NTA JEE Mains 31st Jan 2024 Shift 2

If two vectors $$\vec{A}$$ and $$\vec{B}$$ having equal magnitude $$R$$ are inclined at an angle $$\theta$$, then

Consider two physical quantities $$A$$ and $$B$$ related to each other as $$E = \frac{B - x^2}{At}$$ where $$E$$, $$x$$ and $$t$$ have dimensions of energy, length and time respectively. The dimension of $$AB$$ is

A light string passing over a smooth light fixed pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of masses is

A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If $$\vec{F_1}$$ is the force required to just move the block up the inclined plane and $$\vec{F_2}$$ is the force required to just prevent the block from sliding down, then the value of $$|\vec{F_1}| - |\vec{F_2}|$$ is: [Use $$g = 10$$ m s$$^{-2}$$]

A body of mass 2 kg begins to move under the action of a time dependent force given by $$\vec{F} = (6t)\hat{i} + (6t^2)\hat{j}$$ N. The power developed by the force at the time $$t$$ is given by:

The mass of the moon is $$\frac{1}{144}$$ times the mass of a planet and its diameter $$\frac{1}{16}$$ times the diameter of a planet. If the escape velocity on the planet is $$v$$, the escape velocity on the moon will be:

A small spherical ball of radius $$r$$, falling through a viscous medium of negligible density has terminal velocity $$v$$. Another ball of the same mass but of radius $$2r$$, falling through the same viscous medium will have terminal velocity:

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature $$T$$. Neglecting all vibrational modes, the total internal energy of the system is

The speed of sound in oxygen at S.T.P. will be approximately: (Given, $$R = 8.3$$ J K$$^{-1}$$, $$\gamma = 1.4$$)

Force between two point charges $$q_1$$ and $$q_2$$ placed in vacuum at $$r$$ cm apart is $$F$$. Force between them when placed in a medium having dielectric $$K = 5$$ at $$\frac{r}{5}$$ cm apart will be: