NTA JEE Mains 24th jan 2023 Shift 1

As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3 $$\Omega$$. The currents through the resistors $$R_4$$ and $$R_5$$ are $$I_4$$ and $$I_5$$ respectively. The values of $$I_4$$ and $$I_5$$ are:

Two long straight wires $$P$$ and $$Q$$ carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire $$P$$ is $$F_1$$. If distance between wires is halved and currents on them are doubled, force $$F_2$$ on 10 cm length of wire $$P$$ will be:

A circular loop of radius $$R$$ is carrying current $$i$$ A. The ratio of magnetic field at the centre of circular loop and at a distance $$R$$ from the center of the loop on its axis is :

A conducting loop of radius $$\frac{10}{\sqrt{\pi}}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

If $$\vec{E}$$ and $$\vec{K}$$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ($$\omega$$ - angular frequency)

Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is $$\theta_B$$, then Brewster's angle for the light propagating from glass to air is $$\frac{\pi}{2} - \theta_B$$.
Statement II : The Brewster's angle for the light propagating from glass to air is $$\tan^{-1}\mu_g$$, where $$\mu_g$$ is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below :

From the photoelectric effect experiment, following observations are made. Identify which of these are correct
A. The stopping potential depends only on the work function of the metal.
B. The saturation current increases as the intensity of incident light increases.
C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light.
D. Photoelectric effect can be explained using wave theory of light.
Choose the correct answer from the options given below:

Consider the following radioactive decay process:
$$^{218}_{84}A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^-} A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^+} A_5 \xrightarrow{\gamma} A_6$$
The mass number and the atomic number of $$A_6$$ are given by:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement.
Reason R: The current in the forward bias is more than the current in the reverse bias for a $$p - n$$ junction diode.
In the light of the above statement, choose the correct answer from the options given below :

A modulating signal is a square wave, as shown in the figure. If the carrier wave is given as $$c(t) = 2\sin(8\pi t)$$ volts, the modulation index is: