1
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0 $$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 4)}^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 8)}^3}} }} + .... + {{\sqrt n } \over {\sqrt {{{[n + 4(n - 1)]}^3}} }}} \right\}$$ is
A
$${{5 - \sqrt 5 } \over {10}}$$
B
$${{5 + \sqrt 5 } \over {10}}$$
C
$${{2 + \sqrt 3 } \over {2}}$$
D
$${{2 - \sqrt 3 } \over {2}}$$
2
WB JEE 2020
MCQ (More than One Correct Answer)
+2
-0 Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^k}}} \ne 0$$ is
A
4
B
3
C
2
D
1
3
WB JEE 2019
MCQ (More than One Correct Answer)
+1
-0.25 Let $$f:[1,3] \to R$$ be a continuous function that is differentiable in (1, 3) an

f'(x) = | f(x) |2 + 4 for all x$$\in$$ (1, 3). Then,
A
f(3) $$-$$ f(1) = 5 is true
B
f(3) $$-$$ f(1) = 5 is false
C
f(3) $$-$$ f(1) = 7 is false
D
f(3) $$-$$ f(1) > 0 only at one point of (1, 3)
4
WB JEE 2019
MCQ (More than One Correct Answer)
+2
-0 Consider the function $$f(x) = {{{x^3}} \over 4} - \sin \pi x + 3$$
A
f(x) does not attain value within the interval [$$-$$2, 2]
B
f(x) takes on the value $$2{1 \over 3}$$ in the interval [$$-$$2, 2]
C
f(x) takes on the value $$3{1 \over 4}$$ in the interval [$$-$$2, 2]
D
f(x) takes no value p, 1 < p < 5 in the interval [$$-$$2, 2].
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