NTA JEE Mains 28th Jan 2026 Shift 2

A nucleus has mass number $$\alpha$$ and radius $$R_{\alpha}$$ Another nucleus has mass number $$\beta$$ and radius $$R_{\beta}$$. If $$\beta=8\alpha$$ then $$R_{\alpha}/R_{\beta}$$ is:

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be:

In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrwnent used in recording these readings is ___ mm.

The mean free path of a molecule of diameter $$5\times 10^{-10}m$$ at the temperature 41 °C and pressure $$1.38\times 10^{5} Pa$$, is given as ___ m (Given $$k_{B}=1.38\times 10^{-23}J/K$$.)

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

Two tuning forks A and Bare sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is ____ Hz.

A thermodynamic system is taken through the cyclic process $$ABC$$ as shown in the figure. The total work done by the system during the cycle $$ABC$$ is ______ J.

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 5O Hz nows through it. The ratio of inductive reactance to its resistance is_____.$$(\pi=3.14)$$

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is______$$\times10^{-5}$$

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ___ J.$$(g=10 m/s^{2})$$