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
Let f : R $$ \to $$ R be a function defined by
f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then :
A
{0, 1}
B
{0}
C
$$\phi $$(an empty set)
D
{1}
3
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The set of all real values of $$\lambda $$ for which the function

$$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$

has exactly one maxima and exactly one minima, is :
A
$$\left( { - {3 \over 2},{3 \over 2}} \right) - \left\{ 0 \right\}$$
B
$$\left( { - {3 \over 2},{3 \over 2}} \right)$$
C
$$\left( { - {1 \over 2},{1 \over 2}} \right) - \left\{ 0 \right\}$$
D
$$\left( { - {1 \over 2},{1 \over 2}} \right)$$
4
JEE Main 2020 (Online) 6th September Evening Slot
Numerical
+4
-0
Change Language
The sum of distinct values of $$\lambda $$ for which the system of equations

$$\left( {\lambda - 1} \right)x + \left( {3\lambda + 1} \right)y + 2\lambda z = 0$$
$$\left( {\lambda - 1} \right)x + \left( {4\lambda - 2} \right)y + \left( {\lambda + 3} \right)z = 0$$
$$2x + \left( {3\lambda + 1} \right)y + 3\left( {\lambda - 1} \right)z = 0$$

has non-zero solutions, is ________ .
Your input ____
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