NTA JEE Mains 04th April 2024 Shift 2

A bus moving along a straight highway with speed of $$72$$ km/h is brought to halt within $$4$$ s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____ m.

In a system two particles of masses $$m_1 = 3$$ kg and $$m_2 = 2$$ kg are placed at certain distance from each other. The particle of mass $$m_1$$ is moved towards the center of mass of the system through a distance $$2$$ cm. In order to keep the center of mass of the system at the original position, the particle of mass $$m_2$$ should move towards the center of mass by the distance _____ cm.

Mercury is filled in a tube of radius $$2$$ cm up to a height of $$30$$ cm. The force exerted by mercury on the bottom of the tube is _____ N. (Given, atmospheric pressure $$= 10^5$$ Nm$$^{-2}$$, density of mercury $$= 1.36 \times 10^4$$ kg m$$^{-3}$$, $$g = 10$$ m s$$^{-2}$$, $$\pi = \frac{22}{7}$$)

The displacement of a particle executing SHM is given by $$x = 10 \sin\left(\omega t + \frac{\pi}{3}\right)$$ m. The time period of motion is $$3.14$$ s. The velocity of the particle at $$t = 0$$ is _____ m/s.

A parallel plate capacitor of capacitance $$12.5$$ pF is charged by a battery connected between its plates to potential difference of $$12.0$$ V. The battery is now disconnected and a dielectric slab ($$\epsilon_r = 6$$) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ $$ 10^{-12}$$ J.

Two wires $$A$$ and $$B$$ are made up of the same material and have the same mass. Wire $$A$$ has radius of $$2.0$$ mm and wire $$B$$ has radius of $$4.0$$ mm. The resistance of wire $$B$$ is $$2\Omega$$. The resistance of wire $$A$$ is _____ $$\Omega$$.

Two parallel long current carrying wire separated by a distance $$2r$$ are shown in the figure. The ratio of magnetic field at $$A$$ to the magnetic field produced at $$C$$ is $$\frac{x}{7}$$. The value of $$x$$ is _____

A rod of length $$60$$ cm rotates with a uniform angular velocity $$20$$ rad s$$^{-1}$$ about its perpendicular bisector, in a uniform magnetic field $$0.5$$ T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____ V.

A light ray is incident on a glass slab of thickness $$4\sqrt{3}$$ cm and refractive index $$\sqrt{2}$$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _____ cm. (Given $$\sin 15° = 0.25$$)

The disintegration energy $$Q$$ for the nuclear fission of $$^{235}U \rightarrow ^{140}Ce + ^{94}Zr + n$$ is _____ MeV. Given atomic masses of $$^{235}U : 235.0439$$ u; $$^{140}Ce : 139.9054$$ u; $$^{94}Zr : 93.9063$$ u; $$n : 1.0086$$ u, Value of $$c^2 = 931$$ MeV/u