NTA JEE Main 25th February 2021 Shift 2

If $$\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$$, the angle between $$\vec{P}$$ and $$\vec{Q}$$ is $$\theta$$ ($$0° < \theta < 360°$$). The value of $$\theta$$ will be ______ °.

Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $$n : 2$$. The value of $$n$$ will be ______.

The initial velocity $$v_i$$ required to project a body vertically upward from the surface of the earth to reach a height of $$10R$$, where $$R$$ is the radius of the earth, may be described in terms of escape velocity $$v_e$$ such that $$v_i = \sqrt{\frac{x}{y}} \times v_e$$. The value of $$x$$ will be

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled. The temperature in Kelvin of the source will be ______.

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be ______ %.

The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is $$\frac{x}{10}\sqrt{\frac{\mu_0 c}{\pi}}$$ V m$$^{-1}$$. The efficiency of the bulb is 10% and it is a point source. The value of $$x$$ is ______,

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $$\frac{a}{21} \times 10^{-8}$$ C. The value of $$a$$ will be ______. [Given $$g = 10$$ m s$$^{-2}$$]

Two identical conducting spheres with negligible volume have 2.1 nC and $$-0.1$$ nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ______ $$\times 10^{-9}$$ N.
[Given : $$4\pi \epsilon_{\circ}$$ = $$ \frac{1}{9\times 10^{9}}$$ SI Units}]

A current of 6 A enters one corner $$P$$ of an equilateral triangle $$PQR$$ having 3 wires of resistance 2 $$\Omega$$ each and leaves by the corner $$R$$. The currents $$i_1$$ in ampere is ______

The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is $$\frac{x}{3}h$$ kg. The value of $$x$$ is ______. ($$h$$ = Planck's constant)