NTA JEE Main 12th January 2019 Shift 2

In the above circuit, $$C = \frac{\sqrt{3}}{2}\mu F$$, $$R_2 = 20 \Omega$$, $$L = \frac{\sqrt{3}}{10} H$$ and $$R_1 = 10 \Omega$$. Current in $$L$$-$$R_1$$ path is $$I_1$$ and in C-$$R_2$$ path it is $$I_2$$. The voltage of AC source is given by, $$V = 200\sqrt{2} \sin(100t)$$ volts. The phase difference between $$I_1$$ and $$I_2$$ is:

The mean intensity of radiation on the surface of the Sun is about $$10^8 W/m^2$$. The rms value of the corresponding magnetic field is closest to:

A plano-convex lens (focal length $$f_2$$, refractive index $$\mu_2$$, radius of curvature R) fits exactly into a plano-concave lens (focal length $$f_1$$, refractive index $$\mu_1$$, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

Formation of real image using a biconvex lens is shown below.

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

When a certain photosensitive surface is illuminated with monochromatic light of frequency $$\nu$$, the stopping potential of the photo current is $$-\frac{V_0}{2}$$. When the surface is illuminated by monochromatic light of frequency $$\frac{\nu}{2}$$, the stopping potential is $$-V_0$$. The threshold frequency for photoelectric emission is

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to:

In a radioactive decay chain, the initial nucleus is $$^{232}_{90}Th$$. At the end, there are 6 $$\alpha$$-particles and 4$$\beta$$-particles which are emitted. If the end nucleus is $$^A_Z X$$, A and Z are given by:

In the figure, given that $$V_{BB}$$ supply can vary from 0 to 5.0 V, $$V_{CC} = 5$$ V, $$\beta_{dc} = 200$$, $$R_B = 100$$ k$$\Omega$$, $$R_C = 1$$ k$$\Omega$$ and $$V_{BE} = 1.0$$ V. The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively:

To double the covering range of a TV transmitting tower, its height should be multiplied by:

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is: