NTA JEE Main 9th January 2020 Shift 2

A wire of length $$L$$ and mass per unit length $$6.0 \times 10^{-3}$$ kg m$$^{-1}$$ is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz. Then $$L$$ in meters is:

A small circular loop of conducting wire has radius $$a$$ and carries current $$I$$. It is placed in a uniform magnetic field $$B$$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period $$T$$. The mass of the loop is $$m$$ then:

An electron gun is placed inside a long solenoid of radius $$R$$ on its axis. The solenoid has $$n$$ turns/length and carries a current $$I$$. The electron gun shoots an electron along the radius of the solenoid with speed $$v$$. If the electron does not hit the surface of the solenoid, maximum possible value of $$v$$ is (all symbols have their standard meaning):

In $$LC$$ circuit the inductance $$L = 40$$ mH and capacitance $$C = 100$$ $$\mu$$F. If a voltage $$V(t) = 10\sin(314t)$$ is applied to the circuit, the current in the circuit is given as:

Two identical capacitors $$A$$ and $$B$$, charged to the same potential $$5V$$ are connected in two different circuits as shown below at time $$t = 0$$. If the charge on capacitors $$A$$ and $$B$$ at time $$t = CR$$ is $$Q_A$$ and $$Q_B$$ respectively, then (Here $$e$$ is the base of natural logarithm)

A plane electromagnetic wave is propagating along the direction $$\frac{\hat{i}+\hat{j}}{\sqrt{2}}$$, with its polarization along the direction $$\hat{k}$$. The correct form of the magnetic field of the wave would be (here $$B_0$$ is an appropriate constant):

There is a small source of light at some depth below the surface of water (refractive index $$= \frac{4}{3}$$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly):
[Use the fact that surface area of a spherical cap of height $$h$$ and radius of curvature $$r$$ is $$2\pi rh$$]

An electron of mass $$m$$ and magnitude of charge $$e$$ at rest, gets accelerated by a constant electric field $$E$$. The rate of change of de-Broglie wavelength of this electron at time $$t$$ is (ignore relativistic effects):

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state?

The current $$i$$ in the network is: