1
WB JEE 2022
+1
-0.25

If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then

A
$$(1 + {x^2}){y_2} + (2x - 1){y_1} = 0$$
B
$$(1 + {x^2}){y_2} + 2xy = 0$$
C
$$(1 - {x^2}){y_2} - {y_1} = 0$$
D
$$(1 + {x^2}){y_2} + 3x{y_1} + 4y = 0$$
2
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
3
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
4
WB JEE 2020
+1
-0.25
If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respectively such that p2 = q, then a is equal to
A
2
B
$${1 \over 2}$$
C
$${1 \over 4}$$
D
3
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