1
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
For all twice differentiable functions f : R $$ \to $$ R,
with f(0) = f(1) = f'(0) = 0
A
f''(x) $$ \ne $$ 0, at every point x $$ \in $$ (0, 1)
B
f''(x) = 0, for some x $$ \in $$ (0, 1)
C
f''(0) = 0
D
f''(x) = 0, at every point x $$ \in $$ (0, 1)
2
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :
A
e(4e + 1)
B
e(2e – 1)
C
e(4e – 1)
D
4e2 – 1
3
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
For a suitably chosen real constant a, let a

function, $$f:R - \left\{ { - a} \right\} \to R$$ be defined by

$$f(x) = {{a - x} \over {a + x}}$$. Further suppose that for any real number $$x \ne - a$$ and $$f(x) \ne - a$$,

(fof)(x) = x. Then $$f\left( { - {1 \over 2}} \right)$$ is equal to :
A
$$ {1 \over 3}$$
B
–3
C
$$ - {1 \over 3}$$
D
3
4
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1} $$ , then z lies on the :
A
line, y = –x
B
real axis
C
line, y = x
D
imaginary axis
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