CDS Elementary Mathematics 2017 Question Paper

What is the value of $\alpha$ $(\alpha \ne 0)$ for which $x^2-5x+\alpha$ and $x^2-7x+2\alpha$ have a common factor ?

How many numbers from 1 to 1000 are divisible by 2, 3, 4 and 5 ?

What are the factors of $x^3+4x^2-11x-30$ ?

If $x=111\dots 1$ (20 digits), $y=333\dots 3$ (10 digits) and $z=222\dots 2$ (10 digits), then what is $\frac{x-y^2}{z}$ equal to ?

What is the positive value of $m$ for which the roots of the equation $12x^2+mx+5=0$ are in the ratio $3:2$ ?

Let $f(x)$ and $g(x)$ be two polynomials (with real coefficients) having degrees 3 and 4 respectively. What is the degree of $f(x)g(x)$ ?

If $5x^3+5x^2-6x+9$ is divided by $(x+3)$, then the remainder is

The product of two non-zero expressions is $(x+y+z)p^3$. If their HCF is $p^2$, then their LCM is

If the points P and Q represent the real numbers $0.8\overline{3}$ and $0.6\overline{2}$ on the number line, then the distance between P and Q is

Sudhir purchased a chair with three consecutive discounts of 20%, 12.5% and 5%. The actual deduction will be