NTA JEE Main 2025 April 8th Shift 2

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $$T_1$$ and $$T_2$$ are the total flying times of first and second ball, respectively, then the ratio of $$T_1$$ and $$T_2$$ is :

The amplitude and phase of a wave formed by the superposition of two harmonic travelling waves, $$y_1(x, t) = 4\sin(kx - \omega t)$$ and $$y_2(x, t) = 2\sin(kx - \omega t + \frac{2\pi}{3})$$, are :
(Take the angular frequency of initial waves same
as $$\omega$$)

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be :

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$$-\sigma$$'. The rate of change of de-Broglie wave length associated with the electron varies inversely as $$n^{th}$$ power of time. The numerical value of n is _____.

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$$^3$$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _____ litre. (Take 1 atm = $$10^5$$ Pa)

Space between the plates of a parallel plate capacitor of plate area 4 cm$$^2$$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is _____ pF. (Given $$\epsilon_0 = 8.85 \times 10^{-12}$$ F/m)

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $$25\pi$$ Nm for 40s, the speed increases to 2100 rpm. The diameter of the disk is _____ m.

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. The unknown mass is _____ kg.