1
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
$$ - {2 \over {{a^2}}}$$
2
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
3
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$ is equal to
A
$$1 + {4 \over 3}{\log _e}3$$
B
$$1 + {3 \over 4}{\log _e}3$$
C
$$1 - {4 \over 3}{\log _e}3$$
D
$$1 - {3 \over 4}{\log _e}3$$
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right\}}^{1/2}}} dx$$ is equal to
A
$${\log _e}\left( {{4 \over 3}} \right)$$
B
$$4\,{\log _e}\left( {{3 \over 4}} \right)$$
C
$$4\,{\log _e}\left( {{4 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 4}} \right)$$
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