WB JEE 2023 | Differentiation Question 21 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-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

$$\log x$$

$$x$$

$${\log ^n}x$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.5

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

$$-$$k

$$-$$k$$^2$$

k$$^2$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

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

$$(1 + {x^2}){y_2} + (2x - 1){y_1} = 0$$

$$(1 + {x^2}){y_2} + 2xy = 0$$

$$(1 - {x^2}){y_2} - {y_1} = 0$$

$$(1 + {x^2}){y_2} + 3x{y_1} + 4y = 0$$

WB JEE 2021

MCQ (Single Correct Answer)

-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

g(x) is strictly increasing function

g(x) is strictly decreasing function

g(x) is constant function

g(x) is not derivable function

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