1
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} \,\,{{{{\left( {27 + x} \right)}^{{1 \over 3}}} - 3} \over {9 - {{\left( {27 + x} \right)}^{{2 \over 3}}}}}$$ equals.
A
$${1 \over 3}$$
B
$$-$$ $${1 \over 3}$$
C
$$-$$ $${1 \over 6}$$
D
$${1 \over 6}$$
2
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$\left( {{1 \over 3},\,2} \right)$$
3
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
4
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
{$$\pi $$}
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