JEE Main 2021 (18 March Shift 1)

In a series $$LCR$$ resonance circuit, if we change the resistance only, from a lower to higher value:

An $$AC$$ source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

A plane electromagnetic wave of frequency 100 MHz is traveling in a vacuum along the $$x$$-direction. At a particular point in space and time, $$\vec{B} = 2.0 \times 10^{-8}\hat{k}$$ T. (where, $$\hat{k}$$ is unit vector along $$z$$-direction) What is $$\vec{E}$$ at this point?

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as nonuniform and distorted. The doctor diagnosed the problem as:

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 $$\mathring{\mathrm{A}}$$ is:

An oil drop of the radius 2 mm with a density 3 g cm$$^{-3}$$ is held stationary under a constant electric field $$3.55 \times 10^5$$ V m$$^{-1}$$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $$g = 9.81$$ m s$$^{-2}$$).

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is:

Imagine that the electron in a hydrogen atom is replaced by a muon ($$\mu$$). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

A radioactive sample disintegrates via two independent decay processes having half lives $$T_{1/2}^{(1)}$$ and $$T_{1/2}^{(2)}$$ respectively. The effective half-life $$T_{1/2}$$ of the nuclei is:

Match List-I with List-II:
                   List-I                                                                             List-II
(a) 10 km height over earth's surface                                (i) Thermosphere
(b) 70 km height over earth's surface                                (ii) Mesosphere
(c) 180 km height over earth's surface                              (iii) Stratosphere
(d) 270 km height over earth's surface                              (iv) Troposphere