1
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
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 $${1 \over 2}$$
2
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let f : R $$\to$$ R be such that f(0) = 0 and $$\left| {f'(x)} \right| \le 5$$ for all x. Then f(1) is in
A
(5, 6)
B
[$$-$$5, 5]
C
($$-$$ $$\infty$$, $$-$$5) $$\cup$$ (5, $$\infty$$)
D
[$$-$$4, 4]
3
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \over {a + b\cos x}}} \right] + c$$, then $$\alpha$$ is equal to
A
$${2 \over {{b^2}}}$$
B
$${2 \over {{a^2}}}$$
C
$$ - {2 \over {{b^2}}}$$
D
$$ - {2 \over {{a^2}}}$$
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be continuous function and f(2x) = f(x), then
A
g(x) is strictly increasing function
B
g(x) is strictly decreasing function
C
g(x) is constant function
D
g(x) is not derivable function
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