1
JEE Main 2016 (Offline)
+4
-1 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)
+4
-1 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 2015 (Offline)
+4
-1 $$\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)} \over {x\tan 4x}}$$ is equal to
A
2
B
$${1 \over 2}$$
C
4
D
3
4
JEE Main 2015 (Offline)
+4
-1 If the function.

$$g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.$$

is differentiable, then the value of $$k+m$$ is :
A
$${{10} \over 3}$$
B
$$4$$
C
$$2$$
D
$${{16} \over 5}$$
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