1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The value of k for which the function

$$f\left( x \right) = \left\{ {\matrix{ {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \cr } } \right.$$

is continuous at x = $${\pi \over 2},$$ is :
A
$${{17} \over {20}}$$
B
$${{2} \over {5}}$$
C
$${{3} \over {5}}$$
D
$$-$$ $${{2} \over {5}}$$
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 3}$$ $${{\sqrt {3x} - 3} \over {\sqrt {2x - 4} - \sqrt 2 }}$$ is equal to :
A
$$\sqrt 3$$
B
$${1 \over {\sqrt 2 }}$$
C
$${{\sqrt 3 } \over 2}$$
D
$${1 \over {2\sqrt 2 }}$$
3
JEE Main 2017 (Offline)
+4
-1
$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\cot x - \cos x} \over {{{\left( {\pi - 2x} \right)}^3}}}$$ equals
A
$${1 \over {16}}$$
B
$${1 \over 8}$$
C
$${1 \over {4}}$$
D
$${1 \over {24}}$$
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} \,{{{{\left( {1 - \cos 2x} \right)}^2}} \over {2x\,\tan x\, - x\tan 2x}}$$ is :
A
$$-$$ 2
B
$$-$$ $${1 \over 2}$$
C
$${1 \over 2}$$
D
2
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