- Which of the following
statements is not correct for the
relation R defined by aRb if and
only if b lives within one kilometer
from a?
(a) R is reflexive (b) R is
symmetric (c) R is not anti-
symmetric (d) None of these - Let X be any non-empty set
containing n elements. Then what
is the number of relations on X?
(a) (b) (c) (d)
- On the set Z of integers,
relation R is defined as “a Rb a
- 2b is an integral multiple of 3”.
Which one of the following
statements is correct for R?
(a) R is only reflexive (b) R is only
symmetric (c) R is only transitive
(d) R is an equivalence relation
- If f(x) = , then
(⏟ ) ( ) is
19 times
equal to:
(a) ( ) (b). /
(c) (^ ) (d)
x
- If 2f (x + 1) + f. /= 2x and x
≠ -1, then f (2) is equal to:
(a) -1 (b) 2 (c) 5/3 (d) 5/2
- IF f(x)=^ , then (fof) (2) is
equal to:
(a) 1 (b) 3 (c) 4 (d) 2
- Let the function f be defined by
f(x)=^ , then (x) is:
(a) (b)^ (c) (d)^ - If f(x)=^ , (x ≠ -1) then,
(x) equals to:
(a) f(x) (b) 1/f(x) (c) –f(x) (d) -
1/f(x) - The inverse of the function
is:^
(a)^.^ / (b).
/^ (c)
.
/^ (d)
none of these- If f : R R and g : R R
defined by f(x)= 2x + 3 and g(x)=
, then the value of x for
which f(g (x)) = 25, are:
(a) ±1 (b) ±2 (c) ±3 (d) ±4 - If f(x)=^
(^)
for x^ R,
then f(2002) equals to:
(a) 1 (b) 2 (c) 3 (d) 4
- If f(x)= √
√^
(^) √
√^
,
for x > 2, then f(11) is equal to:
(a) 7/6 (b) 5/6 (c) 6/7 (d) 5/7- If (^ )=^ , x (-10, 10) and
f(x)= kf. /, then k is equal to:
(a) 0.5 (b) 0.6 (c) 0.7 (d) 0.8