NTA JEE Main 2025 April 02 Shift 1

A river is flowing from west to east direction with speed of 9 km h$$^{-1}$$. If a boat capable of moving at a maximum speed of 27 km h$$^{-1}$$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150° to direction of river flow, then the width of the river is:

A point charge $$+q$$ is placed at the origin. A second point charge $$+9q$$ is placed at $$(d, 0, 0)$$ in Cartesian coordinate system. The point in between them where the electric field vanishes is:

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged?

A particle is subjected to two simple harmonic motions as:
$$x_1 = \sqrt{7} \sin 5t$$ cm
and $$x_2 = 2\sqrt{7} \sin\left(5t + \frac{\pi}{3}\right)$$ cm
where x is displacement and $$t$$ is time in seconds. The maximum acceleration of the particle is $$x \times 10^{-2}$$ ms$$^{-2}$$. The value of x is:

The relationship between the magnetic susceptibility ($$\chi$$) and the magnetic permeability ($$\mu$$) is given by: ($$\mu_0$$ is the permeability of free space and $$\mu_r$$ is relative permeability)

A zener diode with 5V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a 400 $$\Omega$$ resistor connected in series, the zener current is found to be 4 times load current. The load current ($$I_L$$) and load resistance ($$R_L$$) are:

In an adiabatic process, which of the following statements is true?

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act on Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is:

Let $$B_1$$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let $$B_2$$ be the magnitude of magnetic field at an axial distance 'x' from the center. For $$x : R = 3 : 4$$, $$\frac{B_2}{B_1}$$ is:

Considering Bohr's atomic model for hydrogen atom:
(A) the energy of H atom in ground state is same as energy of He$$^+$$ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li$$^{++}$$ ion in its second excited state.
(C) the energy of H atom in ground state is same as that of He$$^+$$ ion for its ground state.
(D) the energy of He$$^+$$ ion in its first excited state is same as that for Li$$^{++}$$ ion in its ground state.
Choose the correct answer from the options below: