WB JEE 2023 | Application of Derivatives Question 23 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-0.5

The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point of it, intercepted between the axes

varies as abscissa

varies as ordinate

is constant

varies as the product of abscissa and ordinate

WB JEE 2023

MCQ (Single Correct Answer)

-0.5

Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$

does not exist.

exists at a point in $$\left( {0,{\pi \over 2}} \right)$$ and its value is $$2{e^{{1 \over {\sqrt 2 }}}}$$.

exists at infinitely many points.

exists at $$x=0$$ only.

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k are positive constants. The maximum velocity attained by the particle is

$${2 \over 3}\sqrt {{{{a^3}} \over k}} $$

$${1 \over 3}\sqrt {{{{a^3}} \over k}} $$

$$\sqrt {{{{a^3}} \over k}} $$

$$2\sqrt {{{{a^3}} \over k}} $$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

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

(5, 6)

[$$-$$5, 5]

($$-$$ $$\infty$$, $$-$$5) $$\cup$$ (5, $$\infty$$)

[$$-$$4, 4]

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