NTA JEE Main 25th January 2023 Shift 2

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be $$(\frac{x}{3})^{\frac{1}{3}}$$. The value of '$$x$$' is:

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m s$$^{-1}$$. The initial speed of the smaller body before collision is _____ m s$$^{-1}$$.

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $$\frac{x}{7}$$. The value of $$x$$ is _____.

A spherical drop of liquid splits into 1000 identical spherical drops. If $$u_i$$ is the surface energy of the original drop and $$u_f$$ is the total surface energy of the resulting drops, the (ignoring evaporation), $$\frac{u_f}{u_i} = (\frac{10}{x})$$. Then value of $$x$$ is _____:

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m s$$^{-1}$$. The frequency observed by the observer will be (given speed of sound = 330 m s$$^{-1}$$) _____ Hz.

A capacitor has capacitance 5 $$\mu$$F when its parallel plates are separated by air medium of thickness $$d$$. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $$\frac{d}{2}$$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be _____ $$\mu$$F.

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3 $$\Omega$$. Cell 2 has emf of 6 V and internal resistance of 6 $$\Omega$$. An external resistor R of 4 $$\Omega$$ is connected across A and B. The current flowing through R will be _____ A.

Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _____ $$\times 10^{-6}$$ T. (Given: $$\sqrt{2}$$ = 1.4)

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $$R = 80$$ $$\Omega$$, an inductor of inductive reactance $$X_L = 70$$ $$\Omega$$, and a capacitor of capacitive reactance $$X_C = 130$$ $$\Omega$$. The power factor of circuit is $$\frac{x}{10}$$. The value of $$x$$ is:

An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is _____ cm.