NTA JEE Main 11th April 2023 Shift 1

Given below are two statements:
Statement I: Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statement II: Au < Parsec (Pc) < ly
In the light of the above statements, choose the most appropriate answer from the options given below:

From the $$v - t$$ graph shown, the ratio of distance to displacement in 25 s of motion is:

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _______ from the centre:

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s$$^{-1}$$ to keep it in position. The number of bullets fired per second by the machine gun is:

The radii of two planets A and B are R and 4R and their densities are $$\rho$$ and $$\frac{\rho}{3}$$ respectively. The ratio of acceleration due to gravity at their surfaces $$g_A : g_B$$ will be

1 kg of water at 100$$^\circ$$C is converted into steam at 100$$^\circ$$C by boiling at atmospheric pressure. The volume of water changes from $$1.00 \times 10^{-3}$$ m$$^3$$ as a liquid to 1.671 m$$^3$$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation = 2257 kJ/kg, Atmospheric pressure $$= 1 \times 10^5$$ Pa)

On a temperature scale 'X', the boiling point of water is 65$$^\circ$$X and the freezing point is $$-15^\circ$$X. Assuming that the X scale is linear. The equivalent temperature corresponding to $$-95^\circ$$X on the Fahrenheit scale would be

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $$v_{rms}$$ and choose the correct answer from the options given below:

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by

The electric field in an electromagnetic wave is given as $$\vec{E} = 20\sin(\omega t - \frac{x}{c})\hat{j}$$ N C$$^{-1}$$, where $$\omega$$ and $$c$$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $$5 \times 10^{-4}$$ m$$^3$$ will be
(Given $$\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)