In a zoo, there are Rabbits and Pigeons. If their heads are 90 and their legs are 224. Then the number of Pigeons in the zoo is …………

If x = $\sqrt{-1+4\sqrt{3}}\backslash sqrt\{-1+4\backslash sqrt3\}$ then $x+\frac{1}{x}x+\backslash frac\{1\}\{x\}$ = …………

The value of $\frac{1}{2+\sqrt{3}}+\frac{1}{2-\sqrt{3}}\backslash frac\{1\}\{2+\backslash sqrt3\}+\backslash frac\{1\}\{2-\backslash sqrt3\}$ is ………………

If $x=\frac{2}{3+\sqrt{7}}x=\backslash frac\{2\}\{3+\backslash sqrt7\}$ then $(x-3{)}^2(x-3)^2$ = ……………

If $\frac{4+3\sqrt{3}}{2+\sqrt{3}}=a+\sqrt{b}\backslash frac\{4+3\backslash sqrt3\}\{2+\backslash sqrt3\}=a+\backslash sqrt\; b$ then (a, b) = ……………

If $\frac{\sqrt{7}-\sqrt{3}}{x}=\frac{x}{\sqrt{7}+\sqrt{3}}\backslash frac\{\backslash sqrt7-\backslash sqrt3\}\{x\}=\backslash frac\{x\}\{\backslash sqrt7+\backslash sqrt3\}$ then the value of x = ……………

If $p^3+q^3=r^{3}p^3+q^3=r^3$ then $lo{g}_p(r-q)+lo{g}_p(r^2+qr+q^2)log\_p(r-q)+log\_p(r^2+qr+q^2)$ = ..............

$\frac{log\sqrt{27}+log8-log\sqrt{1000}}{log1.2}\backslash frac\{log\backslash sqrt\{27\}+log\backslash ,8-\backslash ,log\backslash ,\backslash sqrt\{1000\}\}\{log\backslash ,1.2\}$ = ……………

$\frac{1}{lo{g}_2\mathrm{.}lo{g}_2\mathrm{.}lo{g}_{2}16}\backslash frac\{1\}\{log\_2\backslash ,.\backslash ,\; log\_2\backslash ,.\backslash ,\; log\_2\backslash ,16\}$ = …………

If $log(x+y)=log(\frac{3x-3y}{2})log(x+y)=log(\backslash frac\{3x-3y\}\{2\})$ then log x – log y = ...........