1
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1

The maximum number of compound propositions, out of p$$\vee$$r$$\vee$$s, p$$\vee$$r$$\vee$$$$\sim$$s, p$$\vee$$$$\sim$$q$$\vee$$s, $$\sim$$p$$\vee$$$$\sim$$r$$\vee$$s, $$\sim$$p$$\vee$$$$\sim$$r$$\vee$$$$\sim$$s, $$\sim$$p$$\vee$$q$$\vee$$$$\sim$$s, q$$\vee$$r$$\vee$$$$\sim$$s, q$$\vee$$$$\sim$$r$$\vee$$$$\sim$$s, $$\sim$$p$$\vee$$$$\sim$$q$$\vee$$$$\sim$$s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to __________.

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2
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $${v_2} = {n \over {{m^2}}}{v_1}$$ and $${a_2} = {{{a_1}} \over {mn}}$$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

A
$${{{n^3}} \over {{m^3}}}{L_1} = {L_2}$$ and $${{{n^2}} \over m}{T_1} = {T_2}$$
B
$${L_1} = {{{n^4}} \over {{m^2}}}{L_2}$$ and $${T_1} = {{{n^2}} \over m}{T_2}$$
C
$${L_1} = {{{n^2}} \over m}{L_2}$$ and $${T_1} = {{{n^4}} \over {{m^2}}}{T_2}$$
D
$${{{n^2}} \over m}{L_1} = {L_2}$$ and $${{{n^4}} \over {{m^2}}}{T_1} = {T_2}$$
3
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 2t where t is in second and $$\alpha$$ is in rads$$-$$2. At t = 0, the ball has angular velocity of 10 rads$$-$$1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

A
$${3 \over 2}{t^4} - {t^2} + 10t$$
B
$${{{t^4}} \over 2} - {{{t^3}} \over 3} + 10t + 4$$
C
$${{2{t^4}} \over 3} - {{{t^3}} \over 6} + 10t + 12$$
D
$$2{t^4} - {{{t^3}} \over 2} + 5t + 4$$
4
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms$$-$$1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = $$-$$kx where k = 12 Nm$$-$$1. The speed of the block as it just crosses the rough surface will be :

A
zero
B
1.5 ms$$-$$1
C
2.0 ms$$-$$1
D
2.5 ms$$-$$1
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