NTA JEE Mains 2nd April Shift 2 2026

One side of an equilateral prism is painted by a transparent material of refractive index $$n_2$$. The refractive index of prism is 1.6. The minimum value of $$n_2$$ required for total internal reflection from painted face is ________ .

The figure given below shows an LCR series circuit with two switches $$S_1$$ and $$S_2$$. When switch $$S_1$$ is closed keeping $$S_2$$ open, the phase difference $$\phi$$ between the current and source voltage is $$30°$$ and phase difference is $$60°$$ when $$S_2$$ is closed keeping $$S_1$$ open. The value of $$(3L_1 - L_2)$$ is _________ H. 

A circular current loop of radius $$R$$ is placed inside square loop of side length $$L$$ ($$L \gg R$$) such that they are co-planar and their centers coincide. The permeability of free space is $$\mu_0$$. The mutual inductance between circular loop and square loop is :

The binding energy per nucleon of $${}^{209}_{83}\text{Bi}$$ is _________ MeV. [Take $$m({}^{209}_{83}\text{Bi}) = 208.980388$$ u, $$m_p = 1.007825$$ u, $$m_n = 1.008665$$ u, $$1$$ u $$= 931$$ MeV/c$$^2$$]

The equation of motion of a particle is given by $$x = a\sin\left(50t + \frac{\pi}{3}\right)$$ cm. The particle will come to rest at time $$t_1$$ and it will have zero acceleration at time $$t_2$$. The $$t_1$$ and $$t_2$$ respectively are _____.

In a Young's double slit experiment, the intensity at some point on the screen is found to be $$\frac{3}{4}$$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $$\frac{\lambda}{x}$$ where $$\lambda$$ is wavelength of the incident light. The value of $$x$$ is _________.

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _________.

5 moles of unknown gas is heated at constant volume from 10 °C to 20 °C. The molar specific heat of this gas at constant pressure $$c_p = 8$$ cal/mol.°C and $$R = 8.36$$ J/mol.°C. The change in internal energy of the gas is _________ calorie.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is $$\frac{\alpha}{10}$$. The value of $$\alpha$$ is _________.

Moment of inertia about an axis $$AB$$ for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass 10 kg and radius $$R$$ about an axis parallel to $$AB$$ axis with separation of 3 m as shown in figure. The value of $$R$$ is given as $$\sqrt{\frac{\alpha}{2}}$$. The value of $$\alpha$$ is _________.