1
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0

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

A
f has no extrema.
B
f is maximum at two points x = 1 and x = $$-$$1.
C
f is minimum at x = 0.
D
f has maximum at x = 1 only.
2
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

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]

A
220 ft
B
240 ft
C
256 ft
D
260 ft
3
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
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
A
$${f_{\min }} = \sqrt 3 - 1$$
B
$${f_{\max }} = {\pi \over 6} + {1 \over 4}\ln 3$$
C
$${f_{\min }} = {\pi \over 3} - {1 \over 4}\ln 3$$
D
$${f_{\max }} = {\pi \over {12}} + \ln 5$$
4
WB JEE 2020
MCQ (More than One Correct Answer)
+2
-0
A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
A
velocity of projection is 192 ft/sec
B
greatest height attained is 600 ft
C
velocity of projection is 196 ft/sec
D
greatest height attained is 576 ft
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