1
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
$${f_{\max }} = {\pi \over {12}} + \ln 5$$
2
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
3
WB JEE 2020
MCQ (More than One Correct Answer)
+2
-0
Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A and B respectively. If AP : BP = 3 : 1, then
A
The differential equation of the curve is $$3x{{dy} \over {dx}} + y = 0$$
B
the differential equation of the curve is $$3x{{dy} \over {dx}} - y = 0$$
C
the curve passes through $$\left( {{1 \over 8},2} \right)$$
D
the normal at (1, 1) is x + 3y = 4
4
WB JEE 2019
MCQ (More than One Correct Answer)
+2
-0
Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then
A
$$(f + h){m^2} = fhn$$
B
$$(f - h){m^2} = fhn$$
C
$$(h - f)n = {1 \over 2}fh{m^2}$$
D
$${1 \over 2}(f + h)n = fh{m^2}$$
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