Inbreeding is carried out in animal husbandry because it

$IPM$ (Integrated Pest Management) involves

Two semicircular rings of linear mass densities $\lambda$ and $3 \lambda$ and of radius $R$ each,are joined to form a complete ring. The distance of the centre of mass of the complete ring from its geometrical centre is

Given $0 \leq x \leq \frac{1}{2}$,then the value of $\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)-\sin ^{-1} x\right)$ is

An aqueous solution of $6.3 \ g$ of oxalic acid dihydrate is made up to $250 \ mL$. The volume of $0.1 \ N \ NaOH$ required to completely neutralize $10 \ mL$ of this solution is ............. $mL$.

If the equation of one tangent to the circle with centre at $(2, -1)$ from the origin is $3x + y = 0$,then the equation of the other tangent through the origin is