ExamSIDE
Questions
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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 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$x = \sqrt {{2^{\cos e{c^{ - 1}}}}} $$ and $$y = \sqrt {{2^{se{c^{ - 1}}t}}} \,\,\left( {\left| t \right| \ge 1} \right),$$ then $${{dy} \over {dx}}$$ is equal to :
A
$${y \over x}$$
B
$${x \over y}$$
C
$$-$$ $${y \over x}$$
D
$$-$$ $${x \over y}$$
4
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+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
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