NTA JEE Mains 1st feb 2023 Shift 2

As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi}{10}$$ m is carrying current $$I = 3A$$. The magnitude of the magnetic field at the center $$O$$ of the arc is: (The permeability of the vacuum $$= 4\pi \times 10^{-7} \text{ NA}^{-2}$$)

A square shaped coil of area $$70 \text{ cm}^2$$ having 600 turns rotates in a magnetic field of $$0.4 \text{ Wb m}^{-2}$$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $$60°$$ with the field, will be ______ V.
(Take $$\pi = \frac{22}{7}$$)

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

Two objects $$A$$ and $$B$$ are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t = 10 \mu m$$ and refractive index $$\mu = 1.2$$ is inserted infront of slit $$S_1$$. The experiment is conducted in air ($$\mu = 1$$) and uses a monochromatic light of wavelength $$\lambda = 500$$ nm. Due to the insertion of the plate, central maxima is shifted by a distance of $$x\beta_0$$. $$\beta_0$$ is the fringe-width before the insertion of the plate. The value of the $$x$$ is ______

The threshold frequency of metal is $$f_0$$. When the light of frequency $$2f_0$$ is incident on the metal plate, the maximum velocity of photoelectron is $$v_1$$. When the frequency of incident radiation is increased to $$5f_0$$, the maximum velocity of photoelectrons emitted is $$v_2$$. The ratio of $$v_1$$ to $$v_2$$ is:

An electron of a hydrogen like atom, having $$Z = 4$$, jumps from $$4^{th}$$ energy state to $$2^{nd}$$ energy state. The energy released in this process, will be: (Given $$Rch = 13.6$$ eV)
Where $$R =$$ Rydberg constant, $$c =$$ Speed of light in vacuum, $$h =$$ Planck's constant

Nucleus $$A$$ having $$Z = 17$$ and equal number of protons and neutrons has 1.2 MeV binding energy per nucleon. Another nucleus $$B$$ of $$Z = 12$$ has total 26 nucleons and 1.8 MeV binding energy per nucleons. The difference of binding energy of $$B$$ and $$A$$ will be ______ MeV.

Choose the correct statement about Zener diode:

In an amplitude modulation, a modulating signal having amplitude of $$X$$ V is superimposed with a carrier signal of amplitude $$Y$$ V in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude $$2Y$$ V. The ratio of modulation index in the two case respectively will be :