NTA JEE Mains 22nd Jan 2026 Shift 2

A uniform bar of length 12 cm and mass 20m lies on a smooth horizontal table. Two point masses m and 2m are moving in opposite directions with same speed of $$\nu$$ and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $$\omega$$. The ratio of $$\nu$$ and $$\omega$$ is :

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly __ nm.

Given below are two statements:
Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is $$T= 2\pi \sqrt{\frac{R_{e}}{g}}$$ (for satellite very close to the earth surface), where $$R_{e}$$ radius of earth and g acceleration due to gravity. In the light of the above statements , choose the correct answer from the options given below:

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

Which of the following are true for a single slit diffraction?
A. Width of central maxima increases with increase in wavelength keeping slit width constant.
B. Width of central maxima increases with decrease in wavelength keeping slit width constant.
C. Width of central maxima increases with decrease in slit width at constant wavelength.
D. Width of central maxima increases with increase in slit width at constant wavelength.
E. Brightness of central maxima increases for decrease in wavelength at constant slit width.

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is m/ s. (Assume string does not slip and $$g = 10m/s^{2}$$)

An insulated cylinder of volume $$60cm^{3}$$ is filled with a gas at $$27 ^{\circ}C$$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $$20cm^{3}$$ while allowing the temperature to rise to $$77 ^{\circ}C$$. The final pressure is ___________ atmospheric pressure.

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $$30 ^{\circ}$$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ____ mm. (Take $$\pi = \frac{22}{7}$$)

A capacitor P with capacitance $$10 \times 10^{-6} F$$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance $$20 \times 10^{-6} F$$. The charge on capacitor Q when equilibrium is established will be $$\alpha \times 10^{-5}C$$ (assume capacitor Q does not have any charge initially), the value of $$\alpha$$ is _________.

A cylindrical conductor of length 2 m and area of cross-section $$0.2mm^{2}$$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $$\alpha \times 10^{-3}m^{2}/V.s.$$ The value of $$\alpha$$ is :
(electron concentration = $$5 \times 10^{28}/m^{3}$$ and electron charge = $$1.6 \times 10^{-19}C$$)