Real Number Quiz 9

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

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

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

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

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

If $p^3+q^3=r^3$ then $log_p(r-q)+log_p(r^2+qr+q^2)$ = ..............

$\frac{log\sqrt{27}+log\,8-\,log\,\sqrt{1000}}{log\,1.2}$ = ……………

$\frac{1}{log_2\,.\, log_2\,.\, log_2\,16}$ = …………

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