WB JEE 2023 | Application of Derivatives Question 19 | Mathematics

WB JEE 2023

MCQ (More than One Correct Answer)

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A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec$$^2$$. At the end of 5 sec, a stone is dropped from it. If T be the time to reach the stone to the ground and H be the height of the balloon when the stone reaches the ground, then

T = 6 sec

H = 112.5 ft

T = 5/2 sec

225 ft

WB JEE 2023

MCQ (More than One Correct Answer)

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If $$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then

f has no extrema.

f is maximum at two points x = 1 and x = $$-$$1.

f is minimum at x = 0.

f has maximum at x = 1 only.

WB JEE 2022

MCQ (More than One Correct Answer)

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From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon above the ground when the stone reaches the ground after 4 sec is [g = 32 ft/sec²]

220 ft

240 ft

256 ft

260 ft

WB JEE 2021

MCQ (More than One Correct Answer)

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The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 } \right]$$ are

$${f_{\min }} = \sqrt 3 - 1$$

$${f_{\max }} = {\pi \over 6} + {1 \over 4}\ln 3$$

$${f_{\min }} = {\pi \over 3} - {1 \over 4}\ln 3$$

$${f_{\max }} = {\pi \over {12}} + \ln 5$$

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