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

Let f be a non-negative function defined on $$\left[ {0,{\pi \over 2}} \right]$$. If $$\int\limits_0^x {(f'(t) - \sin 2t)dt = \int\limits_x^0 {f(t)\tan t\,dt} } ,f(0) = 1$$ then $$\int\limits_0^{{\pi \over 2}} {f(x)dx} $$ is

A
3
B
$$3 - {\pi \over 2}$$
C
$$3 + {\pi \over 2}$$
D
$${\pi \over 2}$$
2
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

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

A
T = 6 sec
B
H = 112.5 ft
C
T = 5/2 sec
D
225 ft
3
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

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.
4
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}} \right| = 1$$, then $${{{z_1}} \over {{z_2}}}$$ may be

A
real positive
B
real negative
C
zero
D
purely imaginary
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