Derivative of $\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right)$ is

A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amount is

In $\triangle A B C$, with the usual notations, if $\sin B \sin C=\frac{b c}{a^2}$, then the triangle is. ...........

If $A=\left\{x \in R / x^2+5|x|+6=0\right\}$ then $n(A)=\ldots \ldots$