NTA JEE Mains 23rd Jan 2026 Shift 1

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $$(g=10m/s^{2})$$ through a uniform horizontal magnetic fie ld of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of200 m is ____ mV.

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. the energy stored in A is E. The energy stored in B, when spring constants $$K_{A},K_{B}$$ of A and B, respectively satisfy the relation $$4K_{A}=3K_{B}$$ is:

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion w ithout deviation. The angle of second prism is ____ .

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in $$^{\circ}C$$), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material 31 cal/kg.$$^{\circ}C$$ and 1 cal =4.2 J)

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulwn is released from an angle of 60° with vertical, then maximum induced EMF between the point of s uspension and point of oscillation is ______mV (Take $$g= 10 m/s^{2}$$)

The equation of the electric field of an electromagnetic wave propagating through free space is given
by: E=$$\sqrt{377}$$ $$\sin(6.27\times10^{3}t-2.09\times 10^{-5}x)N/C$$
The average power of the electromagnetic wave is $$\left(\frac{1}{\alpha}\right)W/m^{2}$$. The value of $$\alpha$$ is______
$$\left(Take \sqrt{\frac{\mu_{\circ}}{\epsilon_{\circ}}}=377 in SI units \right)$$

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. the ratios of the slits separations and that of the wavelengths of light used are 2: 1 and 1 : 2 respectively. The corresponding ratio of the distances between the slits and the respective screens $$(D_{1}/D_{2})$$ is ______.

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $$K_{1}=2,K_{2}=3\text{ and } K_{3}=5$$ (as shown in figtue). lf new capacitance is $$\frac{n}{3}C$$ then the value of n is_____.

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V= 5 sin(100t) The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ____ µF.