NTA JEE Main 2025 April 7th Shift 1

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius(r). Which of the following curves represents the variation of r with E?

An object of mass 1000 g experiences a time dependent force $$\vec{F} = (2t\hat{i} + 3t^2\hat{j})$$ N. The power generated by the force at time t is :

Two wires A and B are made of same material having ratio of lengths $$\frac{L_A}{L_B} = \frac{1}{3}$$ and their diameters ratio $$\frac{d_A}{d_B} = 2$$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Two charges $$q_1$$ and $$q_2$$ are separated by a distance of 30 cm. A third charge $$q_3$$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $$q_3$$ from C to D is given by $$\frac{q_3 K}{4\pi\epsilon_0}$$, the value of K is :

A, B and C are disc, solid sphere, and spherical shell respectively with same radii and masses. These masses are placed as shown in the figure. The moment of inertia of the given system about PQ is $$\frac{x}{15}I$$, where I is the moment of inertia of the disc about its diameter. The value of x is ______.

For ac circuit shown in figure, R = 100 k$$\Omega$$ and C = 100 pF and the phase difference between $$V_{in}$$ and $$(V_B - V_A)$$ is $$90^{\circ}$$. The input signal frequency is $$10^x$$ rad/sec, where 'x' is ______.

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ___ cm.
(Consider liquids are immisible)

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727 degrees C and power radiated by the wire is 94.2 W. Its emissivity is $$\frac{x}{8}$$ where x = ______.
(Given $$\sigma = 6.0 \times 10^{-8}$$ W m$$^{-2}$$ K$$^{-4}$$, $$\pi = 3.14$$ and assume that the emissivity of wire material is same at all wavelength. )

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $$\times 10^{-1}$$ J. (Take $$\pi = 3.14$$)