1
WB JEE 2021
+1
-0.25
Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt}$$ where x > 0 and f be continuous function and f(2x) = f(x), then
A
g(x) is strictly increasing function
B
g(x) is strictly decreasing function
C
g(x) is constant function
D
g(x) is not derivable function
2
WB JEE 2021
+1
-0.25
A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of 10 m/sec. Starting from P the speed with which his shadow is running along the wall when he is at an angular distance of 60$$^\circ$$ from P is
A
30 m/sec
B
40 m/sec
C
60 m/sec
D
80 m/sec
3
WB JEE 2019
+1
-0.25
Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be
A
1 + log(f(x))
B
1 + f(x)
C
1 $$-$$ log(f(x))
D
log f(x)
4
WB JEE 2019
+1
-0.25
Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,
A
f(x) > 0 for all x > 0
B
f(x) < 0 for all x > 0
C
no sign of f(x) can be ascertained
D
f(x) is a constant function
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