1
JEE Main 2021 (Online) 24th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$$ is equal to :
A
$${1 \over {15}}$$
B
0
C
$${2 \over 3}$$
D
$${3 \over 2}$$
3
JEE Main 2021 (Online) 24th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :
A
1050
B
575
C
560
D
1625
4
JEE Main 2021 (Online) 24th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $${1 \over 4}$$. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then, which of these stones is / are on the path of the man?
A
A only
B
All the three
C
C only
D
B only
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