NTA JEE Main 28th June 2022 Shift 2

Two point charges $$A$$ and $$B$$ of magnitude $$+8 \times 10^{-6}$$C and $$-8 \times 10^{-6}$$C respectively are placed at a distance $$d$$ apart. The electric field at the middle point $$O$$ between the charges is $$6.4 \times 10^4$$ N C$$^{-1}$$. The distance '$$d$$' between the point charges $$A$$ and $$B$$ is

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $$1.2 \times 10^{-5}$$. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of $$x$$ A in the same direction. If the force of attraction per meter of each wire is $$2 \times 10^{-6}$$ N, then the value of $$x$$ is approximately

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be (Assume the coil to be short circuited.)

An EM wave propagating in $$x$$-direction has a wavelength of 8 mm. The electric field vibrating $$y$$-direction has maximum magnitude of 60 Vm$$^{-1}$$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum:

In young's double slit experiment performed using a monochromatic light of wavelength $$\lambda$$, when a glass plate ($$\mu = 1.5$$) of thickness $$x\lambda$$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of $$x$$ will be

Let $$K_1$$ and $$K_2$$ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $$\lambda_1$$ and $$\lambda_2$$, respectively are incident on a metallic surface. If $$\lambda_1 = 3\lambda_2$$ then:

Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of undecayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of $$\log_e$$ (no. of undecayed nuclei) vs. time represents the reciprocal of mean life time ($$\tau$$).
(D) Product of decay constant ($$\lambda$$) and half-life time $$\left(T_{\frac{1}{2}}\right)$$ is not constant.
Choose the most appropriate answer from the options given below:

In the given circuit the input voltage $$V_{in}$$ is shown in figure. The cut-in voltage of $$p-n$$ junction diode ($$D_1$$ or $$D_2$$) is 0.6 V. Which of the following output voltage ($$V_0$$) waveform across the diode is correct?

Amplitude modulated wave is represented by $$V_{AM} = 10\left[1 + 0.4 \cos(2\pi \times 10^4 t)\right] \cos(2\pi \times 10^7 t)$$. The total bandwidth of the amplitude modulated wave is