1
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let S be the set of all functions ƒ : [0,1] $$\to$$ R, which are continuous on [0,1] and differentiable on (0,1). Then for every ƒ in S, there exists a c $$\in$$ (0,1), depending on ƒ, such that
A
$$\left| {f(c) - f(1)} \right| < \left| {f'(c)} \right|$$
B
$$\left| {f(c) + f(1)} \right| < \left( {1 + c} \right)\left| {f'(c)} \right|$$
C
$$\left| {f(c) - f(1)} \right| < \left( {1 - c} \right)\left| {f'(c)} \right|$$
D
None
2
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to
A
$$- {1 \over 5}$$
B
$$- {1 \over 10}$$
C
0
D
$${1 \over 10}$$
3
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {\left( {{{3{x^2} + 2} \over {7{x^2} + 2}}} \right)^{{1 \over {{x^2}}}}}$$ is equal to
A
e
B
e2
C
$${1 \over {{e^2}}}$$
D
$${1 \over e}$$
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x3 - 4x2 + 8x + 11, when x $$\in$$ [0, 1] is:
A
$${2 \over 3}$$
B
$${{\sqrt 7 - 2} \over 3}$$
C
$${{4 - \sqrt 5 } \over 3}$$
D
$${{4 - \sqrt 7 } \over 3}$$
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