1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :
A
both R1 and R2 are not symmetric.
B
R1 is not symmetric but it is transitive.
C
R2 is symmetric but it is not transitive.
D
both R1 and R2 are transitive.
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The function f : N $$\to$$ N defined by f (x) = x $$-$$ 5 $$\left[ {{x \over 5}} \right],$$ Where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :
A
one-one and onto
B
one-one but not onto.
C
onto but not one-one.
D
neither one-one nor onto.
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Let f(x) = 210.x + 1 and g(x)=310.x $$-$$ 1. If (fog) (x) = x, then x is equal to :
A
$${{{3^{10}} - 1} \over {{3^{10}} - {2^{ - 10}}}}$$
B
$${{{2^{10}} - 1} \over {{2^{10}} - {3^{ - 10}}}}$$
C
$${{1 - {3^{ - 10}}} \over {{2^{10}} - {3^{ - 10}}}}$$
D
$${{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}$$
4
JEE Main 2017 (Offline)
+4
-1
The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is
A
invertible
B
injective but not surjective.
C
surjective but not injective
D
neither injective nor surjective.
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