NTA JEE Main 26th August 2021 Shift 2

The two thin coaxial rings, each of radius $$a$$ and having charges $$+Q$$ and $$-Q$$ respectively are separated by a distance of $$s$$. The potential difference between the centres of the two rings is:

A parallel-plate capacitor with plate area $$A$$ has separation $$d$$ between the plates. Two dielectric slabs of dielectric constant $$K_1$$ and $$K_2$$ of same area $$\frac{A}{2}$$ and thickness $$\frac{d}{2}$$ are inserted in the space between the plates. The capacitance of the capacitor will be given by:

An electric bulb of 500 W at 100 V is used in a circuit having a 200 V supply. Calculate the resistance $$R$$ to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

If you are provided a set of resistances, 2 $$\Omega$$, 4 $$\Omega$$, 6 $$\Omega$$ and 8 $$\Omega$$. Connect these resistances to obtain an equivalent resistance of $$\frac{46}{3}$$ $$\Omega$$.

In the given circuit the AC source has $$\omega = 100$$ rad s$$^{-1}$$. Considering the inductor and capacitor to be ideal, what will be the current $$I$$ flowing through the circuit?

A light beam is described by $$E = 800 \sin\omega\left(t - \frac{x}{c}\right)$$. An electron is allowed to move normal to the propagation of light beam with a speed of $$3 \times 10^7$$ m s$$^{-1}$$. What is the maximum magnetic force exerted on the electron?

The de-Broglie wavelength of a particle having kinetic energy $$E$$ is $$\lambda$$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

At time $$t = 0$$, a material is composed of two radioactive atoms $$A$$ and $$B$$, where $$N_A(0) = 2N_B(0)$$. The decay constant of both kind of radioactive atoms is $$\lambda$$. However, $$A$$ disintegrates to $$B$$ and $$B$$ disintegrates to $$C$$. Which of the following figures represents the evolution of $$\frac{N_B(t)}{N_B(0)}$$ with respect to time $$t$$?

Four NOR gates are connected as shown in figure. The truth table for the given figure is:

A transmitting antenna at top of a tower has a height of 50 m, and the height of receiving antenna is 80 m. What is the range of communication for the line of sight (LOS) mode?
[use radius of the earth = 6400 km]