The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

A uniform magnetic field of $$2 \times 10^{-3} \mathrm{~T}$$ acts along positive $$Y$$-direction. A rectangular loop of sides $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ with current of $$5 \mathrm{~A}$$ is in $$Y-Z$$ plane. The current is in anticlockwise sense with reference to negative $$X$$ axis. Magnitude and direction of the torque is:

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

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