1
WB JEE 2018
+1
-0.25
Let f : [a, b] $$\to$$ R be such that f is differentiable in (a, b), f is continuous at x = a and x = b and moreover f(a) = 0 = f(b). Then
A
there exists at least one point c in (a, b) such that f'(c) = f(c)
B
f'(x) = f(x) does not hold at any point in (a, b)
C
at every point of (a, b), f'(x) > f(x)
D
at every point of (a, b), f'(x) < f(x)
2
WB JEE 2018
+1
-0.25
Let f : R $$\to$$ R be a twice continuously differentiable function such that f(0) = f(1) = f'(0) = 0. Then
A
f''(0) = 0
B
f''(c) = 0 for some c$$\in$$R
C
if c $$\ne$$ 0, then f''(c) $$\ne$$ 0
D
f'(x) > 0 for all x $$\ne$$ 0
3
WB JEE 2018
+2
-0.5
Let $$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if\,x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if\, - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x} & {if\,x \ge {\pi \over 2}} \cr } } \right.$$. Then,
A
f is discontinuous for all A and B
B
f is continuous for all A = $$-$$ 1 and B = 1
C
f is continuous for all A = 1 and B = $$-$$ 1
D
f is continuous for all real values of A, B
4
WB JEE 2017
+1
-0.25
Consider the non-constant differentiable function f one one variable which obeys the relation $${{f(x)} \over {f(y)}} = f(x - y)$$. If f' (0) = p and f' (5) = q, then f' ($$-$$5) is
A
$${{{p^2}} \over q}$$
B
$${q \over p}$$
C
$${p \over q}$$
D
q
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