The centre of mass of three particles of masses $1 ~kg, 2 ~kg$ and $3 ~kg$ is at $(2,2,2)$. The position of the fourth mass of $4 ~kg$ to be placed in the system so that the new centre of mass is at $(0,0,0)$ is:

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is

What products are formed when $1 \ mol$ of calcium phosphide reacts with an excess of water?

If $a = \hat{i} + 4 \hat{j}$,$b = 2 \hat{i} - 2 \hat{j}$,and $c = 5 \hat{i} + 9 \hat{j}$,then $c$ is equal to:

Identify the fibrous protein from the following.

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has a moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is