1
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
For $$x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,$$

and $$\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,$$ then :
A
$$g$$ is not differentiable at $$x=0$$
B
$$g'\left( 0 \right) = \cos \left( {\log 2} \right)$$
C
$$g'\left( 0 \right) = - \cos \left( {\log 2} \right)$$
D
$$g$$ is differentiable at $$x=0$$ and $$g'\left( 0 \right) = - \sin \left( {\log 2} \right)$$
2
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}}$$ then $$log$$ $$p$$ is equal to :
A
$${1 \over 2}$$
B
$${1 \over 4}$$
C
$$2$$
D
$$1$$
3
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
A value of $$\theta \,$$ for which $${{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}$$ is purely imaginary, is :
A
$${\sin ^{ - 1}}\left( {{{\sqrt 3 } \over 4}} \right)$$
B
$${\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)\,$$
C
$${\pi \over 3}$$
D
$${\pi \over 6}$$
4
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
A
3$$a$$2 - 26$$a$$ + 55 = 0
B
3$$a$$2 - 32$$a$$ + 84 = 0
C
3$$a$$2 - 34$$a$$ + 91 = 0
D
3$$a$$2 - 23$$a$$ + 44 = 0
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