1
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
If the line x = $$\alpha $$ divides the area of region R = {(x, y) $$ \in $$R2 : x3 $$ \le $$ y $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ 1} into two equal parts, then
A
2$$\alpha $$4 $$-$$ 4$$\alpha $$2 + 1 =0
B
$$\alpha $$4 + 4$$\alpha $$2 $$-$$ 1 =0
C
$${1 \over 2} < \alpha < 1$$
D
0 < $$\alpha $$ $$ \le $$ $${1 \over 2}$$
2
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
$$\sqrt 3 \tan \left( {{\alpha \over 2}} \right) + \tan \left( {{\beta \over 2}} \right) = 2$$
3
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
4
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
$$g'\left( {{\pi \over 2}} \right) = 0$$
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