WB JEE 2022 | Limits, Continuity and Differentiability Question 38 | Mathematics

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WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Let f : [a, b] $$\to$$ R be continuous in [a, b], differentiable in (a, b) and f(a) = 0 = f(b). Then

there exists at least one point $$c \in (a,b)$$ for which $$f'(c) = f(c)$$

$$f'(x) = f(x)$$ does not hold at any point of (a, b)

at every point of $$(a,b),f'(x) > f(x)$$

at every point of $$(a,b),f'(x) < f(x)$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

$$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + 1} \over {x + 1}} - ax - b} \right),(a,b \in R)$$ = 0. Then

a = 0, b = 1

a = 1, b = $$-$$1

a = $$-$$1, b = 1

a = 0, b = 0

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

If $$I = \mathop {\lim }\limits_{x \to 0} sin\left( {{{{e^x} - x - 1 - {{{x^2}} \over 2}} \over {{x^2}}}} \right)$$, then limit

does not exist

exists and equals 1

exists and equals 0

exists and equals $${1 \over 2}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - 1}}32 + ....$$ to n^th term. Then $$\mathop {\lim }\limits_{n \to \infty } {S_n}$$ is

$${\pi \over 3}$$

$${\pi \over 4}$$

$${\pi \over 6}$$

$${\pi \over 8}$$

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