JEE Main 2019 (Online) 8th April Morning Slot | Limits, Continuity and Differentiability Question 134 | Mathematics

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JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}x} \over {\sqrt 2 - \sqrt {1 + \cos x} }}$$ equals:

$$ \sqrt 2$$

$$2 \sqrt 2$$

$$4 \sqrt 2$$

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to {1^ - }} {{\sqrt \pi - \sqrt {2{{\sin }^{ - 1}}x} } \over {\sqrt {1 - x} }}$$ is equal to :

$$\sqrt {{2 \over \pi }} $$

$${1 \over {\sqrt {2\pi } }}$$

$$\sqrt {{\pi \over 2}} $$

$$\sqrt \pi $$

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to \infty } \left( {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + {n \over {{n^2} + {3^2}}} + ..... + {1 \over {5n}}} \right)$$ is equal to :

tan^–1(2)

tan^–1(3)

$${\pi \over 4}$$

$${\pi \over 2}$$

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x $$ \in $$ R R. If h(x) = f(f(x)), then h'(1) is equal to :

2e²

4e²

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