1
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
$${{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}$$
2
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.
3
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let P = {$$\theta$$ : sin$$\theta$$ $$-$$ cos$$\theta$$ = $$\sqrt 2 \,\cos \theta$$}

and Q = {$$\theta$$ : sin$$\theta$$ + cos$$\theta$$ = $$\sqrt 2 \,\sin \theta$$} be two sets. Then
A
P $$\subset$$ Q and Q $$-$$ P $$\ne$$ $$\phi$$
B
Q $$\not\subset$$ P
C
P $$\not\subset$$ Q
D
P = Q
4
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
For x $$\in$$ R, x $$\ne$$ 0, Let f0(x) = $${1 \over {1 - x}}$$ and
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .

Then the value of f100(3) + f1$$\left( {{2 \over 3}} \right)$$ + f2$$\left( {{3 \over 2}} \right)$$ is equal to :
A
$${8 \over 3}$$
B
$${5 \over 3}$$
C
$${4 \over 3}$$
D
$${1 \over 3}$$
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