1
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
The function
f(x) = $${{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$$ :
A
increases in $$\left( { - \infty ,{1 \over 2}} \right]$$
B
decreases in $$\left( { - \infty ,{1 \over 2}} \right]$$
C
increases in $$\left[ {{1 \over 2},\infty } \right)$$
D
decreases in $$\left[ {{1 \over 2},\infty } \right)$$
2
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
Out of Syllabus
If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1 : 2 is :
A
0
B
2t3
C
-2t3
D
-t3
3
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
$$\left( { - {1 \over 2},{1 \over 2}} \right)$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+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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