1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25

If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x{\log ^2}x{\log ^3}x\,.....\,{\log ^{n - 1}}x{\log ^n}x{{dy} \over {dx}}$$ is equal to

A
$$\log x$$
B
$$x$$
C
1
D
$${\log ^n}x$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5

If $$x = \sin \theta$$ and $$y = \sin k\theta$$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$

A
k
B
$$-$$k
C
$$-$$k$$^2$$
D
k$$^2$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25

If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then

A
$$(1 + {x^2}){y_2} + (2x - 1){y_1} = 0$$
B
$$(1 + {x^2}){y_2} + 2xy = 0$$
C
$$(1 - {x^2}){y_2} - {y_1} = 0$$
D
$$(1 + {x^2}){y_2} + 3x{y_1} + 4y = 0$$
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
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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