CDS MATHEMATICS QUIZ 13

There are two numbers, first number is 24 more than the second number. The average of the two numbers is 38 . If 4 is added in both numbers, find the ratio of the numbers.

If $2\sqrt{y}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

If $5x+9y=5$ and $125x^3+729y^3=120$ then the value of the product of $x$ and $y$ is

If $x=\frac{2\sqrt{6}}{\sqrt{3}+\sqrt{2}}$, then the value of $\frac{x+\sqrt{2}}{x-\sqrt{2}}+\frac{x+\sqrt{3}}{x-\sqrt{3}}$ is

If $a+\frac{1}{a}+2=0$, then the value of $(a+2{)}^2+\frac{1}{(a+2{)}^3}$ is

If $x=\frac{2\sqrt{24}}{\sqrt{3}+\sqrt{2}}$, then the value of $\frac{x+\sqrt{8}}{x-\sqrt{8}}+\frac{x+\sqrt{12}}{x-\sqrt{12}}$ is

If $x+\frac{1}{x}=1$ then the value of $\frac{x^2+4x+1}{x^2+5x+1}$

If $a=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ then $\frac{a^2}{b}+\frac{b^2}{a}$

If $x=2+\sqrt{3}$, then the value, $\sqrt{x}+\frac{1}{\sqrt{x}}$

If $x+\frac{1}{x}=5$, the value of $x^5+\frac{1}{x^5}$ is