1
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then

A
f is only injective
B
f is only surjective
C
f is bijective
D
f is neither injective nor surjective
2
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} } $$ and f (0) = 0. Then

A
$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
B
$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
C
$$f\left( {{4 \over 3}} \right) < {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) < {2 \over 3}$$
D
$$f\left( {{4 \over 3}} \right) > {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) > {2 \over 3}$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OPQ$$ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

A
$$1 < e < {2 \over {\sqrt 3 }}$$
B
$$e = {2 \over {\sqrt 3 }}$$
C
$$e = 2\sqrt 3 $$
D
$$e > {2 \over {\sqrt 3 }}$$
4
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

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
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