NTA JEE Main 15th April 2018 Shift 1

A monochromatic beam of light has a frequency $$\nu = \frac{3}{2\pi} \times 10^{12}$$ Hz and is propagating along the direction $$\frac{\hat{i}+\hat{j}}{\sqrt{2}}$$. It is polarized along the $$\hat{k}$$ direction. The acceptable form for the magnetic field is:

A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig. A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is:

A particle is oscillating on the X-axis with an amplitude 2 cm about the point $$x_0 = 10$$ cm with a frequency $$\omega$$. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the correct statements: (A) The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at x = 10 cm (D) The distance between the turning points of the oscillation of the image is $$\frac{100}{21}$$ cm.

Light of wavelength 550 nm falls normally on a slit of width $$22.0 \times 10^{-5}$$ cm. The angular position of the second minima from the central maximum will be (in radians):

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are $$\lambda_1$$ and $$\lambda_2$$, their de Broglie wavelength in the frame of reference attached to their centre of mass is:

The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is:

A solution containing active cobalt $$^{60}_{27}$$Co having activity of 0.8 $$\mu$$Ci and decay constant $$\lambda$$ is injected in an animal's body. If 1 cm$$^3$$ of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1 Ci = $$3.7 \times 10^{10}$$ decay per second and at t = 10 hrs the value of $$e^{-\lambda t}$$ = 0.84)

In a common emitter configuration with suitable bias, it is given than $$R_L$$ is the load resistance and $$R_{BE}$$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [$$\beta$$ is current gain, $$I_B$$, $$I_C$$, $$I_E$$ are respectively base, collector and emitter currents]

The number of amplitude modulated broadcast stations that can be accommodated in a 300 kHz band width for the highest modulating frequency 15 kHz will be:

In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is: