NTA JEE Main 17th March 2021 Shift 2

A sound wave of frequency 245 Hz travels with the speed of 300 m s$$^{-1}$$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

Two cells of emf $$2E$$ and $$E$$ with internal resistance $$r_1$$ and $$r_2$$ respectively are connected in series to an external resistor $$R$$ (see figure). The value of $$R$$, at which the potential difference across the terminals of the first cell becomes zero is:

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15$$\Omega$$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC.

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $$P$$ which lies on the centre of the semicircle?

Match List-I with List-II:
      List-I |                                                                                                                                             List-II
a. Phase difference between current and voltage in a purely resistive AC circuit |          i. $$\frac{\pi}{2}$$; current leads voltage
b. Phase difference between current and voltage in a pure inductive AC circuit |           ii. zero
c. Phase difference between current and voltage in a pure capacitive AC circuit |         iii. $$\frac{\pi}{2}$$; current lags voltage
d. Phase difference between current and voltage in an LCR series circuit |                    iv. $$\tan^{-1}\left(\frac{X_C - X_L}{R}\right)$$
Choose the most appropriate answer from the options given below:

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

Two identical photocathodes receive the light of frequencies $$f_1$$ and $$f_2$$ respectively. If the velocities of the photo-electrons coming out are $$v_1$$ and $$v_2$$ respectively, then:

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

Which one of the following will be the output of the given circuit?

A carrier signal $$C(t) = 25\sin(2.512 \times 10^{10}t)$$ is amplitude modulated by a message signal $$m(t) = 5\sin(1.57 \times 10^{8}t)$$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?