NTA JEE Main 27th June 2022 Shift 2

The equation of a particle executing simple harmonic motion is given by $$x = \sin\pi\left(t + \frac{1}{3}\right)$$ m. At $$t = 1$$ s, the speed of particle will be (Given: $$\pi = 3.14$$)

If a wave gets refracted into a denser medium, then which of the following is true?

If a charge $$q$$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be

Three identical charged balls each of charge $$2C$$ are suspended from a common point $$P$$ by silk threads of $$2$$ m each (as shown in figure). They form an equilateral triangle of side $$1$$ m. The ratio of net force on a charged ball to the force between any two charged balls will be

Two long parallel conductors $$S_1$$ and $$S_2$$ are separated by a distance $$10$$ cm and carrying currents of $$4$$ A and $$2$$ A respectively. The conductors are placed along $$x$$-axis in $$X-Y$$ plane. There is a point $$P$$ located between the conductors (as shown in figure).
A charge particle of $$3\pi$$ coulomb is passing through the point $$P$$ with velocity $$\vec{v} = (2\hat{i} + 3\hat{j})$$ m s$$^{-1}$$.
The force acting on the charge particle is $$4\pi \times 10^{-5}(-x\hat{i} + 2\hat{j})$$ N. The value of $$x$$ is

Given below are two statements :
Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.
Statement II: In a material medium, the EM wave travels with speed $$v = \frac{1}{\sqrt{\mu_0\varepsilon_0}}$$.
In the light of the above statements, choose the correct answer from the options given below.

A convex lens has power $$P$$. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

Given below are two statements
Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit ($$E_1$$) to higher energy orbit ($$E_2$$), is given as $$hf = E_1 - E_2$$
Statement II: The jumping of electron from higher energy orbit ($$E_2$$) to lower energy orbit ($$E_1$$) is associated with frequency of radiation given as $$f = \frac{(E_2-E_1)}{h}$$. This condition is Bohr's frequency condition.
In the light of the above statements, choose the correct answer from the options given below:

For a transistor to act as a switch, it must be operated in

We do not transmit low frequency signal to long distances because
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.
(b) Effective power radiated by a long wavelength baseband signal would be high.
(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously.
(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well.
Therefore, the most suitable option will be :