1
JEE Main 2020 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x $$ \in $$ (a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c $$ \in $$ (a, b), $${{f(c) - f(a)} \over {f(b) - f(c)}}$$ is greater than :
A
1
B
$${{b - c} \over {c - a}}$$
C
$${{b + a} \over {b - a}}$$
D
$${{c - a} \over {b - c}}$$
2
JEE Main 2020 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$f(x) = \left\{ {\matrix{ {{{\sin (a + 2)x + \sin x} \over x};} & {x < 0} \cr {b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;} & {x = 0} \cr {{{{{\left( {x + 3{x^2}} \right)}^{{1 \over 3}}} - {x^{ {1 \over 3}}}} \over {{x^{{4 \over 3}}}}};} & {x > 0} \cr } } \right.$$
is continuous at x = 0, then a + 2b is equal to :
A
0
B
-1
C
-2
D
1
3
JEE Main 2020 (Online) 8th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
4
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} {\left( {{{3{x^2} + 2} \over {7{x^2} + 2}}} \right)^{{1 \over {{x^2}}}}}$$ is equal to
A
e
B
e2
C
$${1 \over {{e^2}}}$$
D
$${1 \over e}$$
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