1
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
For each x$$\in$$R, let [x] be the greatest integer less than or equal to x.

Then $$\mathop {\lim }\limits_{x \to {0^ - }} \,\,{{x\left( {\left[ x \right] + \left| x \right|} \right)\sin \left[ x \right]} \over {\left| x \right|}}$$ is equal to :
A
$$-$$ sin 1
B
1
C
sin 1
D
0
2
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
Let f : R $$\to$$ R be a function defined as
$$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$$

Then, f is
A
continuous if a = 0 and b = 5
B
continuous if a = –5 and b = 10
C
continuous if a = 5 and b = 5
D
not continuous for any values of a and b
3
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
$$\mathop {\lim }\limits_{y \to 0} {{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 } \over {{y^4}}}$$
A
exists and equals $${1 \over {2\sqrt 2 }}$$
B
exists and equals $${1 \over {4\sqrt 2 }}$$
C
exists and equals $${1 \over {2\sqrt 2 (1 + \sqrt {2)} }}$$
D
does not exists
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} \,\,{{{{\left( {27 + x} \right)}^{{1 \over 3}}} - 3} \over {9 - {{\left( {27 + x} \right)}^{{2 \over 3}}}}}$$ equals.
A
$${1 \over 3}$$
B
$$-$$ $${1 \over 3}$$
C
$$-$$ $${1 \over 6}$$
D
$${1 \over 6}$$
EXAM MAP
Medical
NEET