1
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let ƒ : R $$\to$$ R be a differentiable function satisfying ƒ'(3) + ƒ'(2) = 0.
Then $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + f(3 + x) - f(3)} \over {1 + f(2 - x) - f(2)}}} \right)^{{1 \over x}}}$$ is equal to
A
e
B
e2
C
e–1
D
1
2
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let ƒ : [–1,3] $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ {\left| x \right| + \left[ x \right]} & , & { - 1 \le x < 1} \cr {x + \left| x \right|} & , & {1 \le x < 2} \cr {x + \left[ x \right]} & , & {2 \le x \le 3} \cr } } \right.$$

where [t] denotes the greatest integer less than or equal to t. Then, ƒ is discontinuous at:
A
only three points
B
four or more points
C
only two points
D
only one point
3
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}x} \over {\sqrt 2 - \sqrt {1 + \cos x} }}$$ equals:
A
$$\sqrt 2$$
B
$$2 \sqrt 2$$
C
4
D
$$4 \sqrt 2$$
4
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to {1^ - }} {{\sqrt \pi - \sqrt {2{{\sin }^{ - 1}}x} } \over {\sqrt {1 - x} }}$$ is equal to :
A
$$\sqrt {{2 \over \pi }}$$
B
$${1 \over {\sqrt {2\pi } }}$$
C
$$\sqrt {{\pi \over 2}}$$
D
$$\sqrt \pi$$
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