NTA JEE Mains 21st Jan 2026 Shift 2

Two cars A and B each of mass $$10^{3}$$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is __________ J.s.

A capacitor C is first charged fully with potential difference of $$V_{0}$$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In t s 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is ____________s.

Two known resistances of $$R \Omega$$ and $$2R \Omega$$ and one unknown resistance $$X \Omega$$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $$X \Omega$$, then the value of X is __________ $$\Omega$$.

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading tl1en the length AP is ____ cm.

A spherical body of radius r and density $$\sigma$$ falls freely through a viscous liquid having density $$\rho$$ and viscosity $$\eta$$ and attains a terminal velocity $$\upsilon_{0}$$. Estimated maximum error in the quantity $$\eta$$ is: (Ignore errors associated with $$\sigma,\rho$$ and g, gravitational acceleration)

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $$\sigma$$ = 10mho/m. The ratio of maximum conduction current density to maximum displacement current
density is ___________.
[Take $$\frac{1}{4\pi \epsilon_{0}} = 9 \times 10^{9} Nm^{2}/C^{2}$$]

A diatomic gas ( y= 1.4) does 100 J of work when it is expanded isobarically. Then the heat given to the gas ____ J.

In a Young's double slit experiment set up, the two slits are kept 0.4. mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness $$20\mu m$$ is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by $$\frac{\alpha}{10}$$, where $$\alpha$$ is __________.

A particle having electric charge $$3\times 10^{-19}$$ C and mass $$6 \times 10^{-27}$$ kg is accelerated by applying an electric Potential of 1.21 V. Wavelength of the matter wave
associated with the particle is $$\alpha \times 10^{-12}m$$. The value of $$\alpha$$ is __________. (Take Planck's constant = $$6.6 \times 10^{-34}$$ J.s. )

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ________ cm/ s.