1
WB JEE 2020
+1
-0.25
Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then
A
$$\phi$$ is monotonic increasing in $$\left[ {0,{1 \over 2}} \right]$$ and monotonic decreasing in $$\left[ {{1 \over 2}, 1} \right]$$
B
$$\phi$$ is monotonic increasing in $$\left[ {{1 \over 2}, 1} \right]$$ and monotonic decreasing in $$\left[ {0, {1 \over 2}} \right]$$
C
$$\phi$$ is neither increasing nor decreasing in any sub-interval of [0, 1]
D
$$\phi$$ is increasing in [0, 1]
2
WB JEE 2020
+1
-0.25
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
3
WB JEE 2020
+1
-0.25
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
4
WB JEE 2020
+2
-0.5
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
$$\infty$$
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