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NCERT Solutions for class 11 Maths | Chapter 2 - Relations and Functions

Questions
1 The domain of the definition of the real function f(x) = √(log12 x2 ) of the real variable x is
A x > 0
B |x| ≥ 1
C |x| > 4
D x ≥ 4

Answer:|x| ≥ 1
2 The number of binary operations on the set {1, 2} are
A 8
B 10
C 16
D 20

Answer:16
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3 A function f(x) is said to be an odd function if
A f(-x) = f(x)
B f(-x) = -f(x)
C f(-x) = k * f(x) where k is a constant
D None of these

Answer:f(-x) = -f(x)
4 The domain of modulus function f(x) = |x| is
A R
B R - {0}
C (0, ∞)
D None of these

Answer:R
5 Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
A 1
B 2
C 3
D 4

Answer:1
6 The function f(x) = sin (‎πx/2) + 2cos (πx/3) - tan (πx/4) is periodic with period
A 4
B 6
C 8
D 12

Answer:12
7 The function f(x) = |cos x| is periodic with period
A π
B π/2
C π/3
D 2π

Answer:π
8 The function sin[log{x + √(x2 + 1)}] is a/an
A Even function
B Odd function
C Either even or odd function
D Neither even nor odd function

Answer:Odd function
9 The values of b and c for which the identity f(x + 1) - f(x) = 8x + 3 is satisfied where f(x) = bx2 + cx + d, are
A 4, 1
B 4, -1
C 2, 4
D -2, 4

Answer:4, -1
10 The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period
A 4
B 6
C 12
D 24

Answer:4
11 The domain for which the functions defined by f (x) =3x2-1 and g(x)=3+x are equal is
A {-1, 4/3}
B (-1, 4/3)
C [-1, 4/3]
D (-1, 4/3]

Answer:{-1, 4/3}
12 Let f and g be two functions given by

f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}

g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)}

then. Domain of f + g is

A {2,8,10}
B {2,10,11}
C {2, 5,10}
D {2,7,8}

Answer:{2,8,10}
13 Let P ={1,2,3,4} and Q={11,12,13,14}. Relation are defined from P to Q as R:P-> Q

Which of the following relations is functions?

A R ={(1,11),(2,12),(3,13),(4,14)}
B R ={(1,11),(1,11),(3,11), (4,11),(4,14)}
C R ={(1,11),(2,12),(3,13)}
D R ={(1,11),(2,11),(3,11), (3,12)}

Answer:R ={(1,11),(2,12),(3,13),(4,14)}
14 The value {-.95} where {.} is the fractional part is
A .95
B .-05
C -.95
D .05

Answer:.05
15 Let f(x)=|x−1| +|x−3|+|x−4|, which one of the below is incorrect
A f(0)=7
B f(1) =4
C f(3.5)=3.5
D f(5)=7

Answer:f(0)=7
16 Let R be the relation on the set N of natural numbers defined by

R={(a,b): a + 3b=12 , a ∈ N ,b ∈ N}

A R= {(9,1},(6,2),(3,3)}
B Range of R = {1,2,3}
C Domain of R ={9,6,3}
D 1

Answer:None of these
17 The value of x and y if (x – y, x + y) = (8, 10)
A 9,1
B 8,2
C 1,9
D 2,8

Answer:9,1
18 The domain of the function f given by ƒ(x)=x2+2x+1/x2+5x+6
A R – (3, – 2)
B R – {–3, 2}
C R – {-3, – 2}
D R – [3, 2]

Answer:R – {-3, – 2}
19 Let A = {1, 2, 3} and B = {5, 7}. Then possible number of relation from A to B ?
A 256
B 64
C 16
D 32

Answer:64
20 If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and b are equal to
A a = 0, b = 2
B a = 2, b = 3
C a = 2, b = – 3
D a = – 3, b = –1

Answer:a = 2, b = – 3

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