1
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let $$\alpha $$ and $$\beta $$ be non zero real numbers such that $$2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1$$. Then which of the following is/are true?
A
$$\sqrt 3 \tan \left( {{\alpha \over 2}} \right) - \tan \left( {{\beta \over 2}} \right) = 2$$
B
$$\tan \left( {{\alpha \over 2}} \right) - \sqrt 3 \tan \left( {{\beta \over 2}} \right) = 0$$
C
$$\tan \left( {{\alpha \over 2}} \right) + \sqrt 3 \tan \left( {{\beta \over 2}} \right) = 0$$
D
$$\sqrt 3 \tan \left( {{\alpha \over 2}} \right) + \tan \left( {{\beta \over 2}} \right) = 2$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let $$f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$$

for x $$ \ne $$ 1. Then
A
$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ = 0
B
$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ does not exist
C
$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ = 0
D
$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ does not exist
3
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
If $$g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt$$, then
A
$$g'\left( { - {\pi \over 2}} \right) = 0$$
B
$$g'\left( { - {\pi \over 2}} \right) = - 2\pi $$
C
$$g'\left( {{\pi \over 2}} \right) = 2\pi $$
D
$$g'\left( {{\pi \over 2}} \right) = 0$$
4
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
If $$f(x) = \left| {\matrix{ {\cos 2x} & {\cos 2x} & {\sin 2x} \cr { - \cos x} & {\cos x} & { - \sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right|$$,

then
A
f(x) attains its minimum at x = 0
B
f(x) attains its maximum at x = 0
C
f'(x) = 0 at more than three points in ($$-$$$$\pi $$, $$\pi $$)
D
f'(x) = 0 at exactly three points in ($$-$$$$\pi $$, $$\pi $$)
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