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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
View Answer
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
View Answer
Answer:reflexive but not symmetric
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3
Let f: [0, 1| → [0, 1| be defined by
A
Constant
B
1 + x
C
x
D
None of these
View Answer
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
View Answer
5
f(x) =
is the domain of
A
R – {-1, -2}
B
(- 2, ∞) .
C
R- {- 1,-2, -3}
D
(-3, + ∞) – {-1, -2}
View Answer
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
View Answer
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
View Answer
8
The maximum number of equivalence relations on the set A = {1, 2, 3} are
View Answer
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
View Answer
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
View Answer
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
View Answer
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)}.
View Answer
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
View Answer
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 .
View Answer
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)}
View Answer
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
View Answer
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)}
View Answer
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
View Answer
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)
View Answer
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
View Answer
Chapters
is the domain of