1
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]
2
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
3
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
$$1 + \sqrt {{2 \over 3}}$$
4
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

Let $$f:(0,1) \to R$$ be defined by $$f(x) = {{b - x} \over {1 - bx}}$$, where be is a constant such that $$0 < b < 1$$. Then

A
f is not invertible on (0, 1).
B
f $$\ne$$ f$$-$$1 on (0, 1) and $$f'(b) = {1 \over {f'(0)}}$$.
C
f = f$$-$$1 on (0, 1) and $$f'(b) = {1 \over {f'(0)}}$$.
D
f$$-$$1 is differentiable on (0, 1).
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