NTA JEE Mains 8th April Shift 2 2026

Two point charges $$q_1 = 3 \, \mu C$$ and $$q_2 = -4 \, \mu C$$ are placed at points $$(2\hat{i} + 3\hat{j} + 3\hat{k})$$ and $$(\hat{i} + \hat{j} + \hat{k})$$ respectively. Force on charge $$q_2$$ is __________ N. $$\left(\text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI Units}\right)$$

Light ray incident along a vector $$\vec{AO}$$ ($$\vec{AO} = 2\hat{i} - 3\hat{j}$$) emerges out along vector $$\vec{OB}$$ ($$\vec{OB} = C\hat{i} - 4\hat{j}$$) as shown in the figure below. The value of C is __________.

$$K_1$$ and $$K_2$$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $$\lambda_1$$ and $$\lambda_2$$, respectively. If $$\lambda_1 = 2\lambda_2$$ then the work function of material is given by :

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $$\alpha$$-decay with same Q value of 1 MeV. The ratio of energies of $$\alpha$$-rays produced by A and B is __________.

The output $$Y$$ for the given inputs $$A$$ and $$B$$ to the circuit is :

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 $$\mu$$F when the space between the plates is filled with an insulating material of resistivity $$1 \times 10^{13}$$ $$\Omega$$m and resistance $$17.7 \times 10^{14}$$ $$\Omega$$. Relative permittivity of the insulating material is $$a \times 10^7$$. The value of $$a$$ is __________. (Take permittivity of free space $$= 8.85 \times 10^{-12}$$ F/m)

Some distant star is to be observed by some telescope of diameter of objective lens $$a$$, at an angular resolution of $$3.0 \times 10^{-7}$$ radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is __________ cm. (nearest integer)

A 5 mg particle carrying a charge of $$5\pi \times 10^{-6}$$ C is moving with velocity of $$(3\hat{i} + 2\hat{k}) \times 10^{-2}$$ m/s in a region having magnetic field $$\vec{B} = 0.1 \hat{k}$$ Wb/m$$^2$$. It moves a distance of $$a$$ meter along $$\hat{k}$$ when it completes 5 revolutions. The value of $$a$$ is __________.

The stored charge in the capacitor in steady state of the following circuit is __________ $$\mu$$C.

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5$$^{\text{th}}$$ second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is $$\frac{x}{8}$$. The value of $$x$$ is __________.