Class 11 Maths Chapter 2 Relations and Functions Questions and Answers

(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

(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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