NTA JEE Mains 4th April Shift 2 2026

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because

A. The size of gold nucleus is very small as compared to the size of gold atom.

B. Alpha particle and gold nucleus have equal charge.

C. The impact parameter is minimum for a few alpha particles.

D. A few alpha particles have very high kinetic energy.

E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below: 

The de Broglie wavelength associated with an electron accelerated through a potential difference V is $$\lambda_e$$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $$\lambda_p$$. If their corresponding masses are $$m_e$$ and $$m_p$$, respectively, then the ratio of their de Broglie wavelengths $$\left(\frac{\lambda_e}{\lambda_p}\right)$$ is ______.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: A diode under reverse-biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases drastically.

Reason R: Below the critical voltage limit, only majority charge carriers flow which increases drastically above critical voltage.
Choose the correct answer from the options given below : 

A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W, then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is ______ $$\Omega$$.

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s.

(take $$g = 10$$ m/s$$^2$$)

Two identical small bar magnets each of dipole moment $$3\sqrt{5}$$ J/T are placed at a center to center separation of 10 cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is $$\alpha \times 10^{-3}$$ T. The value of $$\alpha$$ is ______

($$\mu_0 = 4\pi \times 10^{-7}$$ Tm/A)

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of 30° with the direction of the magnetic field. The torque acting on the coil is $$\alpha \times 10^{-4}$$ N.m. The value of $$\alpha$$ is ______.

($$\pi = 3.14$$)

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of 7$$^{th}$$ bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is $$\alpha \times 10^{-9}$$ m. The value of $$\alpha$$ is ______.