$A$ mass of $1\, kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If a sudden jerk is given to $C$,then

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

Which of the following taxonomic categories of the housefly is incorrectly matched?

The concentration of a $100 \ mL$ solution containing $X \ g$ of $Na_2CO_3$ (molecular weight $= 106$) is $Y \ M$. The values of $X$ and $Y$ are respectively.

An alloy of gold and copper crystallizes in a cubic lattice in which the gold atoms occupy the lattice points at the corners of the cube and copper atoms occupy the centers of each of the cube faces. Determine the formula of this compound.

If the eccentricity of a hyperbola is $\sqrt{3}$,then the eccentricity of its conjugate hyperbola is: