NTA JEE Main 24th June 2022 Shift 1

A vertical electric field of magnitude $$4.9 \times 10^{5}$$ N C$$^{-1}$$ just prevents a water droplet of a mass $$0.1$$ g from falling. The value of charge on the droplet will be : (Given $$g = 9.8$$ m s$$^{-2}$$)

A parallel plate capacitor is formed by two plates each of area $$30\pi$$ cm$$^2$$ separated by $$1$$ mm. A material of dielectric strength $$3.6 \times 10^{7}$$ V m$$^{-1}$$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $$7 \times 10^{-6}$$ C, the value of dielectric constant of the material is :
[Use $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$$ N m$$^2$$ C$$^{-2}$$]

Two identical cells each of emf $$1.5$$ V are connected in parallel across a parallel combination of two resistors each of resistance $$20$$ $$\Omega$$. A voltmeter connected in the circuit measures $$1.2$$ V. The internal resistance of each cell is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

The magnetic field at the centre of a circular coil of radius $$r$$, due to current $$I$$ flowing through it, is $$B$$. The magnetic field at a point along the axis at a distance $$\frac{r}{2}$$ from the centre is :

A resistance of $$40$$ $$\Omega$$ is connected to a source of alternating current rated $$220$$ V, $$50$$ Hz. Find the time taken by the current to change from its maximum value to the rms value :

A plane electromagnetic wave travels in a medium of relative permeability $$1.61$$ and relative permittivity $$6.44$$. If magnitude of magnetic intensity is $$4.5 \times 10^{-2}$$ A m$$^{-1}$$ at a point, what will be the approximate magnitude of electric field intensity at that point?
(Given : Permeability of free space $$\mu_0 = 4\pi \times 10^{-7}$$ N A$$^{-2}$$, speed of light in vacuum $$c = 3 \times 10^{8}$$ m s$$^{-1}$$)

Choose the correct option from the following options given below :

Nucleus $$A$$ is having mass number $$220$$ and its binding energy per nucleon is $$5.6$$ MeV. It splits in two fragments $$B$$ and $$C$$ of mass numbers $$105$$ and $$115$$. The binding energy of nucleons in $$B$$ and $$C$$ is $$6.4$$ MeV per nucleon. The energy $$Q$$ released per fission will be:

A baseband signal of $$3.5$$ MHz frequency is modulated with a carrier signal of $$3.5$$ GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?