NTA JEE Main 3rd September 2020 Shift 1

Model a torch battery of length $$l$$ to be made up of a thin cylindrical bar of radius $$a$$ and a concentric thin cylindrical shell of radius $$b$$ filled in between with an electrolyte of resistivity $$\rho$$ (see figure). If the battery is connected to a resistance of value $$R$$, the maximum Joule heating in $$R$$ will take place for:

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current $$I$$ (Ampere) in units of $$\frac{\mu_0 I}{\pi}$$ is:

A charged particle carrying charge 1 $$\mu C$$ is moving with velocity $$\left(2\hat{i} + 3\hat{j} + 4\hat{k}\right)$$ m s$$^{-1}$$. If an external magnetic field of $$\left(5\hat{i} + 3\hat{j} - 6\hat{k}\right) \times 10^{-3}$$ T exists in the region where the particle is moving then the force on the particle is $$\vec{F} \times 10^{-9}$$ N. The vector $$\vec{F}$$ is:

A 750 Hz, 20 V(rms) source is connected to a resistance of 100 $$\Omega$$, an inductance of 0.1803 H and a capacitance of 10 $$\mu$$F all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C (assume no loss of heat to the surroundings) is close to:

The magnetic field of a plane electromagnetic wave is $$\vec{B} = 3 \times 10^{-8} \sin\left[200\pi(y + ct)\right]\hat{i}$$ T. Where, $$c = 3 \times 10^8$$ m s$$^{-1}$$ is the speed of light. The corresponding electric field is:

In a Young's double slit experiment, light of 500 nm is used to produce and interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to:

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:

In a radioactive material, a fraction of active material remaining after the time $$t$$ is $$\frac{9}{16}$$. The fraction that was remaining after the time $$\frac{t}{2}$$ is:

When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is:

Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as: