NTA JEE Mains 29th Jan 2025 Shift 2

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

Match List - I with List - II.

Choose the correct answer from the options given below :

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v)of the belt, i.e. $$\frac{dm}{dt} \propto \sqrt{v}$$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0, they are given an initial velocity $$\vec{V}_A = V_0 \overrightarrow{AC}$$, $$\vec{V}_B = V_0 \overrightarrow{BA}$$ and $$\vec{V}_C = V_0 \overrightarrow{CB}$$. Here $$\overrightarrow{AC}$$, $$\overrightarrow{CB}$$ and $$\overrightarrow{BA}$$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

The number of spectral lines emitted by atomic hydrogen that is in the $$4^{th}$$ energy level, is

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index 1.33), its focal length changes to

In an experiment with photoelectric effect, the stopping potential,

A capacitor $$C_1 = 6\,\mu\text{F}$$, is charged to a potential difference of $$V_{0} = 5$$ using a 5 V battery. The battery is removed and another capacitor, $$C_2 = 12\,\mu\text{F}$$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($$q_{1}$$ and $$q_{2}$$ on the capacitors $$C_{1}$$ and $$C_{2}$$ when equilibrium condition is reached.

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $$\vec{E}$$ and magnetic field, $$\vec{B}$$
vectors associated with the wave in Cartesian frame are

A cup of coffee cools from $$90^{\circ}$$ to $$80^{\circ}$$ in t minutes when the room temperature is $$20^{\circ}$$. The time taken by the similar cup of coffee to cool from $$80^{\circ}$$ to $$60^{\circ}$$ at the same room temperature is :