CDS Elementary Mathematics 2022 Question Paper

What is the ratio of interior angle to exterior angle of a regular polygon of $n$ sides?

$41^{43}+43^{43}$ is divisible by

If $x=7+4\sqrt{3}$, then what is the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$?

$4^{61}+4^{62}+4^{63}+4^{64}$ is divisible by

Suppose $p$ and $q$ are the LCM and HCF respectively of two positive numbers. If $p:q=14:1$ and $pq=1134$, then what is the difference between the two numbers?

What is the value of the following?
$\frac{(5.4{)}^3-0.064}{(5.4{)}^2+2.16+0.16}$

A man walks at an average speed of 3 km/hr from his residence and reaches office 40 minutes early. If he walks at an average speed of 2 km/hr, he reaches 40 minutes late. What is the distance between his residence and office?

What is the value of the following?
$\frac{1}{5\sqrt{4}+4\sqrt{5}}+\frac{1}{6\sqrt{5}+5\sqrt{6}}+\frac{1}{7\sqrt{6}+6\sqrt{7}}+\frac{1}{8\sqrt{7}+7\sqrt{8}}+\frac{1}{9\sqrt{8}+8\sqrt{9}}$

If $x=9999$, then what is the value of the following?
$\frac{4x^3-x}{(2x+1)(6x-3)}$

If $(x+\sqrt{1+x^2})(y+\sqrt{1+y^2})=1$, where $x$ and $y$ are real numbers, then what is the value of $(x+y{)}^2$?