NTA JEE Mains 31st Jan 2024 Shift 2

Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $$\frac{x}{20}$$ kg m$$^2$$, where the value of $$x$$ is

A body of mass $$m$$ is projected with a speed $$u$$ making an angle of $$45°$$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $$\frac{\sqrt{2}mu^3}{Xg}$$. The value of $$X$$ is

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $$4.0 \times 10^{-5}$$ m and Young's modulus of the metal is $$2.0 \times 10^{11}$$ N m$$^{-2}$$. The longitudinal strain developed in the wire is $$\frac{1}{\alpha\pi}$$. The value of $$\alpha$$ is [Use $$g = 10$$ m s$$^{-2}$$]

The time period of simple harmonic motion of mass $$M$$ in the given figure is $$\pi\sqrt{\frac{\alpha M}{5K}}$$, where the value of $$\alpha$$ is

The distance between charges $$+q$$ and $$-q$$ is $$2l$$ and between $$+2q$$ and $$-2q$$ is $$4l$$. The electrostatic potential at point $$P$$ at a distance $$r$$ from centre $$O$$ is $$-\alpha\frac{ql}{r^2} \times 10^9$$ V, where the value of $$\alpha$$ is. (Use $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$)

In the following circuit, the battery has an emf of 2 V and an internal resistance of $$\frac{2}{3}$$ $$\Omega$$. The power consumption in the entire circuit is ______ W.

Two circular coils $$P$$ and $$Q$$ of 100 turns each have same radius of $$\pi$$ cm. The currents in $$P$$ and $$Q$$ are 1 A and 2 A respectively. $$P$$ and $$Q$$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $$\sqrt{x}$$ mT, where $$x =$$ [Use $$\mu_0 = 4\pi \times 10^{-7}$$ T m A$$^{-1}$$]

The magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance 8 $$\Omega$$ varies with time (in seconds) as $$\phi = 5t^2 - 36t + 1$$. The induced current in the circuit at $$t = 2$$ s is ______ A.

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and volume $$V_2$$. If relation between mass number is $$A_2 = 4A_1$$, then $$\frac{V_2}{V_1} =$$