What is $Strigula$?

$A$ die is thrown four times. The probability of getting a perfect square in at least one throw is

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

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

Consider the following anions:
$(I)$ $CF_{3}SO_{3}^{-}$
$(II)$ $C_{6}H_{5}SO_{3}^{-}$
$(III)$ $C_{6}H_{5}O^{-}$
$(IV)$ $CH_{3}COO^{-}$
When attached to $sp^{3}$-hybridized carbon,their leaving group ability in nucleophilic substitution reaction decreases in the order:

If $y = \cos^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right) + \sin^{-1}\left(\frac{2ax}{a^2+x^2}\right)$,then $\frac{dy}{dx}$ is equal to