \hat{k}\)
Answer:
Let \(\hat{a}\) = \(5 \hat{i}-3 \hat{j}+4 \hat{k}\)

Question 27.
Define a continuous function on the closed interval [a, b]
Answer:
A function f : [a, b] → R is said to be continuous on the closed interval [a, b] if it continuous on the open interval (a, b) and
\(\underset { x\rightarrow { a }^{ + } }{ lim } \) f(x) = f(a) and \(\underset { x\rightarrow { b }^{ – } }{ lim } \) f(x) = 1 f(x) = f(b)

Question 28.
Consider the function f(x) = √x, x ≥ 0. Does \(\underset { x\rightarrow { 0 }}{ lim } \) f(x) exist?
Answer:
\(\underset { x\rightarrow { 0 }^{ – } }{ lim } \) √x is does not exist
\(\underset { x\rightarrow { 0 }^{ + } }{ lim } \) √x = 0
\(\underset { x\rightarrow { 0 } }{ lim } \) √x is does not exist

Question 29.
An integer is chosen at random from the first ten positive integers. Find the probability that it is multiple of three.
Answer:
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {3, 6, 9}
n(S) = 10; n(A) = 3
P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{3}{10}\)

Question 30.
Is it correct to say A × A = {(a, a): a ∈ A}? Justify your answer.
Answer:
It is not correct
Since A × A = {(a, b); a, b ∈ A} is true

PART-III

Answer any seven questions. Question no. 40 is compulsory [7 × 3]

Question 31.
A football player can kick a football from ground level with an initial velocity (u) of 80 ft/second. Find the maximum horizontal distance the football travels and at what angle
Take R = \(\frac{u² sin 2α}{g}\), and g = 32
Answer:

Maximum distance = 200ft
The required angle is \(\frac{π}{4}\)

Question 32.
Find the coefficient of x3 in the expansion of (2 – 3x)⁷.
Answer:
The general term is (2 – 3x)⁷ is t_{r + 1} = ⁷C_r (2)^{7 – r} (-3x)^r
= ⁷C_r (2)^{7 – r} (-3x)^r (x)^r
So the co-efficient of x^r is ⁷C_r (2)^{7 – r} (-3)^r
To find co-efficient of x³
equate r to 3 (i.e.,) r = 3
∴ co-efficient of x³ is ⁷C_r (2)^{7 – 3} (-3)³
= \(\frac{7×6×5}{3×2×1}\) (2)₄ (-27)
= 7 × 5 × (16) (-27)
= -15120

Question 33.
Find the nearest point on the line x – 2y – 5 from the origin.
Answer:

x = 1, y = -2
Nearest point is (x₁, y₁) = (1, -2)

Question 34.
Prove that square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.
Answer:
Let A be a square matrix. Then A = \(\frac{1}{2}\)(A + A^T) + \(\frac{1}{2}\)(A – A^T)
We know that, (A + A^T) is a symmetric, (A – A^T) is a skew-symmetric
A can be written as sum of a symmetric skew symmetric matrices.

Question 35.
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, find the angle between \(\vec { a }\) and \(\vec { b }\).
Answer:
\(\vec { a }\) + 2\(\vec { b }\) + \(\vec { c }\) = 0
∴ \(\vec { a }\) + 2\(\vec { b }\) = \(\vec { c }\)
squaring on both sides
(\(\vec { a }\) + 2\(\vec { b }\))² = c²
a² + 4b² + 4\(\vec { a }\)\(\vec { b }\) = c²
3² + 4(4²) + 4 \(\vec { a }\) \(\vec { b }\) = 7²
9 + 64 + 4\(\vec { a }\) \(\vec { b }\) = 49
4\(\vec { a }\) \(\vec { b }\) = 49 – 73 = -24
\(\vec { a }\) \(\vec { b }\) = –\(\frac {24}{4}\) = -6
|\(\vec { a }\)| |\(\vec { b }\)| cos θ = -6 ⇒ (3) (4) cos θ = -6
⇒ cos θ = –\(\frac {6}{12}\) = –\(\frac {1}{2}\) ⇒ θ = π – \(\frac {π}{3}\) = \(\frac {2π}{3}\)

Question 36.
Examine the continuity of the function cot x + tan x.
Answer:
Let f (x) = cot x + tan x
cot x is continuous in R – nπ
tan x is continuous in R – (n + 1) \(\frac {π}{2}\)
∴ f(x) is continuous in R – \(\frac {nπ}{2}\), (n∈Z)

Question 37.
Differentiate y = sin^-1 (\(\frac {1-x²}{1+x²}\))
Answer:

Question 38.
find \(\frac {dy}{dx}\) if x = a (t – sin t), y = a(1 – cos t)
Answer:
x = a (t – sin t) ⇒ \(\frac {dy}{dx}\) = a(1 – cos t)
y = a(1 – cos t) ⇒ \(\frac {dy}{dt}\) = a(sin t)

Question 39.
Evaluate \(\int { (x+3) } \sqrt { x+2 }\) dx
Answer:

Question 40.
Construct a suitable domain X such that f : X → N defined by/(n) = n + 3 to be one to one and onto.
Answer:
f : X → N is defined by f(x) = n + 3
Since f is one-one and onto function
suitable Domain is (-2, 1,0} ∪ N (or) {-2, -1, 0, 1, 2}

PART- IV

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

Question 41 (a).
For the given base curve y = sin x, draw y = \(\frac {1}{2}\) sin 2x
Answer:

[OR]

(b) Write any five different forms of an equation of a straight line.
Answer:
(i) Slope intercept form : y = mx + c, c ≠ 0
(ii) Point and slope form : y – y₁ = m (x – x₁)
(iii) Two Point form : \(\frac {y – y_1}{y_{2}-y_1}\) \(\frac {x – x_1}{x_{2}-x_1}\)
(iv) Intercept form : \(\frac {x}{a}\) + \(\frac {y}{b}\) = 1
(v) Normal form : x cos α + y sin α

Question 42 (a).
Solve the equation \(\sqrt {6-4x-x²}\) = x + 4
Answer:
Squaring both sides
6 – 4x – x² = (x + 4)²
(i.e.,) x² + 6x + 5 = 0 ⇒ (x + 1) (x + 5) = 0
⇒ x = -1, x = -5
But x ≥ – 4
⇒ x = -1

[OR]

(b) Prove that in any ΔABC, Δ = \(\sqrt{s(s-a)(s-b)(s-c)}\), where s is the semi-perimeter of ΔABC.
Answer:
Δ = \(\frac {1}{2}\) ab sin C = \(\frac {1}{2}\) ab (2sin \(\frac {C}{2}\) cos \(\frac {C}{2}\))

Question 43 (a).
State and prove any one of the Napier’s formulae.
Answer:

[OR]

(b) Do the limit of the function \(\frac {sin(x-\left\lfloor x \right\rfloor)}{x – \left\lfloor x \right\rfloor}\) exist as x → 0? State the reasons for your answer.
Answer:

So, the limit does not exist.

Question 44. (a)
Prove that for any natural number n, aⁿ – bⁿ is divisible by a – b, where a > b.
Answer:
a = a – b + b
So, aⁿ =[a- b + b]ⁿ = [(a -b) + b]ⁿ
= ⁿC₀ (a – b)ⁿ + ⁿC₁ (a – b)^n-1b¹ + ⁿC₂ (a – b)^n-2b² + ……. + ⁿC_n-1, (a – b) b^n-1+ ⁿC_n(bⁿ)
⇒ aⁿ – bⁿ = (a – b)ⁿ + ⁿC₁ (a – b)^n-1b + ⁿC₂ (a – b)^n-2b²) + …….. + ⁿC_n-1 (a – b) b^n-1
= (a – b) [(a – b)^n-1 + ⁿC₁ (a – b)^n-2b + ⁿC₂ (a – b)^n-3b² + …….. + ⁿC_n-1 b^n-1]
= (a – b) [aⁿ integer]
⇒ aⁿ – bⁿ If is divisible by(a – b).

[OR]

(b) Evaluate: \(\int \frac{2 x+4}{x^{2}+4 x+6}\)
Answer:
Let 2x + 4 = A \(\frac {d}{dx}\) (x² + 4x + 6) + B
(i.e.,) 2x + 4 = A(2x + 4) + B
Equating the coefficient of x and constant term we get
A = 1, B = 0

Question 45 (a).
Prove that \(\sqrt[3]{x^{3}+7}-\sqrt[3]{x^{3}+4}\) is approximately equal to \(\frac {1}{x²}\)when x is large.
Answer:

[OR]

(b) Find the unit vectors perpendicular to each of the vectors \(\vec { a }\) + \(\vec { b }\) and \(\vec { a }\) – \(\vec { b }\) where \(\vec { a }\) = \(\hat { i }\) + \(\hat { j }\) + \(\hat { j }\) and \(\vec { b }\) = \(\hat { i }\) + 2\(\hat { j }\) + 3\(\hat { k }\).
Answer:

Question 46 (a).
Find \(\frac {d²y}{dx}\) if x² + y² = 4
Answer:
we have x² + y² = 4

[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. If the bonus scheme has been introduced, what is the probability that Z was appointed as the manager?
Answer:
Given X : Y : Z = 4 : 2 : 3

Question 47 (a).
Prove that

Answer:

∴ (x – y) is a factor
Similarly (y – z)(z – x) are also factors.
The other factor is k(x² + y² + z²) + l(xy + yz + zx)

Putting x = 0, y = 1, z = 2 ⇒ 5k + 2l = 2 …. (1)
Putting x = 0, y = – 1, z = 1 ⇒ 2k – l = -1 …. (2)
from (1) & (2) k = 0, l = -1

[OR]

(b) Evaluate \(\int \sqrt{x^{2}+x+1}\) dx
Answer:

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 and score more marks in your examinations.

TN State Board 12th Computer Science 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 – I

All questions are compulsory. [15 × 1 = 15]

Choose the most appropriate answer from the given four ‘alternatives and write the option code with the corresponding answer.

Question 1.
Bundling two values together into one can be considered as
(a) Pair
(b) Triplet
(c) Single
(d) Quadrat
Answer:
(a) Pair

Question 2.
The kind of scope of the variable ‘a’ used in the pseudo code given below
(i) Disp():
(ii) a: = 7
(iii) print a
(iv) Disp()
(a) Local
(b) Global
(c) Enclosed
(d) Built-in
Answer:
(b) Global

Question 3.
Big Q is the reverse of…………
(a) Big O
(b) Big 0
(c) Big A
(d) Big S
Answer:
(a) Big O

Question 4.
Extension of Python files is………..
(a) .Pyt
(b) .txt
(c) .Pdm
(d) .Py
Answer:
(d) .Py

Question 5.
The output of the Segment
for i in range (10, 0, 2)
print (i)
(a) 10 8 6 420
(b) 10 8 6 4 2
(c) 0 2 4 6 8 10
(d) Error
Answer:
(d) Error

Question 6.
The bin() function returns a binary string prefixed with:
(a) 0
(b) 1
(c) 0b
(d) lb
Answer:
(c) 0b

Question 7.
The positive and negative index value of’P’ in the string Strl = ‘COMPUTER’ are
(a) 3, -4
(b) 4, -4
(c) 3, -5
(d) 4, -5
Answer:
(c) 3, -5

Question 8.
Which of the following set operation includes all the elements that are in two sets but not the one that are common to two sets?
(a) Symmetric difference
(b) Difference
(c) Intersection
(d) Union
Answer:
(a) Symmetric difference

Question 9.
A variable prefixed with double underscore is
(a) private
(b) public
(c) protected
(d) static
Answer:
(a) private

Question 10.
The data model developed by IBM is
(a) hierarchical
(b) relational
(c) network
(d) ER
Answer:
(a) hierarchical

Question 11.
The SQL command to make a database as current active database is
(a) CURRENT
(b) USE
(c) DATABASE
(d) NEW
Answer:
(b) USE

Question 12.
The expansion of CRLF is…………..
(a) Control Return and Line Feed
(b) Carriage Return and Form Feed
(c) Control Router and Line Feed
(d) Carriage Return and Line Feed
Answer:
(d) Carriage Return and Line Feed

Question 13.
The function call statement of the segment………….
if_name_ == ‘_main_’:
main(sys.argv[1:])
is
(a) main(sys.argv[l:])
(b) _name_
(c) _main_
(d) argv
Answer:
(b) _name_

Question 14.
Which is not a SQL clause?
(a) GROUP BY
(b) ORDER BY
(c) HAVING
(d) CONDITION
Answer:
(d) CONDITION

Question 15.
To make a bar chart with Matplotlib, which function should be used?
(a) plt.bar()
(b) plt.chart()
(c) pip.bar()
(d) pip.chart()
Answer:
(a) plt.bar()

PART – II

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

Question 16.
What do you mean by Namespaces?
Answer:
Namespaces are containers for mapping names of variables to objects.

Question 17.
What is searching? Write its types.
Answer:
A search algorithm is the step-by-step procedure used to locate specific data among a collection of data. Types of searching algorithms are:

1. Linear search
2. Binary search
3. Hash search
4. Binary Tree search

Question 18.
Define Operator and Operand.
Answer:
In computer programming languages operators are special symbols which represent computations, conditional matching etc. The value of an operator used is called operands. Operators are categorized as Arithmetic, Relational, Logical, Assignment etc. Value and variables when used with operator are known as operands.

Question 19.
What are the types of looping supported by Python?
Answer:
Python provides two types of looping constructs:
while loop:
In the ‘while loop’, the condition is any valid Boolean expression returning True or False. The else part of while is optional part of while.

for loop:
‘for loop’ is the most comfortable loop. It is also an entry check loop. The condition is checked in the beginning and the body of the loop(statements-block 1) is executed if it is only True otherwise the loop is not executed.

Question 20.
What is the use of the operator += in python string operation?
Answer:
Adding more strings at the end of an existing string is known as append (+=). The operator += is used to append a new string with an existing string.
Example:
>>> strl = “Welcome to”
>>> strl += “Leam Python”
>>> print (strl)
Welcome to Learn Python

Question 21.
What will be the output of the following snippet?
alpha = list(range(65, 70))
for x in alpha:
print(chr(x), end=’\t’)
Answer:
Output:
A B C D E

Question 22.
What is the use of WHERE clause in SQL?
Answer:
The WHERE clause in the SELECT command specifies the criteria for getting the desired result. The general form of SELECT command with WHERE Clause is:
SELECT[,,….] FROM WHERE condition>;
The relational operators like =, <, <=, >, >=, <> can be used to compare two values in the SELECT command used with WHERE clause. The logical operaors OR, AND and NOT can also be used to connect search conditions in the WHERE clause. For example:
SELECT Admno, Name, Age, Place FROM Student WHERE (Age>=18 AND Place = “Delhi”);

Question 23.
What are the steps involved in file operation of Python?
Answer:
When you want to read from or write to a file ,you need to open it. Once the reading is over it needs to be closed. So that, resources that are tied with the file are freed. Hence, in Python, a file operation takes place in the following order.
Step 1 → Open a file
Step 2 → Perform Read or write operation
Step 3 → Close the file

Question 24.
Distinguish compiler and interpreter.
Answer:

PART – III

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

Question 25.
Why strlen is called pure function?
Answer:
strlen (s) is called each time and strlen needs to iterate over the whole of ‘s’. If the compiler is smart enough to work out that strlen is a pure function and that ‘s’ is not updated in the loop, then it can remove the redundant extra calls to strlen and make the loop to execute only one time. This function reads external memory but does not change it, and the value returned derives from the external memory accessed.

Question 26.
Which strategy is used for program designing? Define the strategy.
Answer:
We are using here a powerful strategy for designing programs: ‘wishful thinking’.
Wishful Thinking is the formation of beliefs and making decisions according to what might be pleasing to imagine instead of by appealing to reality.

Question 27.
Which jump statement is used as placeholder? Why?
Answer:
pass statement is generally used as a placeholder. When we have a loop or function that is to be implemented in the future and not now, we cannot develop such functions or loops with empty body segment because the interpreter would raise an error. So, to avoid this we can use pass statement to construct a body that does nothing.

Question 28.
What are the points to be noted while defining a function?
Answer:

1. Function blocks begin with the keyword “def ” followed by function name and parenthesis ().
2. Any input parameters or arguments should be placed within these parentheses when you define a function.
3. The code block always comes after a colon (:) and is indented.
4. The statement “return [expression]” exits a function, optionally passing back an expression to the caller. A “return” with no arguments is the same as return None.

Question 29.
Write a Python program to display the given pattern
COMPUTER
COMPUTE
COM PUT
COMPU
COMP
COM
CO
C
Answer:
Program:
strl = “COMPUTER”
index = len(strl)
for i in strl:
print(strl[: index])
index – = 1

Question 30.
What is the output of the following program?
class Greeting:
def_init_(self, name):
self._name = name
def displayf self):
print (“Good Morning”, self._name)
obj = Greeting(‘Tamil Nadu’)
obj.displayO
Answer:
Output: Tamil Nadu Good Morning

Question 31.
Explain Cartesian product with a suitable example.
Answer:
PRODUCT OR CARTESIAN PRODUCT (Symbol: X)
Cross -product is a way of combining two relations. The resulting relation contains, both relations being combined.
A × B means A times B, where the relation A and B have different attributes.
This type of operation is helpful to merge columns from two relations.

Question 32.
Write a short note on (i) fetchallf) (ii) fetchonef) (iii) fetchmany
Answer:
cursor.fetchall() -fetchall ()method is to fetch all rows from the database table.
cursor. fetchoneQ – The fetchone () method returns the next row of a query result set or None in case there is no row left.
cursor, fetchmany() method that returns the next number of rows (n) of the result set

Question 33.
Write a Python code to display the following chart.

Answer:
Import matplotlib.pyplot as pit
x = [1, 2, 3,4, 5, 7,8]
y = [1,2.5, 4, 5, 6, 7, 7]
plt.plot([1, 2, 3, 4])
plt.show()

PART – IV

Answer all the following questions. [5 x 5 = 25]

Question 34 (a).
Write any five benefits in using modular programming.
Answer:
The benefits of using modular programming include

1. Less code to be written.
2. A single procedure can be developed for reuse, eliminating the need to retype the code many times.
3. Programs can be designed more easily because a small team deals with only a small part of the entire code.
4. Modular programming allows many programmers to collaborate on the same application.
5. The code is stored across multiple files.
6. Code is short, simple and easy to understand.
7. Errors can easily be identified, as they are localized to a subroutine or function.
8. The same code can be used in many applications.
9. The scoping of variables can easily be controlled.

(OR)

(b) Explain input() and print() functions of Python with example.
Answer:
Input() function:
In Python, input() function is used to accept data as input at run time. The syntax for input() function is,
Variable = input (“prompt string”)
Where, prompt string in the syntax is a statement or message to the user, to know what input can be given.
If a prompt string is used, it is displayed on the monitor; the user can provide expected data from the input device. The input() takes whatever is typed from the keyboard and stores the entered data in the given variable. If prompt string is not given in input() no message is displayed on the screen, thus, the user will not know what is to be typed as input.
Example 1:
input() with prompt string
>>> city = input (“Enter Your City: ”)
Enter Your City: Madurai
>>> print (“I am from“, city)
I am from Madurai

Example 2:
input() without prompt string
>>> city = input()
Rajarajan
>>> print (I am from”, city)
I am from Rajarajan

The print() function:
In Python, the print() function is used to display result on the screen. The syntax for print() is as follows:
Example:
print (“string to be displayed as output ”)
print (variable)
print (“String to be displayed as output ”, variable)
print (“String 1 ”, variable, “String 2”, variable, “String 3”………. )

Example:
>>> print (“Welcome to Python Programming”)
Welcome to Python Programming
>>> x = 5
>>> y = 6
>>> z = x + y
>>> print (z)
11
>>> print (“The sum = ”, z)
The sum = 11
>>> print (“The sum of ”, x, “ and ”, y, “ is ”, z)
The sum of 5 and 6 is 11

The print () evaluates the expression before printing it on the monitor. The print () displays an entire statement which is specified within print (). Comma (,) is used as a separator in print () to print more than one item.

Question 35 (a).
Write a detail note on for loop in Python.
Answer:
for loop
for loop is the most comfortable loop. It is also an entry check loop. The condition is checked in the beginning and the body of the loop(statements-block 1) is executed if it is only True otherwise the loop is not executed.
Syntax:
for counter_variable in sequence:
statements block 1
# optional block
[else:
statements block 2]
The counter_variable mentioned in the syntax is similar to the control variable that we used in the for loop of C++ and the sequence refers to the initial, final and increment value. Usually in Python, for loop uses the range() function in the sequence to specify the initial, final and increment values. range() generates a list of values starting from start till stop-1.

The syntax of range() is as follows:
range (start, stop, [step])
Where,
start – refers to the initial value
stop – refers to the final value
step – refers to increment value, this is optional part.

Examples for range()
range (1, 30, 1) will start the range of values from 1 and end at 29
range (2, 30, 2) will.start the range of values from 2 and end at 28
range (30, 3, -3) will start the range of values from 30 and end at 6
range (20) will consider this value 20 as the end value(or upper limit) and starts the range count from 0 to 19 (remember always range() will work till stop -1 value only)

#program to illustrate the use of for loop – to print single digit even number
for i in range (2, 10, 2):
print (i, end = ‘ ‘)
Output:
2 4 6 8

[OR]

(b) Explain the different types of functions in Python with example.
Answer:
Types of Functions
Basically, we can divide functions into the following types:

1. User-defined Functions
2. Built-in Functions
3. Lambda Functions
4. Recursion Functions

1. Syntax for User defined function
def < function_name ([parameter 1, parameter2 …… ])> :

return
Example:
def hello():
print (“hello – Python”)
return

Advantages of User-defined Functions:

1. Functions help us to divide a program into modules. This makes the code easier to manage.
2. It implements code reuse. Every time you need to execute a sequence of statements, all you need to do is to call the function.
3. Functions, allows us to change functionality easily, and different programmers can work on different functions.

2. Anonymous Functions
In Python, anonymous function is a function that is defined without a name. While normal functions are defined using the def keyword, in Python anonymous functions are defined using the lambda keyword. Hence, anonymous functions are also called as lambda functions.
The use of lambda or anonymous function:

1. Lambda function is mostly used for creating small and one-time anonymous function.
2. Lambda functions are mainly used in combination with the functions like filter(), map() and reduce().

Syntax of Anonymous Functions:
The syntax for anonymous functions is as follows:
lambda [argument(s)]:expression
Example:
sum = lambda argl, arg2: argl + arg2
print (‘The Sum is :’, sum(30,40))
print (‘The Sum is :’, sum(-30,40))
Output:
The Sum is : 70
The Sum is : 10
The above lambda function that adds argument argl with argument arg2 and stores the result in the variable sum. The result is displayed using the print().

3. Functions using libraries
Built-in and Mathematical functions

4. Recursive functions
When a function calls itself is known as recursion. Recursion works like loop but sometimes it makes more sense to use recursion than loop. You can convert any loop to recursion.
Example:
def fact(n):
if n = = 0:
return 1
else:
return n * fact (n – 1)
print (fact (0))
print (fact (5))
Output:
1
120

Question 36 (a).
Explain about the find() function in Python with example.
Answer:

(OR)

(b) Compare remove(), pop() and clear() function in Python.
Answer:
The remove( ) function can also be used to delete one or more elements if the index value is not known. Apart from remove() function, pop() function can also be used to delete an element using the given index value. pop() function deletes and returns the last element of a list if the index is not given.
The function clear() is used to delete all the elements in list, it deletes only the elements and retains the list. Remember that, the del statement deletes entire list.
Syntax:
List.remove(element)
# to delete a particular element
List.pop(index of an element)
List, clear ()
Example:
>>> MyList = [12, 89, 34,’Kannan’, ‘Gowrisankar’, ‘Lenin’]
>>> print(MyList)
[12, 89, 34, ‘Kannan’, ‘Gowrisankar’, ‘Lenin’]
>>> MyList.remove(89)
>>> print(MyList)
[12, 34, ‘Kannan’, ‘Gowrisankar’, ‘Lenin’]
In the above example, MyList has been created with three integer and three string elements, the following print statement shows all the elements available in the list. In the statement.
>>> MyList.remove(89), deletes the element 89 from the list and the print statement shows the remaining elements.
Example:
>>> MyList.pop(l)
34
>>> print(MyList)
[12, ‘Kannan’, ‘Gowrisankar’, ‘Lenin’]
In the above code, pop() function is used to delete a particular element using its index value, as soon as the element is deleted, the pop() function shows the element which is deleted. pop() function is used to delete only one element from a list. Remember that, del statement deletes multiple elements.
Example:
>>> MyList.clear()
>>> print(MyList)
[]
In the above code, clear() function removes only the elements and retains the list. When you try to print the list which is already cleared, an empty square bracket is displayed without any elements, which means the list is empty.

Question 37 (a).
Explain the components of DBMS.
Answer:
Components of DBMS:

The Database Management System can be divided into five major components as follows:

1. Hardware
2. Software
3. Data
4. Procedures/Methods
5. Database Access Languages

1. Hardware: The computer, hard disk, I/O channels for data, and any other physical component involved in storage of data.
2. Software: This main component is a program that controls everything. The DBMS software is capable of understanding the Database Access Languages and interprets into database commands for execution.
3. Data: It is that resource for which DBMS is designed. DBMS creation is to store and utilize data.
4. Procedures/Methods: They are general instructions to use a database management system such as installation of DBMS, manage databases to take backups, report generation, etc.
5. DataBase Access Languages: They are the languages used to write commands to access, insert, update and delete data stored in any database.

[OR]

(b) What are the components of SOL? Write the commands in each.
Answer:
Components of SQL
SQL commands are divided into five categories:

a. Data Definition Language
The Data Definition Language (DDL) consist of SQL statements used to define the database structure or schema. It simply deals with descriptions of the database schema and is used to create and modify the structure of database objects in databases.
SQL commands which comes under Data Definition Language are:

b. Data Manipulation Language
A Data Manipulation Language (DML) is a computer programming language used for adding (inserting), removing (deleting), and modifying (updating) data in a database.
SQL commands which comes under Data Manipulation Language are :

c. Data Control Language:
A Data Control Language (DCL) is used for controlling privileges in the database SQL commands: GRANT, REVOKE

d. Transactional Control Language;
Transactional control language (TCL) is used to manage transactions i.e. changes made to the data in the database.
SQL commands: COMMIT, ROLLBACK, SAVEPOINT.

e. Data Query Language
The Data Query Language (DQL) have commands to query or retrieve data from the database. SQL commands: SELECT.

Question 38 (a).
Explain the following operators in Relational Algebra with suitable example
1. Union, (∪) 20 Intersection (∩)
UNION (Symbol :∪)
It includes all tuples that are in tables A or in B. It also eliminates duplicates. Set A Union Set B would be expressed as A ∪ B
Example 2
Consider the following tables

INTERSECTION (symbol: ∩) A ∩ B
Defines a relation consisting of a set of all tuple that are in both in A and B. However, A and B must be union-compatible.
Example 5 (using Table B)

[OR]

(b) Draw the output for the following data visualization plot.
import matplotlib.pyplot as pit
plt.bar([1, 3, 5, 7, 9],[5, 2, 7, 8, 2], label=”Example one”)
plt.bar([2, 4, 6, 8, 10],[8, 6, 2, 5, 6], label=”Example two”, color=’g’)
plt.legendO
plt.xlabel(‘bar number’)
plt.ylabel(‘bar height’)
plt.title(‘Epic Graph\nAnother Line! Whoa’)
plt.show()
Answer:

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Additional Questions

Question 1.
Use Euclid’s algorithm to find the HCF of 4052 and 12756.
Solution:
Since 12576 > 4052 we apply the division lemma to 12576 and 4052, to get HCF
12576 = 4052 × 3 + 420.
Since the remainder 420 ≠ 0, we apply the division lemma to 4052
4052 = 420 × 9 + 272.
We consider the new divisor 420 and the new remainder 272 and apply the division lemma to get
420 = 272 × 1 + 148, 148 ≠ 0.
∴ Again by division lemma
272 = 148 × 1 + 124, here 124 ≠ 0.
∴ Again by division lemma
148 = 124 × 1 + 24, Here 24 ≠ 0.
∴ Again by division lemma
124 = 24 × 5 + 4, Here 4 ≠ 0.
∴ Again by division lemma
24 = 4 × 6 + 0.
The remainder has now become zero. So our procedure stops. Since the divisor at this stage is 4.
∴ The HCF of 12576 and 4052 is 4.

Question 2.
If the HCF of 65 and 117 is in the form (65m – 117) then find the value of m.
Answer:
By Euclid’s algorithm 117 > 65
117 = 65 × 1 + 52
52 = 13 × 4 × 0
65 = 52 × 1 + 13
H.C.F. of 65 and 117 is 13
65m – 117 = 13
65 m = 130
m = \(\frac { 130 }{ 65 } \) = 2
The value of m = 2

Question 3.
Find the LCM and HCF of 6 and 20 by the prime factorisation method.
Solution:
We have 6 = 2¹ × 3¹ and
20 = 2 × 2 × 5 = 2² × 5¹
You can find HCF (6, 20) = 2 and LCM (6, 20) = 2 × 2 × 3 × 5 = 60. As done in your earlier classes. Note that HCF (6, 20) = 2¹ = product of the smallest power of each common prime factor in the numbers.
LCM (6, 20) = 2² × 3¹ × 5¹ = 60.
= Product of the greatest power of each prime factor, involved in the numbers.

Question 4.
Prove that \(\sqrt { 3 }\) is irrational.
Answer:
Let us assume the opposite, (1) \(\sqrt { 3 }\) is irrational.
Hence \(\sqrt { 3 }\) = \(\frac { p }{ q } \)
Where p and q(q ≠ 0) are co-prime (no common factor other than 1)

Hence, 3 divides p²
So 3 divides p also …………….. (1)
Hence we can say
\(\frac { p }{ 3 } \) = c where c is some integer
p = 3c
Now we know that
3q² = p²
Putting = 3c
3q² = (3c)²
3q² = 9c²
q² = \(\frac { 1 }{ 3 } \) × 9c²
q² = 3c²
\(\frac{q^{2}}{3}\) = C²
Hence 3 divides q²
So, 3 divides q also ……………. (2)
By (1) and (2) 3 divides both p and q
By contradiction \(\sqrt { 3 }\) is irrational.

Question 5.
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
(i) 4, 10, 16, 22, …
(ii) 1, -1,-3, -5,…
(iii) -2, 2, -2, 2, -2, …
(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3,…
Solution:
(i) 4, 10, 16, 22, …….
We have a₂ – a₁ = 10 – 4 = 6
a₃ – a₂ = 16 – 10 = 6
a₄ – a₃ = 22 – 16 = 6
∴ It is an A.P. with common difference 6.
∴ The next two terms are, 28, 34

(ii) 1, -1, -3, -5
t₂ – t₁ = -1 – 1 = -2
t₃ – t₂ = -3 – (-1) = -2
t₄ – t₃ = -5 – (-3) = -2
The given list of numbers form an A.P with the common difference -2.
The next two terms are (-5 + (-2)) = -7, -7 + (-2) = -9.

(iii) -2, 2,-2, 2,-2
t₂ – t₁ = 2-(-2) = 4
t₃ – t₂ = -2 -2 = -4
t₄ – t₃ = 2 – (-2) = 4
It is not an A.P.

(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3
t₂ – t₁ = 1 – 1 = 0
t₃ – t₂ = 1 – 1 = 0
t₄ – t₃ = 2 – 1 = 1
Here t₂ – t₁ ≠ t₃ – t₂
∴ It is not an A.P.

Question 6.
Find n so that the n^th terms of the following two A.P.’s are the same.
1, 7,13,19,… and 100, 95,90,…
Answer:
The given A.P. is 1, 7, 13, 19,….
a = 1, d = 7 – 1 = 6
t_n1 = a + (n – 1)d
t_n1 = 1 + (n – 1) 6
= 1 + 6n – 6 = 6n – 5 … (1)
The given A.P. is 100, 95, 90,….
a = 100, d = 95 – 100 = – 5
tn₂ = 100 + (n – 1) (-5)
= 100 – 5n + 5
= 105 – 5n …..(2)
Given that, t_n1 = t_n2
6n – 5 = 105 – 5n
6n + 5n = 105 + 5
11 n = 110
n = 10
∴ 10^th term are same for both the A.P’s.

Question 7.
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
Answer:
The number of rose plants in the 1st, 2nd, 3rd,… rows are
23, 21, 19,………….. 5
It forms an A.P.
Let the number of rows in the flower bed be n.
Then a = 23, d = 21 – 23 = -2, l = 5.
As, a_n = a + (n – 1)d i.e. t_n = a + (n – 1)d
We have 5 = 23 + (n – 1)(-2)
i.e. -18 = (n – 1)(-2)
n = 10
∴ There are 10 rows in the flower bed.

Question 8.
Find the sum of the first 30 terms of an A.P. whose n^th term is 3 + 2n.
Answer:
Given,
t_n = 3 + 2n
t₁ = 3 + 2 (1) = 3 + 2 = 5
t₂ = 3 + 2 (2) = 3 + 4 = 7
t₃ = 3 + 2 (3) = 3 + 6 = 9
Here a = 5,d = 7 – 5 = 2, n = 30
S_n = \(\frac { n }{ 2 } \) [2a + (n – 1)d]
S₃₀ = \(\frac { 30 }{ 2 } \) [10 + 29(2)]
= 15 [10 + 58] = 15 × 68 = 1020
∴ Sum of first 30 terms = 1020

Question 9.
How many terms of the AP: 24, 21, 18, . must be taken so that their sum is 78?
Solution:
Here a = 24, d = 21 – 24 = -3, S_n = 78. We need to find n.
We know that,
S_n = \(\frac { n }{ 2 } \) (2a + (n – 1)d)
78 = \(\frac { n}{ 2 } \) (48 + 13(-3))
78 = \(\frac { n}{ 2 } \) (51 – 3n)
or 3n² – 51n + 156 = 0
n² – 17n + 52 = 0
(n – 4) (n – 13) = 0
n = 4 or 13
The number of terms are 4 or 13.

Question 10.
The sum of first n terms of a certain series is given as 3n² – 2n. Show that the series is an arithmetic series.
Solution:
Given, S_n = 3n² – 2n
S₁ = 3 (1)² – 2(1)
= 3 – 2 = 1
ie; t₁ = 1 (∴ S₁ = t₁)
S₂ = 3(2)² – 2(2) = 12 – 4 = 8
ie; t₁ + t₂ = 8 (∴ S₂ = t₁ + t₂)
∴ t₂ = 8 – 1 = 7
S₃ = 3(3)² – 2(3) = 27 – 6 = 21
t₁ + t₂ + t₃ = 21 (∴ S₃ = t₁ + t₂ + t₃)
8 + t₃ = 21 (Substitute t₁ + t₂ = 8)
t₃ = 21 – 8 ⇒ t₃ = 13
∴ The series is 1,7,13, …………. and this series is an A.P. with common difference 6.

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Unit Exercise 2

Question 1.
Prove that n² – n divisible by 2 for every positive integer n.
Answer:
To prove n² – n divisible by 2 for every positive integer n.
We know that any positive integer is of the form 2q or 2q + 1, for some integer q.
So, following cases arise:
Case I. When n = 2q.
In this case, we have
n² – n = (2q)² – 2q = 4q² – 2q = 2q(2q – 1)
⇒ n² – n = 2r where r = q(2q – 1)
⇒ n² – n is divisible by 2.

Case II. When n = 2q + 1.
In this case, we have
n² – n = (2q + 1)² – (2q + 1)
= (2q + 1)(2q + 1 – 1) = (2q + 1)2q
⇒ n² – n = 2r where r = q (2q + 1)
⇒ n² – n is divisible by 2.
Hence n² – n is divisible by 2 for every positive integer n.

Question 2.
A milk man has 175 litres of cow’s milk and 105 litres of buffalow’s milk. He wishes to sell the milk by filling the two types of milk in cans of equal capacity. Calculate the following (i) Capacity of a can
(ii) Number of cans of cow’s milk
(iii) Number of cans of buffalow’s milk.
Answer:
Cow’s milk = 175 litres
Buffalow’s milk = 105 litres
Find the H.C.F. of 175 and 105 using Euclid’s division method of factorisation method.

175 = 5 × 5 × 7
105 = 3 × 5 × 7
H.C.F. of 175 and 105 = 5 × 7 = 35
(i) The capacity of the milk can’s is 35 litres

(ii) Cows milk = 175 litres
Number of cans = \(\frac { 175 }{ 35 } \) = 5

(iii) Buffalow’s milk = 105 litres
Number of cans = \(\frac { 105 }{ 35 } \) = 3
(i) Capacity of one can = 35 litres
(ii) Number of can’s for cow’s milk= 5 litres
(iii) Number of can’s for Buffalow’s milk = 3 litres

Question 3.
When the positive integers a, b and c are divided by 13 the respective remainders are 9, 7 and 10. Find the remainder when a + 2b + 3c is divided by 13.
Answer:
Let the positive integers be a, b, and c.
a = 13q + 9
b = 13q + 7
c = 13q + 10
a + 2b + 3c = 13 q + 9 + 2(13q + 7) + 3(13q + 10)
= 13q + 9 + 269 + 14 + 39q + 30
= 78q + 53 = (13 × 6)q + 53
The remainder is 53.
But 53 = 13 × 4 + 1
∴ The remainder is 1

Question 4.
Show that 107 is of the form 4q + 3 for any integer q.
Answer:

107 = 4 x 26 + 3
This is in the form of a = bq + r
Hence it is proved.

Question 5.
If (m + 1)^th term of an A.P. is twice the (n + 1)^th term, then prove that (3m + 1)^th term is twice the (m + n + 1)^th term.
Solution:
t_n = a + (n – 1)d
t_m+1 = a + (m + 1 – 1)d
= a + md
t_n+1 = a + (n + 1 – 1)d
= a + nd
2(t_n+1) = 2(a + nd)
t_m+1 = 2t_n+1 …………… (1)
⇒ a + md = 2(a + nd)
2a + 2nd – a – md = 0
a + (2n – m)d = 0
t_(3m+1) = a + (3m + 1 – 1)d
= a + 3md
t_(m+n+1) = a + (m + n + 1 – 1)d
= a + (m + n)d
2(t_(m+n+1)) = 2(a + (m + n)d)
= 2a + 2md + 2nd
t_(3m+1) = 2t_(m+n+1) ………….. (2)
a + 3md = 2a + 2md + 2nd
2a + 2md + 2nd – a – 3md = 0
a – md + 2nd = 0
a + (2n – m)d = 0
∴ It is proved that t_(3m+1) = 2t_(m+n+1)

Question 6.
Find the 12^th term from the last term of the A.P -2, -4, -6, … -100.
Solution:

12^th term from the last = 39^th term from the beginning
∴ t₃₉ = a + 38d
= -2 + 38(-2)
= – 2 – 76
= – 78

Question 7.
Two A.P.’s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. Show that the difference between their 10^th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms.
Answer:
Let the common difference for the 2 A.P be “d”
For the first A.P
a = 2, d = d, n = 10
t_n = a + (n – 1) d
t₁₀ = 2 + 9 d ….(1)
For the 2^nd A.P
a = 7, d = d n = 10
t₁₀ = 7 + (9)d
= 7 + 9d ….(2)
Difference between their 10th term ⇒ (1) – (2)
= 2 + 9d – (7 + 9d)
= 2 + 9d – 7 – 9d
= -5
For first A.P when n = 21, a = 2, d = d
t₂₁ = 2 + 20d …….(3)
For second A.P when n = 21, a = 7, d = d
t₂₁ = 7 + 20d …….(4)
Difference between the 21^st term ⇒ (3) – (4)
= 2 + 20d – (7 + 20d)
= 2 + 20d – 7 – 20d
= -5
Difference between their 10th term and 21^st term = -5
Hence it is proved.

Question 8.
A man saved ₹16500 in ten years. In each year after the first he saved ₹100 more than he did in the preceding year. How much did he save in the first year?
Solution:
S₁₀ = ₹16500
a, a + d, a + 2d…
d = 100
n = 10
S_n = \(\frac { n }{ 2 } \)(2a+(n-1)d)
S₁₀ = 16500
S₁₀ = \(\frac { 10 }{ 2 } \)(2×a+9×100)
16500 = 5(2a+900)
16500 = 10a + 4500
10a = 16500 – 4500
10a = 12000
a = \(\frac { 12000 }{ 10 } \) = ₹1200
∴ He saved ₹1200 in the first year

Question 9.
Find the G.P. in which the 2nd term is \(\sqrt { 6 }\) and the 6th term is 9\(\sqrt { 6 }\).
Solution:

Question 10.
The value of a motorcycle depreciates at the rate of 15% per year. What will be the value of the motor cycle 3 year hence, which is now purchased for ₹45,000?
Answer:
Value of the motor cycyle = ₹ 45000
a = 45000
Depreciation = 15% of the cost value
= \(\frac { 15 }{ 100 } \) × 45000
= 15 × 450
= 6750
d = – 6750 (decrease it is depreciation
Value of the motor cycle lightning of the 2nd year = 45000 – 6750
= ₹ 38250
Depreciation for the 2nd year = \(\frac { 15 }{ 100 } \) × 38250
= ₹ 57370.50

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Ex 2.10

Multiple choice questions
Question 1.
Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy.
(1) 1 < r < b
(2) 0 < r < b
(3) 0 < r < b
(4) 0 < r < b
Answer:
(3) 0 < r < b

Question 2.
Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are
(1) 0, 1, 8
(2) 1, 4, 8
(3) 0, 1, 3
(4) 1, 3, 5
Answer:
(1) 0,1,8
Hint:
Cube of any +ve integers 1³, 2³, 3³, 4³,. . .
1, 8, 27, 64, 125, 216 …
Remainders when 27, 64, 125 are divided by 9.

Question 3.
If the H.C.F of 65 and 117 is expressible in the form of 65m -117 , then the value of m is ………………….
(1) 4
(2) 2
(3) 1
(4) 3
Answer:
(2) 2
Hint:
117 = 3 × 3 × 13
65 = 5 × 13
H.C.F = 13
65m – 117 = 13 ⇒ 65m = 117 + 13 = 130
m = \(\frac { 130 }{ 65 } \) = 2
The value of m = 2

Question 4.
The sum of the exponents of the prime factors in the prime factorization of 1729 is
(1) 1
(2) 2
(3) 3
(4) 4
Answer:
(3) 3
Hint:
1729 = 7¹ × 13¹ × 19¹

Question 5.
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(1) 2025
(2) 5220
(3) 5025
(4) 2520
Answer:
(4) 2520
Hint:

∴ L.C.M. of 1,2,3,4,…,10 is 2 × 2 × 3 × 5 × 7 × 2 × 3 = 2520

Question 6.
7^4k ≡ …………………. (mod 100)
(1) 1
(2) 2
(3) 3
(4) 4
Answer:
(1) 1
Hint:
7^4k ≡ . . . . . (mod 100)
7^4k = (7⁴)^k ≡ ……….. (mod 100) (7⁴ – 2401)
The value is 1.

Question 7.
Given F₁ = 1, F₂ = 3 and Fn = F_n-1 + F_n-2 then
(1) 3
(2) 5
(3) 8
(4) 11
Answer:
(4) 11
Answer:
F₁ = 1, F₂ = 3
F_n = F_n-1 + F_n-2
F₅ = F_5-1 + F_5-2 = F₄ + F₃
= F₃ + F₂ + F₂ + F₁
= F₂ + F₁ + F₂ + F₂ + F₁
= 3 + 1 + 3 + 3 + 1 = 11

Question 8.
The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P …………..
(1) 4551
(2) 10091
(3) 7881
(4) 13531
Answer:
(3) 7881
Hint:
Here a = 1, d = 4
t_n = a + (n – 1) d = 1 + (n – 1) 4
= 1 + 4n – 4
= 4n – 3
4554
(i) 4n – 3 = 4551 ⇒ 4n = 4551 + 3 ⇒ n = \(\frac { 4554 }{ 4 } \) = 1138.5.
It is not a term of A.P.

(ii) 4n – 3 = 10091 ⇒ 4n = 10091 + 3 = 10094
n = \(\frac { 10094 }{ 4 } \) = 2523.5 it is a term of A.P.

(iii) 4n – 3 = 7881 ⇒ 4n = 7881 + 3
n = \(\frac { 7884 }{ 4 } \) = 1971.
∴ 7881 is a term of the A.P.

Question 9.
If 6 times of 6^th term of an A.P is equal to 7 times the 7th term, then the 13th term of the A.P. is
(1) 0
(2) 6
(3) 7
(4) 13
Answer:
(1) 0
Hint:
6t₆ = 7t₇
6(a + 5d) = 7(a + 6d)
6a + 30d = 7a + 42d
7a + 42d – 6a – 30d = 0
a + 12d = 0 = t₁₃

Question 10.
An A.P consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is …………..
(1) 16m
(2) 62m
(3) 31m
(4) \(\frac { 31 }{ 2 } \)m
Answer:
(3) 31m
Hint:
M = 31
t₁₆ = m ⇒ a + 15d = m
S_n = \(\frac { n }{ 2 } \)[2a + (n – 1)d]
S_n = \(\frac { 31 }{ 2 } \)[2a + 30d]= \(\frac { 31 }{ 2 } \) × 2[a + 15d]
= 31 (m) = 31m

Question 11.
In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P must be taken for their sum to be equal to 120?
(1) 6
(2) 7
(3) 8
(4) 9
Answer:
(3) 8
Hint:

Question 12.
If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² + +2⁰ which of the following is true?
(1) B is 264 more than A
(2) A and B are equal
(3) B is larger than A by 1
(4) A is larger than B by 1
Answer:
(4) A is larger than B by 1
Hint:
A = 2⁶⁵
B = 2⁶⁴ + 2⁶³ + 2⁶² + … + 20
B = 2⁰ + 2¹ + 2² + … + 264
G.P = 1 + 2¹ + 2² + … + 2⁶⁴ it is a G.P
Here a = 1, r = 2, n = 65

A = 2⁶⁵, B = 2⁶⁵ – 1
∴ B is smaller.
A is larger than B by 1.

Question 13.
The next term of the sequence \(\frac { 3 }{ 16 } \),\(\frac { 1 }{ 8 } \),\(\frac { 1 }{ 12 } \),\(\frac { 1 }{ 18 } \), ….
(1) \(\frac { 1 }{ 24 } \)
(2) \(\frac { 1 }{ 27 } \)
(3) \(\frac { 2 }{ 3 } \)
(4) \(\frac { 1 }{ 81 } \)
Answer:
(2) \(\frac { 1 }{ 27 } \)
Hint:

Question 14.
If the sequence t₁, t₂, t₃, …………are in A.P. then the sequence t₆, t₁₂, t₁₈, …… is ………….
(1) a Geometric progression
(2) an Arithmetic progression
(3) neither an Arithmetic progression nor a Geometric progression
(4) a constant sequence
Answer:
(2) an Arithmetic progression
Hint: t₁, t₂, t₃ …. are in A.P
t₆, t₁₂, t₁₈ …… is also an A.P. (6, 12, 18 …….. is an A.P.)

Question 15.
The value of (1³ + 2³ + 3³ + … + 15³) – (1 + 2 + 3 + … + 15) is
(1) 14400
(2) 14200
(3) 14280
(4) 14520
Answer:
(3) 14280
Hint:
\(\left(\frac{15 \times 16}{2}\right)^{2}-\frac{15 \times 16}{2}\) = (120)² – 120 = 14280

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Additional Questions

Question 1.
Solve the following system of linear equations in three variables. x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + 5z = 22
Solution:
x + y + z = 6 ………….. (1)
2x + 3y + 4z = 20 ………… (2)
3x + 2y + 5z = 22 …………(3)

Sub. z = 3 in (5) ⇒ y – 2(3) = -4
y = 2
Sub. y = 2, z = 3 in (1), we get
x + 2 + 3 = 6
x = 1
x = 1, y = 2, z = 3

Question 2.
Using quadratic formula solve the following equations.
(i) p²x² + (p² – q²) x – q² = 0
(ii) 9x² – 9 (a + b)x + (2a² + 5ab + 2b²) = 0
Solution:
(i) p²x² + (p² – q²)x – q² = 0
Comparing this with ax² + bx + c = 0, we have
a = p²
b = p² – q²
c = -q²
Δ = b² – 4ac
= (p² – q²)-4 × p² × -q²
= (p² – q²)² + 4p² q²
= (p² + q²)² > 0
So, the given equation has real roots given by
\(\alpha=\frac{-b-\sqrt{\Delta}}{2 a}=\frac{-\left(p^{2}-q^{2}\right)+\left(p^{2}+q^{2}\right)}{2 p^{2}}=\frac{q^{2}}{p^{2}}\)
\(\beta=\frac{-b-\sqrt{\Delta}}{2 a}=\frac{-\left(p^{2}-q^{2}\right)-\left(p^{2}+q^{2}\right)}{2 p^{2}}\)
= -1

(ii) 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0
Comparing this with ax² + bx + c = 0.
a =9
b = -9 (a + b)
c = (2a² + 5 ab + 2b²)
Δ = B² – 4AC
⇒ 81 (a + b)² – 36(2a² + 5ab + 2b²)
⇒ 9a² + 9b² – 18ab
⇒ 9(a – b)² > 0
∴ the roots are real and given by

Question 3.
Find the HCF of x³ + x² + x + 1 and x⁴ – 1.
Answer:
x³ + x² + x + 1 = x² (x + 1) + 1 (x + 1)
= (x + 1) (x² + 1)
x⁴-1 = (x²)² – 1
= (x² + 1) (x²– 1)
= (x² + 1) (x + 1) (x – 1)
H.C.F. = (x² + 1)(x + 1)

Question 4.
Prove that the equation x²(a² + b²) + 2x(ac + bd) + (c² + d²) = 0 has no real root if ad ≠ bc
Solution:
Δ = b² – 4ac
⇒ 4(ac + bd)² – 4(a² + b²)(c² + d²)
⇒ 4[(ac + bd)² – (a² + b²)(c² + d²)]
⇒ 4(a²c² + b²d² + 2acbd – a²c²b²c² – a²d² – b²d²]
⇒ 4[2acbd – a²d² – b²c²]
⇒ 4 [a²c² + b²c² – 2adbc]
⇒ -4[ad – bc]²
We have ad ≠ bc
∴ ad – bc > 0
⇒ (ad – bc)² > 0
⇒ -4(ad – bc)² < 0 ⇒ Δ < 0
Hence the given equation has no real roots.

Question 5.
Find the L.C.M of 2(x³ + x² – x – 1) and 3(x³ + 3x² – x – 3)
Answer:
2[x³ + x² – x – 1] = 2[x²(x+ 1)- 1 (x + 1)]
= 2(x + 1) (x² – 1)
= 2(x + 1) (x + 1) (x – 1)
= 2(x + 1)² (x – 1)
3[x³ + 3x² – x – 3] = 3[x²(x + 3) -1 (x + 3)]
= 3[(x + 3)(x² – 1)]
= 3(x + 3)(x + 1) (x – 1)
L.C.M. = 6(x + 1)²(x – 1) (x + 3)

Question 6.
A two digit number is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.
Solution:
Let the ten’s digit of the number be x. It is given that the product of the digits is 12.
Unit’s digit = \(\frac{12}{x}\)
Number = 10x + \(\frac{12}{x}\)
If 36 is added to the number the digits interchange their places.

x = -6, 2.
But a number can never be (-ve). So, x = 2.
The number is 10 × 2 + \(\frac{12}{2}\) = 26

Question 7.
Seven years ago, Vanin’s age was five times the square of swati’s age. Three years hence Swati’s age will be two fifth of Varun’s age. Find their present ages.
Solution:
Seven years ago, let Swathi’s age be x years.
Seven years ago, let Varun’s age was 5x² years.
Swathi’s present age = x + 7 years
Varun’s present age = (5x² + 7) years
3 years hence, we have Swathi’s age = x + 7 + 3 years
= x + 10 years
Varun’s age = 5x² + 7 + 3 years
= 5x² + 10 years
It is given that 3 years hence Swathi’s age will be \(\frac{2}{5}\) of Varun’s age.
∴ x + 10 = \(\frac{2}{5}\) (5x² + 10)
⇒ x + 10 = 2x² + 4
⇒ 2x² – x – 6 = 0
⇒ 2x(x – 2) + 3(x – 2) = 0
⇒ (2x + 3)(x – 2) = 0
⇒ x – 2 = 0
⇒ x = 2 (∵ 2x + 3 ≠ 0 as x > 0)
Hence Swathi’s present age = (2 + 7) years
= 9 years
Varun’s present age = (5 × 2² + 7) years = 27 years

Question 8.
A chess board contains 64 equal squares and the area of each square is 6.25 cm². A border round the board is 2 cm wide find its side.
Solution:
Let the length of the side of the chess board be x cm. Then,

Area of 64 squares = (x – 4)²
(x – 4)² = 64 × 6.25
⇒ x² – 8x+ 16 = 400
⇒ x² – 8x-384 = 0
⇒ x² – 24x + 16x – 384 = 0
⇒ (x – 24)(x + 16) = 0
⇒ x = 24 cm.

Question 9.
Find two consecutive natural numbers whose product is 20.
Solution:
Let a natural number be x.
The next number = x + 1
x (x + 1) = 20
x² + x – 20 = 0
(x + 5)(x – 4) = 0
x = -5, 4
∴ x = 4 (∵ x ≠ -5, x is natural number)
The next number = 4 + 1 = 5
Two consecutive numbers are 4, 5

Question 10.
A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.
Solution:
Let the tens digit be x. Then the units digits = \(\frac{18}{x}\)

Students can Download Tamil Nadu 12th Computer Science Model Question Paper 2 English Medium Pdf, Tamil Nadu 12th Computer Science Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

TN State Board 12th Computer Science 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 15 in Part I are Multiple Choice Questions of one mark each.
   These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer
5. Question numbers 16 to 24 in Part II are two-mark questions. These are to be answered in about one or two sentences.
6. Question numbers 25 to 33 in Part III are three-mark questions. These are to be answered in about three to five short sentences.
7. Question numbers 34 to 38 in Part IV are five-mark questions. These are to be answered in detail Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 70

PART – I

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

Question 1.
The members that are accessible from within the class and are also available to its subclasses is called……….
(a) public
(b) protected
(c) secured
(d) private
Answer:
(b) protected

Question 2.
Built in scopes are called as scope.
(a) private
(b) public
(c) protected
(d) module
Answer:
(d) module

Question 3.
The complexity of Bubble sort is…………
(a) θ (n2)
(b) θ (n(logn)2)
(c) θ (n)
(d) θ (2n)
Answer:
(a) θ (n2)

Question 4.
How many integer data types are there?
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(b) 3

Question 5.
Branching statements are otherwise called as………..
(a) alternative
(b) Iterative
(c) loop
(d) sequential
Answer:
(a) alternative

Question 6.
……….. functions are anonymous un-named functions.
(a) User defined
(b) Built-in
(c) Lambda
(d) Recursive
Answer:
(c) Lambda

Question 7.
The code block always comes after……..
(a) ;
(b) +
(c) =
(d) :
Answer:
(d) :

Question 8.
Which one of the following is the membership operator?
(a) is
(b) at
(c) to
(d) in
Answer:
(d) in

Question 9.
Which operator is used to join two tuples?
(a) –
(b) _
(c) +
(d) +:
Answer:
(c) +

Question 10.
A table is otherwise called as…………
(a) tuple
(b) relation
(c) attribute
(d) degree
Answer:
(b) relation

Question 11.
Who developed ER model?
(a) Chen
(b) E F Codd
(c) Chend
(d) Chand
Answer:
(a) Chen

Question 12.
The latest SQL was released in………
(a) 1987
(b) 1992
(c) 2008
(d) 2012
Answer:
(c) 2008

Question 13.
How many ways are there to read the CSV files?
(a) 2
(b) 1
(c) 3
(d) 4
Answer:
(a) 2

Question 14.
CSV files cannot be opened with………
(A) notepad
(b) MS Excel
(c) Open office
(d) html
Answer:
(d) html

Question 15.
getopt mode is given by………..
(a) ;
(b) =
(c) #
(d) :
Answer:
(d) :

PART – II

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

Question 16.
List the characteristics of an algorithm.
Answer:
Input, Output, Finiteness, Definiteness, Effectiveness, Correctness, Simplicity, Unambiguous, Feasibility, Portable and Independent.

Question 17.
What are the escape sequences for Backslash, Newline, Tab, Single quotes.
Answer:

1. Backslash – \\
2. New line – \n
3. Tab – \t
4. Single quotes – \’

Question 18.
Define composition.
Answer:
The value returned by a function may be used as an argument for another function in a nested manner. This is called composition.

Question 19.
Name the different types of functions.
Answer:

1. User-defined Functions
2. Built-in Functions
3. Lambda Functions
4. Recursion Functions

Question 20.
Write note on center function, center (width, fillchar)
Answer:
Returns a string with the original string centered to a total of width columns and filled with fillchar in columns that do not have characters.

Question 21.
Write a program to create a list of numbers in the range 1 to 20. Then delete all the numbers from the list that are divisible by 3.
num = []
for x in range(1 21):
num.append(x)
print(“The list of numbers from 1 to 20 =”, num)
for index, i in enumerate(num):
if (i % 3 = 0)
del num[index]
print (“The list after deleting numbers”, num)
Output:
The list of numbers from 1 to 20 = [1, 2, 3, 4… 20]
The list after deleting numbers [l, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20]

Question 22.
Write note on dictionary comprehensions.
Answer:
In Python, comprehension is another way of creating dictionary. The following is the syntax of creating such dictionary.
Syntax
Diet = {expression for variable in sequence [if condition]}

Question 23.
What is data consistency?
Answer:
On live data, it is being continuously updated and added, maintaining the consistency of data can become a challenge. But DBMS handles it by itself. Data Consistency means that data values are the same at all instances of a database.

Question 24.
Define database.
Answer:
Database is a repository collection of related data organized in a way that data can be easily accessed, managed and updated. Database can be a software or hardware based, with one sole purpose of storing data.

PART – III

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

Question 25.
Define constructors and selectors functions.
Answer:

1. Constructors are functions that build the abstract data type.
2. Selectors are functions that retrieve information from the data type.

Question 26.
What are the steps to do Dynamic programming?
Answer:

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

Question 27.
Write note on delimiters.
Answer:
Python uses the symbols and symbol combinations as delimiters in expressions, lists, dictionaries and strings. Following are the delimiters.

Question 28.
Write note on Nested loop structure.
Answer:
A loop placed within another loop is called as nested loop structure. One can place a while within another while; for within another for; for within while and while within for to construct such nested loops.
Following is an example to illustrate the use of for loop to print the following pattern
1
12
123
1234
12345

Question 29.
Write a program to display the sum of natural numbers upto n.
Answer:
n = input (“Enter any number”)
sum = 0
for i in range (i, n+1):
sum = sum + i
print “sum = “, sum
Output:
Enter any number 5
sum = 15

Question 30
Differentiate list and dictionary.
Answer:

Question 31.
Explain the commands which comes under TCL.
Answer:
SQL command which come under Transfer Control Language are:

1. Commit Saves any transaction into the database permanently.
2. Roll back Restores the database to last commit state.
3. Save point Temporarily save a transaction so that you can rollback.

Question 32.
Differentiate Python from C++.
Answer:

Question 33.
Give the Pseudo code for Bubble sort algorithm.
Answer:
Pseudo code

1. Start with the first element i.e., index = 0, compare the current element with the next element of the array.
2. If the current element is greater than the next element of the array, swap them.
3. If the current element is less than the next or right side of the element, move to the next element. Go to Step 1 and repeat until end of the index is reached.

PART – IV

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

Question 34 (a).
Explain the rules to be followed to format data in a CSV file.
Answer:
Rules to be followed to format data in a CSV file
1. Each record (row of data) is to be located on a separate line, delimited by a line break by pressing enter key.
For example: ↵
xxx, yyy ↵
↵ denotes enter Key to be pressed

2. The last record in the file may or may not have an ending line break.
For example:
ppp, qqq ↵
yyy, xxx

3. There may be an optional header line appearing as the first line of the file with the same format as normal record lines. The header will contain names corresponding to the fields in the file and should contain the same number of fields as the records in the rest of the file.
For example: field_namel, field_name2, field_name3 ↵
aaa,bbb,ccc ↵
zzz, yyy, xxx CRLF (Carriage Return and Line Feed)

4. Within the header and each record, there may be one or more fields, separated by commas. Spaces are considered part of a field and should not be ignored. The last field in the record must not be followed by a comma. For example: Red , Blue

5. Each field may or may not be enclosed in double quotes. If fields are not enclosed with double quotes, then double quotes may not appear inside the fields.
For example:

6. Fields containing line breaks (CRLF), double quotes, and commas should be enclosed in double-quotes.
For example:
Red, ”, “, Blue CRLF # comma itself is a field value. So it is enclosed with double quotes Red, Blue , Green.

7. If double-quotes are used to enclose fields, then a double-quote appearing inside a field ‘ must be preceded with another double quote.
For example:
“Red, ” “Blue”, “Green”, # since double quotes is a field value it is enclosed with another double quotes,, White

[OR]

(b) Write a program to add a prefix text to all the lines in a string.
Answer:
import textwrap
text =
‘”Strings are immutable. Slice is a
substring of a main string. Stride is a third argument in slicing operation'”
text_without_lndentation = textwrap.dedent(text)
wrapped = textwrap.fill(text_without_Indentation, width = 50)
print(textwrap.indent(wrapped, ‘*’)
print()
Output:

1. Strings are immutable. Slice is a
2. substring of a main string. Stride
3. is a third argument in slicing operation.

Question 35 (a).
Explain the purpose of range with an example.
Answer:
The range( ) is a function used to generate a series of values in Python. Using range( ) function, you can create list with series of values. The range() function has three arguments.

Syntax of range () function:
range (start value, end value, step value)
where,
start value – beginning value of series. Zero is the default beginning value.
end value – upper limit of series. Python takes the ending value as upper limit – 1.
step value – It is an optional argument, which is used to generate different interval of values.
Example:
Generating whole numbers upto 10
for x in range (1, 11):
print(x)
Output
1
2
3
4
5
6
7
8
9
10

[OR]

(b) Explain the various processing skills of SQL.
Answer:
The various processing skills of SQL are :

1. Data Definition Language (DDL) : The SQL DDL provides commands for defining relation schemes (structure), deleting relations, creating indexes and modifying relation schemes.
2. data Manipulation Language (DML) : The SQL DML includes commands to insert, delete, and modify tuples in the database.
3. Embedded Data Manipulation Language : The embedded form of SQL is used in high level programming languages.
4. View Definition : The SQL also includes commands for defining views of tables.
5. Authorization : The SQL includes commands for access rights to relations and views of tables.
6. Integrity : The SQL provides forms for integrity checking using condition.
7. Transaction control : The SQL includes commands for file transactions and control over transaction processing.

Question 36 (a).
Explain various set operations.
Answer:
As we leamt in mathematics, the python is also supports the set operations such as Union, Intersection, difference and Symmetric difference.

(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’}

[OR|

(b) Write a program that accept a string from the user and display the same after removing vowels from it.
Answer:
def rem_vowels(s):
temp_str = ”
for i in s:
if i in “aAeEiIoOuU”:
pass
else:
temp_str+ = i
print (“The string without vowels: “, temp str)
strl= input (“Enter a String: “)
rem_vowels (strl)
Output:
Enter a String: Mathematical foundations of Computer Science The string without vowels: Mthmtcl fndtns f Cmptr Scnc

Question 37 (a).
Write a program to display all records using fetchall().
Answer:
The fetchall() method is used to fetch all rows from the database table
import sqlite3
connection = sqlite3.connect(“Academy, db”)
cursor = connection.cursor()
cursor.execute(“SELECT * FROM student”)
print(“fetchall:”)
result = cursor.fetchall()
for r in result:
print(r)
Output:
fetchall:
(1, ‘Akshay’, ‘B’, ‘M’, 87.8, ’2001-12-12′)
(2, ‘Aravind’, ’A’, ‘M’, 92.5, ‘2000-08-17’)
(3, ‘BASKAR’,’C’, ‘M’, 75.2, ‘1998-05-17’)
(4, ‘SAJINT, ‘A’, ‘F’, 95.6, ‘2002-11-01’)
(5, ‘VARUN’,’B’, ‘M’, 80.6,’2001-03-14′)
(6, ‘PRIYA’, ‘A’, ‘F’, 98.6, ‘2002-01-01’)
(7, ‘TARUN’, ‘D’, ‘M’, 62.3, ‘1999-02-01’)

[OR]

(b) Write a C++ program using user defined function to find cube of a number.
Answer:
#include <iostream>
using namespace std;
// Function declaration
int cube(int num);
int main()
{
int num;
int c;
cout <<“Enter any number: “<<endl;
cin>>num;
c = cube(num);
cout<<“Cube of” <<num<<” is “<<c;
return 0;
}
//Function to find cube of any number
int cube(int num)
{
return (num * num * num);
}
// Save this file as cubefile.cpp
#Now select File→New in Notepad and type the Python program
# Save the File as fun.py
# Program that compiles and executes a .cpp file
# Python fun.py -i c:\pyprg\cube_file.cpp
import sys, os, getopt
def main (argv):
cppfile = ”
exefile = ”
opts, args = getopt.getopt(argv, “i:”,[‘ifile=’])
for o, a in opts:
if o in (“-i”, “–ifile”):
cpp_file = a + ‘.cpp’
exe_file = a + ‘.exe’
run (cpp_file, exe_file)
def run (cpp_file, exe_file):
print(“Compiling” + cpp file)
os.system (‘g++ ‘ + cpp_file +’ -o ‘ + exe_file)
print (“Running ” + exe_file)
print(“———-“)
print
os.system(exe_file)
print
if_name_ == ‘_main_’:
main(sys.argv[l:])
Output of the above program
Compiling c:\pyprg\cube_file.cpp
Running c:\pyprg\cube_file.exe
————–
Enter any number:
5
Cube of 5 is 125

Question 38 (a).
Explain reverse Indexing in list using python program.
Answer:
Python enables reverse or negative indexing for the list elements. Thus, python lists index in opposite order. The python sets -1 as the index value for the last element in list and -2 for the preceding element and so on. This is called as Reverse Indexing.
Example:
Marks = [10, 23, 41, 75]
i = -1
while i > = -4:
print (Marks[i])
i = i + -l
Output
75
41
23
10

[OR]

(b) Explain sort function in list with examples.
Answer:
Sorts the element in list
Both arguments are optional
1. If reverse is set as True, list sorting is in descending order.
2. Ascending is default.
3. Key=myFunc; “myFunc” – the name of the user defined function that specifies the sorting criteria.
MyList = [‘Thilothamma’, ‘Tharani’, ‘Anitha’, ‘SaiSree’, ‘Lavanya’]
MyList.sort( )
print (MyList)
MyList.sort(reverse = True)
print (MyList)
Output:.
[‘Anitha’, ‘Lavanya’, ‘SaiSree’, ‘Tharani’, ‘Thilothamma’]
[‘Thilothamma’, ‘Tharani’, ‘SaiSree’, ‘Lavanya’, ‘Anitha’]

Students can Download Tamil Nadu 12th Economics Model Question Paper 5 English Medium Pdf, Tamil Nadu 12th Economics Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

TN State Board 12th Economics Model Question Paper 5 English Medium

General Instructions:

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

Time: 3.00 Hours
Maximum Marks: 90

PART – I

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

Question 1.
Identify the flow variable.
(a) money supply
(b) assets
(c) income
(d) foreign exchange reserves
Answer:
(c) income

Question 2.
Economic planning is an important feature of Economy………..
(a) Mixed
(b) Capitalism
(c) Socialism
(d) Traditional
Answer:
(a) Mixed

Question 3.
The financial year in India is…………
(a) April 1 to March 31
(b) March 1 to April 30
(c) March 1 to March 16
(d) January I to December 31
Answer:
(a) April 1 to March 31

Question 4.
Match the following and choose the correct answer by using codes given below:

Code:

Answer:
(b) A-2, B-3, C-1, D-4

Question 5.
Aggregate supply is equal to…………
(a) C + I + G
(b) C + S + G + (x – m)
(c) C + S + T + (x – m)
(d) C + S + T + Rf
Answer:
(d) C + S + T + Rf

Question 6.
……….. means that persons who are willing to work and able to work must have employment or a job.
(a) Full employment
(b) Unemployment
(c) Educational unemployment
(d) Seasonal unemployment
Answer:
(a) Full employment

Question 7.
The average propensity to consume is measured by
(a) C/Y
(b) C × Y
(c) Y/C
(d) C + Y
Answer:
(a) C/Y

Question 8.
Additional investment that is independent of income is called…………
(a) Autonomous Investment
(b) Autonomous Consumption
(c) Average Investment
(d) Marginal Investment
Answer:
(a) Autonomous Investment

Question 9.
Money is ……….
(a) acceptable only when it has intrinsic value
(b) constant in purchasing power
(c) the most liquid of all assets
(d) needed for allocation of resources
Answer:
(c) the most liquid of all assets

Question 10.
Match the following and choose the correct answer by using codes given below:

Code:

Answer:
(a) A-3, B-2, C-1, D-4

Question 11.
NABARD was set up in…………
(a) July 1962
(b) July 1972
(c) July 1982
(d) July 1992
Answer:
(c) July 1982

Question 12.
Open Market operations enable the ………….. to reduce the money supply in the economy.
(a) Commercial bank
(b) SBI
(c) ICICI
(d) RBI
Answer:
(d) RBI

Question 13.
Exchange rate for currencies is determined by supply and demand under the system of…………
(a) Fixed exchange rate
(b) Flexible exchange rate
(c) Constant
(d) Government regulated
Answer:
(b) Flexible exchange rate

Question 14.
Which of the following is correctly matched:
(a) David Ricardo – Factor Endowment Theory
(b) Eli Heckscher – British Economist
(c) Marshall – Swedish Economist
(d) Adam Smith – Theory of Absolute cost advantage
Answer:
(d) Adam Smith – Theory of Absolute cost advantage

Question 15.
Which of the following is not the member of SAARC?
(a) Pakistan
(b) Sri Lanka
(c) Bhutan
(d) China
Answer:
(d) China

Question 16.
Objectives of WTO are……..
(i) To ensure reduction of tariff and other barriers.
(ii) Low level of standard of living.
(a) Both (i) and (ii) are true
(b) Both (i) and (ii) are false
(c) (i) is true but (ii) is false
(d) (i) is false but (ii) is true
Answer:
(c) (i) is true but (ii) is false

Question 17.
The direct tax has the following merits except……….
(a) equity
(b) convenient
(c) certainty
(d) civic consciousness
Answer:
(b) convenient

Question 18.
The major contributor of Carbon monoxide is……….
(a) Automobiles
(b) Industrial process
(c) Stationary fuel combustion
(d) None of the above
Answer:
(a) Automobiles

Question 19.
Sarvodaya Plan was advocated by
(a) Mahatma Gandhi
(b) J.P. Narayan
(c) S. N Agarwal
(d) M.N. Roy
Answer:
(b) J.P. Narayan

Question 20.
To restructure the planning process into a bottom-up model is called
(a) Decentralized planning
(b) Scenario planning
(c) Partial planning
(d) Comprehensive planning
Answer:
(a) Decentralized planning

PART – II

Answer any seven question in which Question No. 30 is compulsory. [7 x 2 = 14]

Question 21.
What is meant by an ‘Economy’?
Answer:
An economy is referred to any system or area where economic activities are carried out. Each economy has its own character. Accordingly, the functions or activities also vary. An economy, the fundamental economic activities are production and consumption.

Question 22.
Define GDP deflator.
Answer:
GDP deflator is an index of price changes of goods and services included in GDP. It is a price index which is calculated by dividing the nominal GDP in a given year by the real GDP for the same year and multiplying it by 100.
GDP deflator = \(\frac{nominal GDP}{real GDP}\) × 100

Question 23.
Write the headlines of difficulties in Measuring National Income.
Answer:
Difficulties in Measuring National Income:

1. Transfer payments
2. Difficulties in assessing depreciation allowance
3. Unpaid services
4. Income from illegal activities
5. Production for self-consumption and changing price
6. Capital Gains
7. Statistical problems

Question 24.
What are the components of aggregate supply?
Answer:
Aggregate supply has the following components:

1. Aggregate (desired) consumption expenditure (C)
2. Aggregate (desired) private savings (S)
3. Net tax payments (T) (Total tax payment to be received by the government minus transfer payments, subsidy and interest payments to be incurred by the government) and
4. Personal (desired) transfer payments to the foreigners (Rf) (eg. Donations to international relief efforts)

Question 25.
What do you mean by propensity to consume?
Answer:
The consumption function or propensity to consume refers to income consumption relationship. It is a “functional relationship between two aggregates viz., total consumption and gross national income.”
Symbolically, the relationship is represented as C = f (Y)
Where, C = Consumption; Y = Income; f = Function

Thus the consumption function indicates a functional relationship between C and Y, where C is the dependent variable and Y is the independent variable, i.e., C is determined by Y. This relationship is based on the ceteris paribus (other things being same) assumption, as only income consumption relationship is considered and all possible influences on consumption are held constant.

Question 26.
Write Fisher’s Quantity Theory of money equation.
Answer:
The general form of equation given by Fisher is MV = PT. Fisher points out that in a country during any given period of time, the total quantity of money (MV) will be equal to the total value of all goods and services bought and sold (PT)
MV = PT

Question 27.
What are the credit control measures?
Answer:

Question 28.
Specify any two affiliates of World Bank Group.
Answer:

Question 29.
Specify the meaning of seed ball.
Answer:

1. A seed ball (or seed bomb) is a seed that has been wrapped in soil materials, usually a mixture of clay and compost, and then dried.
2. Essentially, the seed is ‘pre-planted’ and can be sown by depositing the seed ball anywhere suitable for the species, keeping the seed safely until the proper germination window arises.
3. Seed balls are an easy and sustainable way to cultivate plants that provide a larger window of time when the sowing can occur.

Question 30.
What is GNP?
Answer:
Gross National Product (GNP):
GNP is the total market value of all final goods and services produced within a nation in a particular year, plus income earned by its citizens (including income of those located abroad), minus income of non-residents located in that country.

GNP is one measure of the economic condition of a country, under the assumption that a higher GNP leads to a higher quality of living, all other things being equal.

PART – III

Answer any seven question in which Question No. 40 is compulsory. [7 x 3 = 21]

Question 31.
Describe the different types of economic systems.
Answer:
There are three major types of economic systems. They are:
Capitalistic Economy (Capitalism):

1. Capitalistic economy is also termed as a free economy (Laissez faire, in Latin) or market
   economy where the role of the government is minimum and market determines the economic activities.
2. The means of production in a capitalistic economy are privately owned.
3. Manufacturers produce goods and services with profit motive.
4. The private individual has the freedom to undertake any occupation and develop any skill.
5. The USA, West Germany, Australia and Japan are the best examples for capitalistic economies.
6. However, they do undertake large social welfare measures to safeguard the downtrodden people from the market forces.

Question 32.
Classify the concepts of Macro Economics.
Answer:
The important concepts used in macro economics are presented below:
Stock and Flow Variables: Variables used in economic analysis are classified as stock and flow. Both stock and flow variables may increase or decrease with time.

Stock refers to a quantity of a commodity measured at a point of time. In macro economics, money supply, unemployment level, foreign exchange reserves, capital etc are examples of stock variables.

Flow variables are measured over a period of time. National Income, imports, exports, consumption, production, investment etc are examples of flow variables.

Economic Models A model is a simplified representation of real situation. Economists use models to describe economic activities, their relationships and their behaviour. A model is an explanation of how the economy, or part of the economy, works. Most economic models are built with mathematics, graphs and equations, and attempt to explain relationships between economic variables. The commonly used economic models are the supply-demand models and circular flow models and Smith models.

Question 33.
Write briefly about national income and welfare.
Answer:
National Income and Welfare:
National Income is considered as an indicator of the economic wellbeing of a country. The per capita income as an index of economic welfare suffers from limitations which are stated below:

1. The economic welfare depends upon the composition of goods and services provided. The greater the proportion of capital goods over consumer goods, the improvement in economic welfare will be lesser.
2. Higher GDP with greater environmental hazards such as air, water and soil pollution will be little economic welfare.
3. The production of war goods will show the increase in national output but not welfare.
4. An increase in per capita income may be due to employment of women and children or forcing workers to work for long hours. But it will not promote economic welfare.

Question 34.
What do you mean by aggregate demand? Mention its components.
Answer:
The aggregate demand is the amount of money which entrepreneurs expect to get by selling the output produced by the number of labourers employed. Therefore, it is the expected income or revenue from the sale of output at different levels of employment.
Aggregate demand has the following four components:

1. Consumption demand
2. Investment demand
3. Government expenditure and
4. Net Export (export – import)

Question 35.
Differentiate autonomous and induced investment.
Answer:

Question 36.
Explain the Trade cycle Depression.
Answer:
Depression:

1. During depression the level of economic activity becomes extremely low.
2. Firms incur losses and closure of business becomes a common feature and the ultimate result is unemployment.
3. Interest prices, profits and wages are low.
4. The agricultural class and wage earners would be worst hit.
5. Banking institutions will be reluctant to advance loans to businessmen.
6. Depression is the worst phase of the business cycle.
7. Extreme point of depression is called as “trough”, because it is a deep point in business cycle.
8. Any person fell down in deeps could not come out from that without other’s help.
9. Similarly, an economy fell down in trough could not come out from this without external help.
10. Keynes advocated that autonomous investment of the government alone can help the economy to come out from the depression.

Question 37.
Explain the Net Barter Terms of Trade.
Answer:
1. Net Barter Terms of Trade:
This type was developed by Taussig in 1927. The ratio between the prices of exports and of imports is called the “net barter terms of trade’. It is named by Viner as the ‘commodity terms of trade’.
It is expressed as:
T_n = (P_x /P_m) × 100 Where,
T_n = Net Barter Terms of Trade
P_x = Index number of export prices
P_m = Index number of import prices
This is used to measure the gain from international trade. If ‘Tn’ is greater than 100, then it is a favourable terms of trade which will mean that for a rupee of export, more of imports can be received by a country.

Question 38.
What is Multilateral Agreement?
Answer:

1. Multilateral trade agreement: It is a multi national legal or trade agreements between countries. It is an agreement between more than two countries but not many.
2. The various agreements implemented by the WTO such as TRIPS, TRIMS, GATS, AoA, MFA have been discussed.

Question 39.
What is primary deficit?
Answer:
Primary Deficit:
Primary deficit is equal to fiscal deficit minus interest payments. It shows the real burden of the government and it does not include the interest burden on loans taken in the past. Thus, primary deficit reflects borrowing requirement of the government exclusive of interest payments.
Primary Deficit (PD) = Fiscal deficit (PD) – Interest Payment (IP)

Question 40.
Explain different types of air pollution.
Answer:
Types of Air pollution:

1. Indoor Air Pollution: It refers to toxic contaminants that we encounter in our daily lives in our homes, schools and workplaces. For example, cooking and heating with solid fuels on open fires or traditional stoves results in high levels of indoor air pollution.
2. Outdoor Air Pollution: It refers to ambient air. The common sources of outdoor air pollution are caused by combustion processes from motor vehicles, solid fuel burning and industry.

PART – IV

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

Question 41 (a).
Compare the features of capitalism and socialism.
Answer:
Features of Socialism:

1. Public Ownership of Means of Production: All resources are owned by the government. It means that all the factors of production are nationalized and managed by the public authority.
2. Central Planning: Planning is an integral part of a socialistic economy. In this system, all decisions are undertaken by the central planning authority.
3. Maximum Social Benefit: Social welfare is the guiding principle behind all economic ‘ activities. Investments are planned in such a way that the benefits are distributed to the society at large.
4. Non-existence of Competition: Under the socialist economic system there is absence of competition in the market. The state has full control over production and distribution of goods and services. The consumers will have a limited choice.
5. Absence of Price Mechanism: The pricing system works under the control and regulation of the central planning authority.
6. Equality of Income: Another essential feature of socialism is the removal and reduction of economic inequalities. Under socialism private property and the law of inheritance do not exist.

[OR]

(b) What are the difficulties involved in the measurement of national income?
Answer:
Difficulties in Measuring National Income:

1. In India, a special conceptual problem is posed by the existence of a large, unorganised and non-monetised subsistence sector where the barter system still prevails for transacting goods and services.
2. Here, a proper valuation of output is very difficult.

Transfer payments:

1. Government makes payments in the form of pensions, unemployment allowance, subsidies, etc. These are government expenditure.
2. But they are not included in the national income.
3. Because they are paid without adding anything to the production processes.
4. During a year, Interest on national debt is also considered transfer payments because it is paid by the government to individuals and firms on their past savings without any productive work.

Difficulties in assessing depreciation allowance:

1. The deduction of depreciation allowances, accidental damages, repair and replacement charges from the national income is not an easy task.
2. It requires high degree of judgment to assess the depreciation allowance and other charges.

Unpaid services:

1. A housewife renders a number of useful services like preparation of meals, serving, tailoring, mending, washing, cleaning, bringing up children, etc.
2. She is not paid for them and her services are not directly included in national income.

Income from illegal activities:

1. Income earned through illegal activities like gambling, smuggling, illicit extraction of liquor, etc., is not included in national income.
2. Such activities have value and satisfy the wants of the people but they are not considered as productive from the point of view of society.

Production for self-consumption and changing price:

1. Farmers keep a large portion of food and other goods produced on the farm for self consumption.
2. The problem is whether that part of the produce which is not sold in the market can be included in national income or not.

Capital Gains:

1. The problem also arises with regard to capital gains.
2. Capital gains arise when a capital asset such as a house, other property, stocks or shares, etc. is sold at higher price than was paid for it at the time of purchase.
3. Capital gains are excluded from national income.

Statistical problems:

1. There are statistical problems, too. Great care is required to avoid double counting. Statistical data may not be perfectly reliable, when they are compiled from numerous sources.
2. Skill and efficiency of the statistical staff and cooperation of people at large are also equally important in estimating national income.

Question 42 (a).
Explain the differences between classical theory and Keynes theory.
Answer:

[OR]

(b) Explain the features of Keynesianism.
Answer:

1. Short-run equilibrium
2. Saving is a vice
3. The function of money is a medium of exchange on the one side and a store of value on the other side.
4. Macro approach to national problems
5. State intervention is advocated.
6. Applicable to all situations – full employment and less than full employment.
7. Capitalism has inherent contradictions.
8. Budgeting should be adjusted to the requirements of economy.
9. The equality between saving and investment is advanced through changes in income.
10. Rate of interest is determined by the demand for and supply of money.
11. Rate of interest is a flow.
12. Demand creates its own supply.
13. Rate of interest is a reward for parting with liquidity.

Question 43 (a).
What are the differences between MEC and MEI?
Answer:

[OR]

(b) Describe the phases of Trade cycle.
Answer:
Phases of Trade Cycle:
The four different phases of trade cycle is referred to as

1. Boom
2. Recession
3. Depression and
4. Recovery.

These are illustrated in the figure.

Phases of Trade Cycle The Economic Cycle
1. Boom or Prosperity Phase:

• The full employment and the movement of the economy beyond full employment is characterized as boom period.
• During this period, there is hectic activity in economy.
• Money wages rise, profits increase and interest rates go up.
• The demand for bank credit increases and there is all-round optimism.

2. Recession:

• The turning point from boom condition is called recession.
• This happens at higher rate, than what was earlier.
• Generally, the failure of a company or bank bursts the boom and brings a phase of recession.
• Investments are drastically reduced, production comes down and income and profits decline.
• There is panic in the stock market and business activities show signs of dullness.
• Liquidity preference of the people rises and money market becomes tight.

3. Depression:

• During depression the level of economic activity becomes extremely low.
• Firms incur losses and closure of business becomes a common feature and the ultimate result is unemployment.
• Interest prices, profits and wages are low. The agricultural class and wage earners would be worst hit.
• Banking institutions will be reluctant to advance loans to businessmen.
• Depression is the worst phase of the business cycle.
• Extreme point of depression is called as “trough”, because it is a deep point in business cycle.

4. Recovery:

• After a period of depression, recovery sets in.
• This is the turning point from depression to revival towards upswing.
• It begins with the revival of demand for capital goods.
• Autonomous investments boost the activity.
• The demand slowly picks up and in due course the activity is directed towards the upswing with more production, profit, income, wages and employment.
• Recovery may be initiated by innovation or investment or by government expenditure (autonomous investment).

Question 44 (a).
What are the functions of NABARD?
Answer:
Functions of NABARD:
NABARD has inherited its apex role from RBI i.e, it is performing all the functions performed by RBI with regard to agricultural credit.
(i) NABARD acts as a refinancing institution for all kinds of production and investment credit to agriculture, small-scale industries, cottage and village industries, handicrafts and rural crafts and real artisans and other allied economic activities with a view to promoting integrated rural development.

(ii) NABARD gives long-term loans (upto 20 Years) to State Government to enable them to subscribe to the share capital of co-operative credit societies.

(iii) NABARD gives long-term loans to any institution approved by the Central Government or contribute to the share capital or invests in securities of any institution concerned with agriculture and rural development.

(iv) NABARD has the responsibility of co-ordinating the activities of Central and State Governments, the Planning Commission (now NITI Aayog) and other all India and State level institutions entrusted with the development of small scale industries, village and cottage industries, rural crafts, industries in the tiny and decentralized sectors, etc.

(v) It maintains a Research and Development Fund to promote research in agriculture and rural development

[OR]

(b) Discuss the various types of disequilibrium in the balance of payments.
Answer:
Types BOP Disequilibrium:
There are three main types of BOP Disequilibrium, which are discussed below.

1. Cyclical Disequilibrium,
2. Secular Disequilibrium,
3. Structural Disequilibrium.

1. Cyclical Disequilibrium: Cyclical disequilibrium occurs because of two reasons. First, two countries may be passing through different phases of business cycle. Secondly, the elasticities of demand may differ between countries.

2. Secular Disequilibrium: The secular or long-run disequilibrium in BOP occurs because of long-run and deep seated changes in an economy as it advances from one stage of growth to another. In the initial stages of development, domestic investment exceeds domestic savings and imports exceed exports, as it happens in India since 1951.

3. Structural Disequilibrium: Structural changes in the economy may also cause balance of payments disequilibrium. Such structural changes include development of alternative sources of supply, development of better substitutes, exhaustion of productive resources or changes in transport routes and costs.

Question 45 (a).
Explain the objectives of IMF.
Answer:
Objectives Of IMF:

1. To promote international monetary cooperation among the member nations.
2. To facilitate faster and balanced growth of international trade.
3. To ensure exchange rate stability by curbing competitive exchange depreciations.
4. To eliminate or reduce exchange controls imposed by member nations.
5. To establish multilateral trade and payment system in respect of current transactions instead of bilateral trade agreements.
6. To promote the flow of capital from developed to developing nations.
7. To solve the problem of international liquidity.

[OR]

(b) Explain the scope of public finance.
Answer:
Scope of Public Finance:
The subject ‘Public Finance’ includes five major sub-divisions, viz., Public Revenue, Public Expenditure, Public Debt, Financial Administration and Fiscal Policy.

(i) Public Revenue:
Public revenue deals with the methods of raising public revenue such as tax and non-tax, the principles of taxation, rates of taxation, impact, incidence and shifting of taxes and their effects.

(ii) Public Expenditure:
This part studies the fundamental principles that govern the Government expenditure, effects of public expenditure and control of public expenditure.

(iii) Public Debt:
Public debt deals with the methods of raising loans from internal and external sources. The burden, effects and redemption of public debt fall under this head.

(iv) Financial Administration:

1. This part deals with the study of the different aspects of public budget.
2. The budget is the Annual master financial plan of the Government.
3. The various objectives and steps in preparing a public budget, passing or sanctioning, allocation evaluation and auditing fall within financial administration.

(v) Fiscal Policy:
Taxes, subsidies, public debt and public expenditure are the instruments of fiscal policy.

Question 46 (a).
Mention the Comparison of Direct and Indirect taxes.
Answer:

[OR]

(b) Write the limitations of statistics.
Answer:
Statistics with all its wide application in every sphere of human activity has its own limitations. Some of them are given below.
(i) Statistics is not suitable to the study of qualitative phenomenon: Since statistics is basically a science and deals with a set of numerical data. It is applicable to the study of quantitative measurements. As a matter of fact, qualitative aspects like empowerment, leadership, honesty, poverty, intelligence etc., cannot be expressed numerically and statistical analysis cannot be directly applied on these qualitative phenomena.

(ii) Statistical laws are not exact: It is well known that mathematical and.physical sciences are exact. But statistical laws are not exact and statistical laws are only approximations. Statistical conclusions are not universally true. They are true only on an average.

(iii) Statistics table may be misused: Statistics must be used only by experts; otherwise, statistical methods are the most dangerous tools on the hands of the inexpert. The use of statistical tools by the inexperienced and untrained persons might lead to wrong conclusions, (zv) Statistics is only one of the methods of studying a problem: Statistical method does not provide complete solution of the problems because problems are to be studied taking the background of the countries culture, philosophy, religion etc., into consideration. Thus the statistical study should be supplemented by other evidences.

Question 47 (a).
Explain the Environmental quality?
Answer:

1. Environmental quality is a set of properties and characteristics of the environment either generalized or local, as they impinge on human beings and other organisms.
2. It is a measure of the condition of an environment relative to the requirements of one or more species and to any human need. Environmental quality has been continuously declining due to capitalistic mode of functioning.
3. Environment is a pure public good that can be consumed simultaneously by everyone and from which no one can be excluded.
4. A pure public good is one for which consumption is non-revival and from which it is impossible to exclude a consumer.
5. Pure public goods pose a freerider problem.
6. As a result, resources are depleted.
7. The contribution of the nature to GDP as well as depletion of natural resources are not accounted in the present system of National Income Enumeration.

[OR]

(b) What are the approaches to Economic Development?
Answer:
There are two main approaches to the concept of development viz

1. the traditional approach and
2. the new welfare oriented approach.

1. Traditional Approach:

• The traditional approach defines development strictly in economic terms.
• The increase in GNP is accompanied by decline in share of agriculture in output and employment while those of manufacturing and service sectors increase.
• It emphasizes the importance of industrialization.
• It was assumed that growth in GNP per capita would trickle down to people at the bottom.

2. New Welfare oriented Approach:

• During 1970s, economic development was redefined in terms of reduction of poverty, ‘inequality’ and unemployment within the context of a growing economy.
• In this phase, ‘Redistribution with Growth’ became the popular slogan.
• To quote Michael P. Todaro, “Development must, therefore, be conceived as a multidimensional process involving major changes in social structures, popular attitudes and national institutions as well as the acceleration of growth, the reduction of inequality and the eradication of absolute poverty”.