NTA JEE Mains 2nd April Shift 1 2026

A particle is rotating in a circular path and at any instant its motion can be described as $$\theta = \frac{5t^4}{40} - \frac{t^3}{3}$$. The angular acceleration of the particle after 10 seconds is __________ rad/s$$^2$$.

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant $$K = 5$$, the percentage increase in the capacitance is __________.

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $$\Delta Q : \Delta U : \Delta W$$ is __________.

Two charged conducting spheres S$$_1$$ and S$$_2$$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S$$_1$$ and S$$_2$$ spheres are E$$_{S1}$$ and E$$_{S2}$$ respectively. The value of $$\frac{E_{S1}}{E_{S2}}$$ is __________.

The equation of a plane progressive wave is given by $$y = 5 \cos \pi \left(200t - \frac{x}{150}\right)$$ where x and y are in cm and t is in second. The velocity of the wave is __________ m/s.

Two short electric dipoles A and B having dipole moment p$$_1$$ and p$$_2$$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of 60° with the line joining points O and x. The ratio of the dipole moments p$$_2$$/p$$_1$$ is __________.

For the given circuit (shown in part (A)) the time dependent input voltage $$v_{in}(t)$$ and corresponding output $$v_o(t)$$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.

When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coil number of turns, area of the coil and radius of the coil wire are 2N, 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is $$\sqrt{2} \alpha P$$. The value of $$\alpha$$ is __________.

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B$$_1$$ and B$$_2$$ respectively, then the ratio $$\frac{B_1}{B_2}$$ is __________.

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be __________.