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 $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to
A
$$e{\log _e}5$$
B
$$e{\log _e}3$$
C
$${1 \over {e{{\log }_e}5}}$$
D
$${1 \over {e{{\log }_e}3}}$$
3
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$ at x = 0 is
A
1
B
$$-$$1
C
$$ - {1 \over e}$$
D
$$-$$ e
4
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
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