If f : R $ \to $ R is a function defined by f(x)= [x - 1]  $\cos \left( {{{2x - 1} \over 2}} \right)\pi $, where [.] denotes the greatestinteger function, then f is :

1

If $\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \r…

Topic: JEE Main 2021 (24 February Morning Shift)

1

The population P = P(t) at time 't' of a certain species follows the differential equation ${{dP} \over {dt}}$ = 0.5P –…

Topic: JEE Main 2021 (24 February Morning Shift)

2

Let $f : R → R$ be defined as $f (x) = 2x – 1$ and $g : R - {1} → R$ be defined as g(x) =${{x - {1 \over 2}} \over {x -…

Topic: JEE Main 2021 (24 February Morning Shift)

3

The function $f(x) = {{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$ :

Topic: JEE Main 2021 (24 February Morning Shift)

4

$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$ is equal…

Topic: JEE Main 2021 (24 February Morning Shift)

5

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double th…

Topic: JEE Main 2021 (24 February Morning Shift)

6

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coord…

Topic: JEE Main 2021 (24 February Morning Shift)

7

Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272. Then p and q areroots of the equation :

Topic: JEE Main 2021 (24 February Morning Shift)

8

The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is :

Topic: JEE Main 2021 (24 February Morning Shift)

9

If ${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$ satisfies the equation …

Topic: JEE Main 2021 (24 February Morning Shift)

10

The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the…

Topic: JEE Main 2021 (24 February Morning Shift)