1
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
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
$$\left( { - {1 \over 2},{1 \over 2}} \right)$$
2
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
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
Out of Syllabus
Consider the statement :
‘‘For an integer n, if n3 – 1 is even, then n is odd.’’
The contrapositive statement of this statement is :
A
For an integer n, if n is even, then n3 – 1 is even.
B
For an integer n, if n3 – 1 is not even, then n is not odd.
C
For an integer n, if n is odd, then n3 – 1 is even.
D
For an integer n, if n is even, then n3 – 1 is odd.
4
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If the tangent to the curve, y = f (x) = xloge x,
(x > 0) at a point (c, f(c)) is parallel to the line-segment
joining the points (1, 0) and (e, e), then c is equal to :
A
$${{e - 1} \over e}$$
B
$${e^{\left( {{1 \over {1 - e}}} \right)}}$$
C
$${e^{\left( {{1 \over {e - 1}}} \right)}}$$
D
$${1 \over {e - 1}}$$
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