NTA JEE Mains 5th April 2024 Shift 1

The angle between vector $$\vec{Q}$$ and the resultant of $$(2\vec{Q} + 2\vec{P})$$ and $$(2\vec{Q} - 2\vec{P})$$ is :

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $$4.62 \text{ s}, 4.632 \text{ s}, 4.6 \text{ s}$$ and $$4.64 \text{ s}$$. The arithmetic mean of these readings in correct significant figure is :

If $$G$$ be the gravitational constant and $$u$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{uG}$$ :

A wooden block of mass $$5 \text{ kg}$$ rests on a soft horizontal floor. When an iron cylinder of mass $$25 \text{ kg}$$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $$0.1 \text{ ms}^{-2}$$. The action force of the system on the floor is equal to:

A body of mass $$50 \text{ kg}$$ is lifted to a height of $$20 \text{ m}$$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $$\sqrt{8/x}$$. The value of $$x$$ is :

A simple pendulum doing small oscillations at a place R height above earth surface has time period of $$T_1 = 4 \text{ s}$$. $$T_2$$ would be its time period if it is brought to a point which is at a height $$2R$$ from earth surface. Choose the correct relation $$[R = \text{radius of earth}]$$ :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

Match List I with List II :

(Where $$a$$ = radius of planet orbit, $$r$$ = radius of planet, $$M$$ = mass of Sun, $$m$$ = mass of planet)

Given below are two statements : 

Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $$0°$$. 

Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. 

In the light of the above statement, choose the correct answer from the options given below.