NTA JEE Mains 8th April 2024 Shift 2

A capacitor has air as dielectric medium and two conducting plates of area $$12 \text{ cm}^2$$ and they are $$0.6$$ cm apart. When a slab of dielectric having area $$12 \text{ cm}^2$$ and $$0.6$$ cm thickness is inserted between the plates, one of the conducting plates has to be moved by $$0.2$$ cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given $$\epsilon_0 = 8.834 \times 10^{-12}$$ F/m)

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _____ to _____ times of its initial length if the water is to be boiled in 15 minutes.

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $$\frac{a}{2}$$ and $$2a$$ from axis of the wire is :

A coil of negligible resistance is connected in series with $$90\Omega$$ resistor across $$120$$ V, $$60$$ Hz supply. A voltmeter reads $$36$$ V across resistance. Inductance of the coil is :

The position of the image formed by the combination of lenses is 

A proton and an electron have the same de Broglie wavelength. If $$K_p$$ and $$K_e$$ be the kinetic energies of proton and electron respectively, then choose the correct relation :

If $$M_o$$ is the mass of isotope $$^{12}_5 B$$, $$M_P$$ and $$M_n$$ are the masses of proton and neutron, then nuclear binding energy of isotope is :

In a hypothetical fission reaction $$_{92}X^{236} \rightarrow _{56}Y^{141} + _{36}Z^{92} + 3R$$. The identity of emitted particles (R) is :

Least count of a vernier caliper is $$\frac{1}{20N}$$ cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :

There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :