1
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$f(x) = \sin \left( {{\pi \over 6}\sin \left( {{\pi \over 2}\sin x} \right)} \right)$$ for all $$x \in R$$ and g(x) = $${{\pi \over 2}\sin x}$$ for all x$$\in$$R. Let $$(f \circ g)(x)$$ denote f(g(x)) and $$(g \circ f)(x)$$ denote g(f(x)). Then which of the following is/are true?

A
Range of f is $$\left[ { - {1 \over 2},{1 \over 2}} \right]$$.
B
Range of f $$\circ$$ g is $$\left[ { - {1 \over 2},{1 \over 2}} \right]$$.
C
$$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {g(x)}} = {\pi \over 6}$$.
D
There is an x$$\in$$R such that (g $$\circ$$ f)(x) = 1.
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
For every pair of continuous function f, g : [0, 1] $$\to$$ R such that max {f(x) : x $$\in$$ [0, 1]} = max {g(x) : x $$\in$$ [0, 1]}. The correct statement(s) is (are)
A
[f(c)]2 + 3f(c) = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
B
[f(c)]2 + f(c) = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
C
[f(c)]2 + 3f(c) = [g(c)]2 + g(c) for some c $$\in$$ [0, 1]
D
[f(c)]2 = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R$$ be given by $$f(x) = {[\log (\sec x + \tan x)]^3}$$. Then,
A
f(x) is an odd function
B
f(x) is a one-one function
C
f(x) is an onto function
D
f(x) is an even function
4
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

Let $$f:( - 1,1) \to R$$ be such that $$f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}$$ for $$\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)$$. Then the value(s) of $$f\left( {{1 \over 3}} \right)$$ is(are)

A
$$1 - \sqrt {{3 \over 2}}$$
B
$$1 + \sqrt {{3 \over 2}}$$
C
$$1 - \sqrt {{2 \over 3}}$$
D
$$1 + \sqrt {{2 \over 3}}$$
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