1
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1 If the function f defined as

$$f\left( x \right) = {1 \over x} - {{k - 1} \over {{e^{2x}} - 1}},x \ne 0,$$ is continuous at

x = 0, then the ordered pair (k, f(0)) is equal to :
A
(3, 2)
B
(3, 1)
C
(2, 1)
D
$$\left( {{1 \over 3},\,2} \right)$$
2
JEE Main 2018 (Offline)
+4
-1
For each t $$\in R$$, let [t] be the greatest integer less than or equal to t.

Then $$\mathop {\lim }\limits_{x \to {0^ + }} x\left( {\left[ {{1 \over x}} \right] + \left[ {{2 \over x}} \right] + ..... + \left[ {{{15} \over x}} \right]} \right)$$
A
does not exist in R
B
is equal to 0
C
is equal to 15
D
is equal to 120
3
JEE Main 2018 (Offline)
+4
-1
Let S = { t $$\in R:f(x) = \left| {x - \pi } \right|.\left( {{e^{\left| x \right|}} - 1} \right)$$$$\sin \left| x \right|$$ is not differentiable at t}, then the set S is equal to
A
{0, $$\pi$$}
B
$$\phi$$ (an empty set)
C
{0}
D
{$$\pi$$}
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1 $$\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}$$ equals :
A
$${1 \over 4}$$
B
1
C
$${1 \over 2}$$
D
$$-$$ $${1 \over 2}$$
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