NTA JEE Mains 2nd April Shift 2 2026 - Physics

Let $$A = \{2, 3, 4, 5, 6\}$$. Let $$R$$ be a relation on the set $$A \times A$$ given by $$(x, y)R(z, w)$$ if and only if $$x$$ divides $$z$$ and $$y \le w$$. Then the number of elements in $$R$$ is _________.

Consider the matrices $$A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}$$. If matrices $$P$$ and $$Q$$ are such that $$PA = B$$ and $$AQ = B$$, then the absolute value of the sum of the diagonal elements of $$2(P + Q)$$ is _________.

Let $$A$$ be the point $$(3, 0)$$ and circles with variable diameter $$AB$$ touch the circle $$x^2 + y^2 = 36$$ internally. Let the curve $$C$$ be the locus of the point $$B$$. If the eccentricity of $$C$$ is $$e$$, then $$72e^2$$ is equal to _________.

If the area of the region bounded by $$16x^2 - 9y^2 = 144$$ and $$8x - 3y = 24$$ is $$A$$, then $$3(A + 6\log_e(3))$$ is equal to _________.

The number of points in the interval $$[2, 4]$$, at which the function $$f(x) = \left\lfloor x^2 - x - \frac{1}{2} \right\rfloor$$, where $$[\cdot]$$ denotes the greatest integer function, is discontinuous, is _________.

Dimensions of universal gravitational constant $$(G)$$ in terms of Planck's constant $$(h)$$, distance $$(L)$$, mass $$(M)$$ and time $$(T)$$ are :

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is : (Take $$g = 10$$ m/s$$^2$$)

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is _________ m. (Take $$g = 10$$ m/s$$^2$$)

A particle having charge $$10^{-9}$$ C moving in the x-y plane in fields of $$0.4\hat{j}$$ N/C and $$4 \times 10^{-3}\hat{k}$$ T experiences a force of $$(4\hat{i} + 2\hat{j}) \times 10^{-10}$$ N. The velocity of the particle at that instant is :

If X and Y are the inputs, the given circuit works as :

If a body of mass 1 kg falls on the earth from infinity, it attains velocity $$(v)$$ and kinetic energy $$(k)$$ on reaching the surface of earth. The values of $$v$$ and $$k$$ respectively are ______.
(Take radius of earth to be 6400 km and $$g = 9.8$$ m/s$$^2$$)

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______mm.

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $$\alpha\pi \times 10^{-4}$$ J. The value of $$\alpha$$ is : (Take $$\pi = 3.14$$)

A mixture of carbon dioxide and oxygen has volume 8310 cm$$^3$$, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _____.
(Assume both gases behave like ideal gases) [$$R = 8.31$$ J/mol.K]

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m$$^3$$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is _________ Poise. (Take $$g = 10$$ m/s$$^2$$)

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is ______ N.
(Take g=10 m/$$s^{2}$$)

An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, $$\vec{B} = 2 \times 10^{-7}\hat{j}$$ T is associated with this wave. The value of corresponding electric field $$\vec{E}$$ at this point is _________ V/m.

Two resistors of 200 $$\Omega$$ and 400 $$\Omega$$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 $$\Omega$$ resistance. The potential drop across the bulb is :

Two metal plates (A, B) are kept horizontally with separation of $$\frac{12}{\pi}$$ cm, with plate A on the top. An atomizer jet sprays oil (density $$1.5$$ g/cm$$^3$$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $$V_A$$ and $$V_B$$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $$V_A$$ and $$V_B$$ are ______.
(Neglect the air resistance to the droplets and take $$g = 10$$ m/s$$^2$$)

Two point charges $$8\,\mu$$C and $$-2\,\mu$$C are located at $$x = 2$$ cm and $$x = 4$$ cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is _______.

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 _____.