1
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
2
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)
3
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].
4
WB JEE 2017
MCQ (More than One Correct Answer)
+2
-0
Let f : R $$\to$$ R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,
A
f''(x) $$\ne$$ 0 for all x
B
f''(c) = 0 for some c $$\in$$ R
C
f''(x) $$\ne$$ 0 if x $$\ne$$ 0
D
f'(x) > 0 for all x
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