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)
+1
-0.25
Change Language
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.

Then
A
f(x) has 13 non-zero real roots
B
f(x) has exactly one real root
C
f(x) has exactly one pair of imaginary roots
D
f(x) has no real root
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The area of the region

$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is
A
$${{{\pi ^2}} \over 2}$$
B
$${\pi \over 4}$$
C
$${\pi \over 4}$$$$ - $$$${1 \over 2}$$
D
$${{{\pi ^2}} \over 3}$$
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