NTA JEE Main 26th August 2021 Shift 1

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3 $$\Omega$$?
(Given resistivities of iron and copper-nickel alloy wire are 12 $$\mu\Omega$$ cm and 51 $$\mu\Omega$$ cm respectively)

The fractional change in the magnetic field intensity at a distance $$r$$ from centre on the axis of current carrying coil of radius $$a$$ to the magnetic field intensity at the centre of the same coil is: (Take $$r < a$$)

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k$$\Omega$$, an inductor of inductive reactance $$X_L = 250\pi$$ $$\Omega$$ and an unknown capacitor. The value of capacitance to maximise the average power should be: (take $$\pi^2 = 10$$)

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8 A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit (in s).

Car $$B$$ overtakes another car $$A$$ at a relative speed of 40 m s$$^{-1}$$. How fast will the image of car $$B$$ appear to move in the mirror of focal length 10 cm fitted in car $$A$$, when the car $$B$$ is 1.9 m away from the car $$A$$?

In a photoelectric experiment, ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $$\phi = 2.5$$ eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential.
($$h = 6.63 \times 10^{-34}$$ J s, $$c = 3 \times 10^8$$ m s$$^{-1}$$)

A particular hydrogen like ion emits radiation of frequency $$2.92 \times 10^{15}$$ Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be:

Identify the logic operation carried out by the given circuit:

Statement I: By doping silicon semiconductors with pentavalent material, the electrons density increases.
Statement II: The n-type of semiconductor has a net negative charge.
In the above statements, choose the most appropriate answer from the options given below:

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.