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Free download in PDF Class 12 Maths Chapter 1 Relations and Functions Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
[A]
symmetric but not transitive
[B]
transitive but not symmetric
[C]
neither symmetric nor transitive
[D]
both symmetric and transitive
Answer: transitive but not symmetric
(2)
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
[A]
reflexive but not symmetric
[B]
reflexive-but not transitive.
[C]
symmetric and transitive
[D]
neither symmetric, nor transitive
Answer: reflexive but not symmetric
(3)
Let f: [0, 1| → [0, 1| be defined by
[A]
Constant
[B]
1 + x
[C]
x
[D]
None of these
(4)
If f: R → R defined by f(x) = 2x + 3 then f-1(x) =
[A]
2x – 3
[B]
x-3/2
[C]
x+3/2
[D]
None of these
(5)
f(x) =
is the domain of
[A]
R – {-1, -2}
[B]
(- 2, ∞) .
[C]
R- {- 1,-2, -3}
[D]
(-3, + ∞) – {-1, -2}
Answer: (-3, + ∞) – {-1, -2}
(6)
f: A → B will be an into function if
[A]
range (f) ⊂ B
[B]
f(a) = B
[C]
B ⊂ f(a)
[D]
f(b) ⊂ A
(7)
If f : R → R such that f(x) = 3x then what type of a function is f?
[A]
one-one onto
[B]
many one onto
[C]
one-one into
[D]
many-one into
(8)
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(9)
Let f: N → R be the function defined by f(x) = 2x−1/2 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 3/2 is
[A]
1
[B]
0
[C]
7/2
[D]
None of these
(10)
If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
[A]
1/3 (x + 4)
[B]
1/3 (x – 4)
[C]
3x – 4
[D]
undefined
(11)
If f(x) is an odd differentiable function on R, then df(x)/dx is
[A]
an even function
[B]
an odd function
[C]
neither even nor odd function
[D]
none of these
(12)
Let A = {1,2,3} . Which of the following relations is a function from A to A ?
[A]
{(1,1),(2,1),(3,2)}
[B]
{(1,1),(1,2)}
[C]
{(2,3),(3,1)}
[D]
{(1,1),(2,2),(3,3),(1,3),(3,1)}.
Answer: {(1,1),(2,1),(3,2)}
(13)
Let A = {a,b,c} and R = {(a,a),(b,b),(c,c),(b,c),(a,b)} be a relation on A, then R is
[A]
symmetric
[B]
transitive
[C]
reflexive
[D]
none of these
(14)
Let ƒ : N → N be defined by the rule f (x) = 2x + 1 for all x ∈ N, then f is
[A]
one - one
[B]
onto
[C]
both one-one and onto
[D]
none of these .
(15)
Let A = {1,2,3} and B = {2,3,4}, then which of the following is a funtion from A to B ?
[A]
{(1,2),(1,3),(2,3)(3,3)}
[B]
{(1,3),(2,4)}
[C]
{(1,3),(2,3),(3,3)}
[D]
{(1,2),(2,3),(3,4),(3,2)}
Answer: {(1,3),(2,3),(3,3)}
(16)
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
[A]
0
[B]
1
[C]
2
[D]
More than 2
(17)
let A = {1,2,3} . Which of the following functions on A is invertible ?
[A]
f = {(1,1),(2,1),(3,1)}
[B]
f = {(1,2),(2,3),(3,1)}
[C]
f = {(1,1),(2,3),(3,2)}
[D]
f = {(1,1),(2,2),(3,1)}
Answer: f = {(1,2),(2,3),(3,1)}
(18)
Let f (x) = x2 and g (x) = √x , then
[A]
(gof) (x) = |x| for all x ∈ R
[B]
(fog) (x) = x2 for all x ∈ R
[C]
(fog) (x) = (gof) (x) for all x ∈ R
[D]
none of these
Answer: (gof) (x) = |x| for all x ∈ R
(19)
If log12 27 = a then the value of log6 16 is
[A]
(3 - a)/{(3 + a)
[B]
2*(3 - a)/{(3 + a)
[C]
3*(3 - a)/{(3 + a)
[D]
4*(3 - a)/{(3 + a)
Answer: 4*(3 - a)/{(3 + a)
(20)
The range of the function f(x) = |x - 3| is
[A]
R
[B]
(0, ∞)
[C]
(-∞, 0)
[D]
None of these
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