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1
JEE Main 2016 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If    $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3},$$ then 'a' is equal to :
A
2
B
$${3 \over 2}$$
C
$${2 \over 3}$$
D
$${1 \over 2}$$
2
JEE Main 2016 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the function

f(x) = $$\left\{ {\matrix{ { - x} & {x < 1} \cr {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \cr } } \right.$$

is differentiable at x = 1, then $${a \over b}$$ is equal to :
A
$${{\pi - 2} \over 2}$$
B
$${{ - \pi - 2} \over 2}$$
C
$${{\pi + 2} \over 2}$$
D
$$ - 1 - {\cos ^{ - 1}}\left( 2 \right)$$
3
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 $$g'\left( 0 \right) = - \sin \left( {\log 2} \right)$$
4
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}$$ is equal to:
A
$${9 \over {{e^2}}}$$
B
$$3\,\log \,3 - 2$$
C
$${{18} \over {{e^4}}}$$
D
$${{27} \over {{e^2}}}$$
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