1
WB JEE 2022
+2
-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
a = 0, b = 1
B
a = 1, b = $$-$$1
C
a = $$-$$1, b = 1
D
a = 0, b = 0
2
WB JEE 2021
+1
-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
A
does not exist
B
exists and equals 1
C
exists and equals 0
D
exists and equals $${1 \over 2}$$
3
WB JEE 2021
+1
-0.25
Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - 1}}32 + ....$$ to nth term. Then $$\mathop {\lim }\limits_{n \to \infty } {S_n}$$ is
A
$${\pi \over 3}$$
B
$${\pi \over 4}$$
C
$${\pi \over 6}$$
D
$${\pi \over 8}$$
4
WB JEE 2021
+1
-0.25
Let f : D $$\to$$ R where D = [$$-$$0, 1] $$\cup$$ [2, 4] be defined by

$$f(x) = \left\{ {\matrix{ {x,} & {if} & {x \in [0,1]} \cr {4 - x,} & {if} & {x \in [2,4]} \cr } } \right.$$ Then,
A
Rolle's theorem is applicable to f in D.
B
Rolle's theorem is not applicable to f in D.
C
there exists $$\xi$$$$\in$$D for which f'($$\xi$$) = 0 but Rolle's theorem is not applicable.
D
f is not continuous in D.
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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