NTA JEE Main 5th September 2020 Shift 1

A particle of mass $$200\,\text{MeV c}^{-2}$$ collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is $$\frac{N}{4}$$. The value of $$N$$ is: (Given the mass of the hydrogen atom to be $$1\,\text{GeV c}^{-2}$$)........

A force $$\vec{F} = \left(\hat{i} + 2\hat{j} + 3\hat{k}\right)\,\text{N}$$ acts at a point $$\left(4\hat{i} + 3\hat{j} - \hat{k}\right)\,\text{m}$$. Then the magnitude of torque about the point $$\left(\hat{i} + 2\hat{j} + \hat{k}\right)\,\text{m}$$ will be $$\sqrt{x}\,\text{N-m}$$. The value of $$x$$ is..........

Two concentric circular coils, $$C_1$$ and $$C_2$$, are placed in the $$XY$$ plane. $$C_1$$ has 500 turns, and a radius of $$1\,\text{cm}$$. $$C_2$$ has 200 turns and radius of $$20\,\text{cm}$$. $$C_2$$ carries a time dependent current $$I(t) = (5t^2 - 2t + 3)\,\text{A}$$ where $$t$$ is in s. The emf induced in $$C_1$$ (in mV) at the instant $$t = 1\,\text{s}$$ is $$\frac{4}{x}$$. The value of $$x$$ is..........

A compound microscope consists of an objective lens of focal length $$1\,\text{cm}$$ and an eye piece of focal length $$5\,\text{cm}$$ with a separation of $$10\,\text{cm}$$. The distance between an object and the objective lens, at which the strain on the eye is minimum is $$\frac{n}{40}\,\text{cm}$$. The value of $$n$$ is.......

A beam of electrons of energy $$E$$ scatters from a target having atomic spacing of $$1\,\text{\AA}$$. The first maximum intensity occurs at $$\theta = 60^\circ$$. Then $$E$$ (in eV) is......... (Planck's constant $$h = 6.64 \times 10^{-34}\,\text{Js}$$, $$1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}$$, electron mass $$m = 9.1 \times 10^{-31}\,\text{kg}$$)

The difference between the radii of 3rd and 4th orbits of $$\text{Li}^{2+}$$ is $$\Delta R_1$$. The difference between the radii of 3rd and 4th orbits of $$\text{He}^+$$ is $$\Delta R_2$$. Ratio $$\Delta R_1 : \Delta R_2$$ is:

In the sixth period, the orbitals that are filled are:

The potential energy curve for the $$\text{H}_2$$ molecule as a function of internuclear distance is:

Consider the following reaction:
$$\text{N}_2\text{O}_4(g) = 2\text{NO}_2(g);\;\Delta H^0 = +58\,\text{k}$$
For each of the following cases (a, b), the direction in which the equilibrium shifts is:
(a) Temperature is decreased.
(b) Pressure is increased by adding $$\text{N}_2$$ at constant T.

The equation that represents the water-gas shift reaction is: