1
IIT-JEE 2011 Paper 1 Offline
Numerical
+4
-0
Let $$f\left( \theta \right) = \sin \left( {{{\tan }^{ - 1}}\left( {{{\sin \theta } \over {\sqrt {\cos 2\theta } }}} \right)} \right),$$ where $$ - {\pi \over 4} < \theta < {\pi \over 4}.$$

Then the value of $${d \over {d\left( {\tan \theta } \right)}}\left( {f\left( \theta \right)} \right)$$ is

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2
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-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 $$Q - P \ne \emptyset $$
B
$$Q \not\subset P$$
C
$$P \not\subset Q$$
D
$$P = Q$$
3
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1

Let f : R $$\to$$ R be a function such that $$f(x + y) = f(x) + f(y),\,\forall x,y \in R$$. If f(x) is differentiable at x = 0, then

A
f(x) is differentiable only in a finite interval containing zero.
B
f(x) is continuous $$\forall x \in R$$.
C
f'(x) is constant $$\forall x \in R$$.
D
f(x) is differentiable except at finitely many points.
4
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1

Let M and N be two 3 $$\times$$ 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)$$-$$1(MN$$-$$1)T is equal to

A
M2
B
$$-$$N2
C
$$-$$M2
D
MN
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