NTA JEE Main 27th July 2021 Shift 2

A swimmer wants to cross a river from point $$A$$ to point $$B$$. Line AB makes an angle of 30° with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle $$\theta$$ with the line AB should be _________ °, so that the swimmer reaches point $$B$$.

A small block slides down from the top of hemisphere of radius $$R = 3$$ m as shown in the figure. The height $$h$$ at which the block will lose contact with the surface of the sphere is _________ m. (Assume there is no friction between the block and the hemisphere)

The water is filled up to a height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth $$h$$ below the water level. The value of $$h$$ for which the emerging stream of water strikes the ground at the maximum range is _________ m.

In the given figure, two wheels $$P$$ and $$Q$$ are connected by a belt $$B$$. The radius of $$P$$ is three times that of $$Q$$. In the case of the same rotational kinetic energy, the ratio of rotational inertias $$\left(\frac{I_1}{I_2}\right)$$ will be $$x : 1$$. The value of $$x$$ will be _________.

A particle executes simple harmonic motion represented by displacement function as $$x(t) = A\sin(\omega t + \phi)$$. If the position and velocity of the particle at $$t = 0$$ s are 2 cm and 2$$\omega$$ cm s$$^{-1}$$ respectively, then its amplitude is $$x\sqrt{2}$$ cm where the value of $$x$$ is _________

For the circuit shown, the value of current at time $$t = 3.2$$ s will be _________ A.

[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

In the given figure the magnetic flux through the loop increases according to the relation $$\phi_B(t) = 10t^2 + 20t$$, where $$\phi_B$$ is in milliwebers and $$t$$ is in seconds. The magnitude of current through $$R = 2 \, \Omega$$ resistor at $$t = 5$$ s is _________ mA.

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is _________ mm. [Refractive index of air = 1.0003, the wavelength of yellow light in vacuum = 6000 Å]

The $$K_\alpha$$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a $$K$$ electron knocked out is 27.5 keV, the energy of this atom when an $$L$$ electron is knocked out will be _________ keV. (Round off to the nearest integer) [$$h = 4.14 \times 10^{-15}$$ eV s, $$c = 3 \times 10^8$$ m s$$^{-1}$$]

The maximum amplitude for an amplitude modulated wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is 0.6$$x$$ where $$x$$ is _________.