1
JEE Main 2020 (Online) 6th September Evening Slot
+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
+4
-1
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
$${1 \over {e - 1}}$$
3
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
The position of a moving car at time t is
given by f(t) = at2 + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t1 , t2 ] is attained at the point :
A
$${{\left( {{t_1} + {t_2}} \right)} \over 2}$$
B
$${{\left( {{t_2} - {t_1}} \right)} \over 2}$$
C
2a(t1 + t2) + b
D
a(t2 – t1) + b
4
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
Which of the following points lies on the tangent to the curve
x4ey + 2$$\sqrt {y + 1}$$ = 3 at the point (1, 0)?
A
(2, 2)
B
(–2, 4)
C
(2, 6)
D
(–2, 6)
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