NTA JEE Main 16th March 2021 Shift 2

A body of mass 2 kg moves under a force of $$\left(2\hat{i} + 3\hat{j} + 5\hat{k}\right)$$ N. It starts from rest and was at the origin initially. After 4 s, its new coordinates are $$(8, b, 20)$$. The value of $$b$$ is ________. (Round off to the Nearest Integer)

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________°. (Round off to the Nearest Integer) (find the angle in degree)

A force $$\vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k}$$ is applied on an intersection point of $$x = 2$$ plane and $$x$$-axis. The magnitude of torque of this force about a point $$(2, 3, 4)$$ is ________. (Round off to the Nearest Integer)

A solid disc of radius $$a$$ and mass $$m$$ rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The acceleration of the disc will be $$\frac{2}{b}g\sin\theta$$, where $$b$$ is ________. (Round off to the Nearest Integer) ($$g$$ = acceleration due to gravity, $$\theta$$ = angle as shown in figure)

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $$\frac{x}{5}\frac{GM^2}{R}$$ where $$x$$ is ________. (Round off to the Nearest Integer)
($$M$$ is the mass of earth, $$R$$ is the radius of earth, $$G$$ is the gravitational constant)

For an ideal heat engine, the temperature of the source is 127°C. In order to have 60% efficiency the temperature of the sink should be ________°C. (Round off to the nearest integer)

A closed organ pipe of length $$L$$ and an open organ pipe contain gases of densities $$\rho_1$$ and $$\rho_2$$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $$\frac{x}{3}L\sqrt{\frac{\rho_1}{\rho_2}}$$, where $$x$$ is ________. (Round off to the Nearest Integer)

In a parallel plate capacitor set up, the plate area of capacitor is 2 m$$^2$$ and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and are 2 m$$^2$$ (see figure) the capacitance of the set-up will be $$\varepsilon_0$$ ________.
(Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

The energy dissipated by a resistor is 10 mJ in 1 s, when an electric current of 2 mA flows through it. The resistance is ________ $$\Omega$$. (Round off to the Nearest Integer)

A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ________° (in degree). (Round off to the Nearest Integer)