NTA JEE Mains 8th April 2024 Shift 2

If $$\epsilon_0$$ is the permittivity of free space and E is the electric field, then $$\epsilon_0 E^2$$ has the dimensions :

The angle of projection for a projectile to have same horizontal range and maximum height is :

A given object takes n times the time to slide down $$45°$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45°$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

A thin circular disc of mass $$M$$ and radius $$R$$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $$\omega$$. If another disc of same dimensions but of mass $$M/2$$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

Two satellites $$A$$ and $$B$$ go round a planet in circular orbits having radii $$4R$$ and $$R$$ respectively. If the speed of $$A$$ is $$3v$$, the speed of $$B$$ will be :

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $$= 0.8$$, specific gravity of ice $$= 0.9$$)

A diatomic gas ($$\gamma = 1.4$$) does 100 J of work in an isobaric expansion. The heat given to the gas is :

Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :

A plane progressive wave is given by $$y = 2\cos 2\pi(330t - x)$$ m. The frequency of the wave is :