Class 11 Maths Chapter 2 Relations and Functions Questions and Answers

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

View Answer

Answer:|x| ≥ 1

2 The number of binary operations on the set {1, 2} are

A 8

B 10

C 16

D 20

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

Answer:12

7 The function f(x) = |cos x| is periodic with period

A π

B π/2

C π/3

D 2π

View Answer

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

View Answer

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

View Answer

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

View Answer

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]

View Answer

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}

View Answer

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)}

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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]

View Answer

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

View Answer

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

View Answer

Answer:a = 2, b = – 3

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