NTA JEE Main 29th June 2022 Shift 2

Two point charges $$Q$$ each are placed at a distance $$d$$ apart. A third point charge $$q$$ is placed at a distance $$x$$ from mid-point on the perpendicular bisector. The value of $$x$$ at which charge $$q$$ will experience the maximum Coulomb's force is:

If the electric potential at any point $$(x, y, z)$$ m in space is given by $$V = 3x^2$$ volt. The electric field at the point $$(1, 0, 3)$$ m will be:

A capacitor is discharging through a resistor $$R$$. Consider in time $$t_1$$, the energy stored in the capacitor reduces to half of its initial value and in time $$t_2$$, the charge stored reduces to one eighth of its initial value. The ratio $$\frac{t_1}{t_2}$$ will be

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 $$\Omega$$. The value of internal resistance of each cell is

Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $$\mu$$T. The equal current flowing in the two conductors is:

Given below are two statements:
Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.
In the light of the above statements, choose the most appropriate answer from the options below:

The speed of light in media 'A' and 'B' are $$2.0 \times 10^{10}$$ cm s$$^{-1}$$ and $$1.5 \times 10^{10}$$ cm s$$^{-1}$$ respectively. A ray of light enters from the medium $$B$$ to $$A$$ at an incident angle $$\theta$$. If the ray suffers total internal reflection, then

The electric field at a point associated with a light wave is given by
$$E = 200\left[\sin(6 \times 10^{15})t + \sin(9 \times 10^{15})t\right]$$ Vm$$^{-1}$$
Given: $$h = 4.14 \times 10^{-15}$$ eVs
If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

In the following nuclear reaction,
$$D \xrightarrow{\alpha} D_1 \xrightarrow{\beta} D_2 \xrightarrow{\alpha} D_3 \xrightarrow{\gamma} D_4$$
Mass number of $$D$$ is 182 and atomic number is 74. Mass number and atomic number of $$D_4$$ respectively will be

The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by