NTA JEE Main 2025 April 02 Shift 1

Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is '$$\alpha$$'. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is:

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object 'O', is: (C is the center of curvature of the spherical surface and R is the radius of curvature)

Match List-I with List-II.

Choose the correct answer from the options below:

A small bob of mass 100 mg and charge $$+10$$ $$\mu$$C is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density '$$\sigma$$' as shown in figure. If string subtends an angle of 45° with sheet at equilibrium the charge density of sheet will be:

(Given, $$\epsilon_0 = 8.85 \times 10^{-12}$$ F/m and acceleration due to gravity, $$g = 10$$ m/s$$^2$$)

A monochromatic light is incident on a metallic plate having work function $$\phi$$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is:

(Given: The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm$$^2$$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $$1.5 \times 10^3$$ kg/m$$^3$$. What force one needs to apply on the hinged door so that it does not get opened?

(Acceleration due to gravity = 10 m/s$$^2$$)

A steel wire of length 2 m and Young's modulus $$2.0 \times 10^{11}$$ Nm$$^{-2}$$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $$10^{-3}$$ respectively, then the elastic potential energy density of the wire is ______ $$\times 10^5$$ (in SI units).

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 30° in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is ______ µm.

$$\gamma_A$$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $$\gamma_B$$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $$\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$$, then the value of n is ______.

A person travelling on a straight line moves with a uniform velocity $$v_1$$ for a distance x and with a uniform velocity $$v_2$$ for the next $$\frac{3}{2}x$$ distance. The average velocity in this motion is $$\frac{50}{7}$$ m/s. If $$v_1$$ is 5 m/s then $$v_2$$ = ______ m/s.