1
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
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
2
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If f'' (0) = k, k $$ \ne $$ 0, then the value of

$$\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^2}}}$$ is
A
k
B
2k
C
3k
D
4k
3
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$f(x) = \left\{ {\matrix{ {{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr {0,} & {if\,x = 0} \cr } } \right.$$, $$(p,q \in R)$$. Then, Lagrange's mean value theorem is applicable to f(x) in closed interval [0, x]
A
for all p, q
B
only when p > q
C
only when p < q
D
for no value of p, q
4
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}$$ is equal to
A
2
B
1
C
0
D
does not exist
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