NTA JEE Mains 28th Jan 2025 Shift 1

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below

Choose the correct nuclear process from the below options [p: proton, n : neutron, $$e^{-}$$:electron, $$e^{+}$$ : positron, $$\upsilon$$ : neutrino, $$\overline{\upsilon}$$ : antineutrino]

A hemispherical vessel is completely filled with a liquid of refractive index $$\mu$$. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is

A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine $$E_{1}$$ works between 473 K to 373 K and engine $$E_{2}$$ works between 373 K to 273 K . If $$\eta_{12},\eta_{1}$$ and $$\eta_{2}$$ are the efficiencies of the engines $$E,E_{1}$$ and $$E_{2}$$, respectively, then

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is released at a distance "a" from the wire with a speed $$\epsilon_{\circ}$$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [$$\mu_{\circ}$$ is vacuum permeability]

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is Options.

In the experiment for measurement of viscosity $$'\eta'$$ of given liquid with a ball having radius R, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of $$\eta$$ will change. Choose the correct answer from the options given below:

Due to presence of an em-wave whose electric component is given by $$E = 100\sin(\omega t - kx)NC^{-1}$$, a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

A bead of mass 'm' slides without friction on the wall of a vertical circular hoop of radius 'R' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is 'R'. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is 'k', g is accleration due to gravity

Find the equivalent resistance between two ends of the following circuit