NTA JEE Mains 24th Jan 2026 Shift 2

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle $$30^{\circ}$$ shown in figure, the velocity at the bottom point (A) of the circular path is
(g = gravitational acceleration)

The velocity (v) - Distance (x) graph is shown in figure. Which graph represents accderation(a) versus distance (x) variation of this system?

Distance between an object and three times magnified real image is 40 cm. The focal length of the minor used is ___ cm.

A moving coil galvanometer of resistance $$100\Omega$$ shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is ____ $$\Omega$$

Five persons $$P_{1},P_{2},P_{3},P{4}, \text{and} P_{5}$$ recorded object distance (u) and image distance (v) using same convex lens having powei· +5D as (25,96), (30,62), (35,37), (45,35)
and (50,32) respectively. Identify correct statement

When 300 J of heat given to an ideal gas with $$C_{p}= \frac{7}{2}R$$ its temperature raises from $$20^{\circ}C$$ to $$50^{\circ}C$$ keeping its volume constant. The mass of the gas is (approximately) __ g. (R = 8.314 J/mol.K)

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to $$I_{1}$$. A small co-centric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of inertia about its axis equals to $$I_{2}$$. The ratio $$I_{1}/I_{2}$$ is __________.

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) $$\mu J$$ of work is done in blowing it further to make its diameterl4 cm, then the value of x is_____.
$$\left(\pi=22/7\right)$$

A point charge q = l $$\mu C$$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 $$\mu C$$, distributed uniformly along its length, as shown in figure. Force between q and wire is __ N.
(Use: $$\frac{1}{4\pi\epsilon_{0}}=9 \times10^{9} N.m^{2}/C^{2}$$)

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $$2\Omega$$ and $$3\Omega$$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance $$x\Omega$$ is connected in parallel to $$3\Omega$$ resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is __________ $$\Omega$$ .