NTA JEE Main 30th January 2023 Shift 1

Two isolated metallic solid spheres of radii $$R$$ and $$2R$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $$\sigma'$$. The ratio $$\frac{\sigma'}{\sigma}$$ is:

The charge flowing in a conductor changes with time as $$Q(t) = \alpha t - \beta t^2 + \gamma t^3$$, where $$\alpha$$, $$\beta$$ and $$\gamma$$ are constants. Minimum value of current is:

A massless square loop, of wire resistance $$10$$ $$\Omega$$, supporting a mass of $$1$$ g, hangs vertically with one of its sides in a uniform magnetic field of $$10^3$$ G, directed outwards in the shaded region. A dc voltage $$V$$ is applied to the loop. For what value of $$V$$, the magnetic force will exactly balance the weight of the supporting mass of $$1$$ g?
(If sides of the loop $$= 10$$ cm, $$g = 10$$ m s$$^{-2}$$)

The magnetic moments associated with two closely wound circular coils $$A$$ and $$B$$ of radius $$r_A = 10$$ cm and $$r_B = 20$$ cm respectively are equal if: (Where $$N_A$$, $$I_A$$ and $$N_B$$, $$I_B$$ are number of turn and current of $$A$$ and $$B$$ respectively)

In a series $$LR$$ circuit with $$X_L = R$$, power factor is $$P_1$$. If a capacitor of capacitance $$C$$ with $$X_C = X_L$$ is added to the circuit the power factor becomes $$P_2$$. The ratio of $$P_1$$ to $$P_2$$ will be:

A person has been using spectacles of power $$-1.0$$ diopter for distant vision and a separate reading glass of power $$2.0$$ diopters. What is the least distance of distinct vision for this person:

A small object at rest, absorbs a light pulse of power $$20$$ mW and duration $$300$$ ns. Assuming speed of light as $$3 \times 10^8$$ m s$$^{-1}$$. The momentum of the object becomes equal to:

Speed of an electron in Bohr's $$7^{th}$$ orbit for Hydrogen atom is $$3.6 \times 10^6$$ m s$$^{-1}$$. The corresponding speed of the electron in $$3^{rd}$$ orbit, in m s$$^{-1}$$ is:

The output waveform of the given logical circuit for the following inputs $$A$$ and $$B$$ as shown below, is

A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of $$120$$ V and $$80$$ V respectively. The amplitude of each side band is: