NTA JEE Main 25th February 2021 Shift 1

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m s$$^{-1}$$. (Take $$g = 10$$ m s$$^{-2}$$)

The potential energy (U) of a diatomic molecule is a function dependent on $$r$$ (interatomic distance) as $$U = \frac{\alpha}{r^{10}} - \frac{\beta}{r^5} - 3$$ where, $$\alpha$$ and $$\beta$$ are positive constants. The equilibrium distance between two atoms will be $$\left(\frac{2\alpha}{\beta}\right)^{\frac{a}{b}}$$, where $$a$$ = ______.

In a certain thermodynamical process, the pressure of a gas depends on its volume as $$kV^3$$. The work done when the temperature changes from 100°C to 300°C will be $$xnR$$ where $$n$$ denotes number of moles of a gas, find $$x$$.

A monoatomic gas of mass 4.0 u is kept in an insulated container. The container is moving with velocity 30 m s$$^{-1}$$. If the container is suddenly stopped then a change in temperature of the gas ($$R$$ = gas constant) is $$\frac{x}{3R}$$. Value of $$x$$ is,

The electric field in a region is given by $$\vec{E} = \left(\frac{3}{5}E_0\hat{i} + \frac{4}{5}E_0\hat{j}\right)$$ N C$$^{-1}$$. The ratio of flux of reported field through the rectangular surface of area 0.2 m$$^2$$ (parallel to $$y-z$$ plane) to that of the surface of area 0.3 m$$^2$$ (parallel to $$x-z$$ plane) is $$a : b = a : 2$$, where $$a$$ = ______?[Here $$\hat{i},\hat{j}$$ and$$\hat{k}$$ are unit vectors along $$x,y$$ and $$z$$-axes respectively]

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ______ V in Volt.

In the given circuit of potentiometer, the potential difference $$E$$ across $$AB$$ (10 m length) is larger than $$E_1$$ and $$E_2$$ as well. For key $$K_1$$ (closed), the jockey is adjusted to touch the wire at point $$J_1$$ so that there is no deflection in the galvanometer. Now the first battery ($$E_1$$) is replaced by second battery ($$E_2$$) for working by making $$K_1$$ open and $$K_2$$ closed. The galvanometer gives then null deflection at $$J_2$$. The value of $$\frac{E_1}{E_2}$$ is $$\frac{a}{2}$$, where $$a$$ = ______.

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by $$V = 3t$$ volt. (where $$t$$ is in second). If the voltage is applied when $$t = 0$$, then the energy stored in the coil after 4 s in J.

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $$\mu$$F is used in the resonant circuit. The self-inductance of coil necessary for resonance is $$x \times 10^{-8}$$ H. Find $$x$$.

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is ______