CDS Elementary Mathematics 2016 Question Paper

If the roots of the equation $l{x}^2+mx+m=0$ are in the ratio $p:q$, then $\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{m}{l}}$ is equal to

If $\sqrt{3x^2-7x-30}-\sqrt{2x^2-7x-5}=x-5$ has $\alpha$ and $\beta$ as its roots, then the value of $\alpha \beta$ is

If $\frac{p}{x}+\frac{q}{y}=m$ and $\frac{q}{x}+\frac{p}{y}=n$, then what is $\frac{x}{y}$ equal to ?

If $a^2-by-cz=0$, $ax-b^2+cz=0$ and $ax+by-c^2=0$, then the value of $\frac{x}{a+x}+\frac{y}{b+y}+\frac{z}{c+z}$ will be

If the equations $x^2-px+q=0$ and $x^2+qx-p=0$ have a common root, then which one of the following is correct ?

If $x=2^{1/3}+2^{-1/3}$, then the value of $2x^3-6x-5$ is equal to

The sum and difference of two expressions are $5x^2-x-4$ and $x^2+9x-10$ respectively. The HCF of the two expressions will be

If $(s-a)+(s-b)+(s-c)=s$, then the value of $\frac{(s-a{)}^2+(s-b{)}^2+(s-c{)}^2+s^2}{a^2+b^2+c^2}$ will be

If the polynomial $x^6+p{x}^5+q{x}^4-x^2-x-3$ is divisible by $(x^4-1)$, then the value of $p^2+q^2$ is

Let $p$ and $q$ be non-zero integers. Consider the polynomial $A(x)=x^2+px+q$. It is given that $(x-m)$ and $(x-km)$ are simple factors of $A(x)$, where $m$ is a non-zero integer and $k$ is a positive integer, $k\ge 2$. Which one of the following is correct ?