1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + 2cx} \over {1 - 2cx}}} \right)^{{1 \over x}}}$$ is
A
2
B
4
C
16
D
64
2
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0) = 0. Then
A
f"(c) = 0 for some c $$ \in $$ R
B
there is no point for which f"(x) = 0
C
at all points f"(x) > 0
D
at all points f"(x) < 0
3
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{1/(k + \alpha )} {{{dx} \over {1 + x}}} $$ is
A
$${\log _e}{\beta \over \alpha }$$
B
$${\log _e}{1+\beta \over 1+\alpha }$$
C
$${\log _e}{1+\alpha \over 1+\beta }$$
D
$$\infty $$
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$
A
Does not exist
B
1
C
$${1 \over 2}$$
D
0
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