CDS Elementary Mathematics 2018 Question Paper

$5^{17}+5^{18}+5^{19}+5^{20}$ is divisible by

If $a+b=2c$, then what is the value of $\frac{a}{a-c}+\frac{c}{b-c}$?

If $x=y^{1/a}$, $y=z^{1/b}$ and $z=x^{1/c}$ where $x\ne 1$, $y\ne 1$, $z\ne 1$, then what is the value of $abc$?

If $2b=a+c$ and $y^2=xz$, then what is $x^{b-c}\cdot y^{c-a}\cdot z^{a-b}$ equal to?

Which one of the following is correct?

If the roots of the equation $p{x}^2+x+r=0$ are reciprocal to each other, then which one of the following is correct?

If $65x-33y=97$ and $33x-65y=1$, then what is $xy$ equal to?

If $\frac{b}{y}+\frac{z}{c}=1$ and $\frac{c}{z}+\frac{x}{a}=1$, then what is $\frac{ab+xy}{bx}$ equal to?

If $\frac{a^2-1}{a}=5$, then what is the value of $\frac{a^6-1}{a^3}$?

If $x+y+z=0$, then what is $(y+z-x{)}^3+(z+x-y{)}^3+(x+y-z{)}^3$ equal to?