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 $5 x+9 y=5$ and $125 x^{3}+729 y^{3}=120$ 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 $\frac{x^{2}+4 x+1}{x^{2}+5 x+1}$

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