NTA JEE Mains 29th Jan 2025 Shift 2

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B . The separation between the images of O , formed by each refracting surface is :

A poly-atomic molecule ($$C_V = 3R,\, C_P = 4R$$, where R is gas constant) goes from phase space point $$A\ (P_A = 10^5\,\text{Pa},\ V_A = 4 \times 10^{-6}\,\text{m}$$ to point $$B\ (P_B = 5 \times 10^4\,\text{Pa},\ V_B = 6 \times 10^{-6}\,\text{m}^3)$$ to point $$C\,(P_C = 10^4\,\text{Pa},\; V_C = 8 \times 10^{-6}\,\text{m}^3).$$ A to B is an adiabatic path B and C to is an isothermal path. The net heat absorbed per unit mole by the system is :

Match List - I with List - II.

A point charge causes an electric flux of $$-2 \times 10^{4}\,\text{N m}^2 \text{C}^{-1}$$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given $$\varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ )

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $$\sigma_{0}$$.

Choose the correct option from the following.

The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 $$\times$$ $$10^{-4}$$ Tesla . If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ $$\pi$$ cm.

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is $$7 \times 10^{8}\,\text{V/s}$$ then the integer value of the distance between the parallel plates is (Take $$\varepsilon_0 = 9 \times 10^{-12}\,\frac{F}{m},\ \pi = \frac{22}{7}$$), ________ $$\mu\text{m}$$.

Two planets, A and B are orbiting a common star in circular orbits of radii $$R_{A}$$ and $$R_{B}$$, respectively, with $$R_{B} = 2R_{A}$$. The planet B is $$4\sqrt{2}$$ times more massive than planet A. The ratio $$\left(\frac{L_{B}}{L_{A}}\right)$$ of angular momentum $$(L_{B})$$ of planet B to that of planet $$A(L_{A})$$ is closest to integer ________.

Two cars P and Q are moving on a road in the same direction. Accleration of car P increases linearly with
time whereas car Q moves with a constant accleration. Both cars cross each other at time t=0, for the first
time. The maximum possible number of crossing(s) (including the crossing at t=0) is ________.

A physical quantity Q is related to four observables a,b,c,d as follows : $$Q = \frac{ab^{4}}{cd}$$ where, $$a = (60 \pm 3)\,\text{Pa}$$; $$b = (20 \pm 0.1)\,\text{m}$$; $$c = (40 \pm 0.2)\,\text{Nsm}^{-2}$$; and $$d = (50 \pm 0.1)\,\text{m}$$ , then the percentage error in Q is $$\frac{x}{1000}$$ , where x = ________ .