WB JEE 2023 | Application of Derivatives Question 18 | Mathematics

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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

Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B and describes n units more than that of B in acquiring the same velocity, then

$$(f + f'){m^2} = ff'n$$

$$(f - ff'){m^2} = ff'n$$

$$(f' - f)n = {1 \over 2}ff'{m^2}$$

$${1 \over 2}(f + f')m = ff'{n^2}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

If the tangent at the point P with co-ordinates (h, k) on the curve y² = 2x³ is perpendicular to the straight line 4x = 3y, then

(h, k) = (0, 0) only

(h, k) = $$\left( {{1 \over 8}, - {1 \over {16}}} \right)$$ only

(h, k) = (0, 0) or $$\left( {{1 \over 8},{1 \over {16}}} \right)$$

no such point P exists

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