CDS Elementary Mathematics 2025 Question Paper

A real number $M$ is squared to give the value $N$. What is the minimum value of $(M+N)$?

What is the sum of all 3-digit numbers that give a remainder of 5 when they are divided by 50?

If the average of 64, 69, 72, 75, $x$ lies between 62 and 76 (excluding 62 and 76), then what is the number of possible integer values of $x$?

Let $x$, $y$, $z$ be variables such that $(x+y+z)=k$, where $k$ is a constant. If $(x+z-y)(x-z+y)$ is proportional to $yz$, then $(y+z-x)$ is proportional to:

Let $p$ be the remainder when $7^{84}$ is divided by 342 and $q$ be the remainder when $7^{84}$ is divided by 344. What is $(p-q)$ equal to?

$N$ is the smallest 5-digit number which when divided by $2,2^2,2^3,2^4,\dots ,2^n$ leaves a remainder 1. What is the value of $n$?

What is the minimum value of $p$ for which $\frac{1}{532900}+\frac{p^2}{266450}+\frac{p^4}{523900}$ is an integer?

If $\alpha$ and $\beta$ are the roots of the equation $x+a+b=\frac{abx}{ab+ax+bx}$, then what is $(\alpha \beta +\alpha +\beta )$ equal to?

Consider a 2-digit number $N$. Let $P$ be the product of the digits of the number. If $P$ is added to the square of the digit in the tens place of $N$, we get 84. If $P$ is added to the square of the digit in the unit place of $N$, we get 60. What is the value of $P+N$?

A mixture of 100 L contains kerosene and turpentine oil in the ratio 3 : 2. What is the minimum quantity of kerosene in litres (whole number) that should be mixed in the mixture so that the resulting mixture has 20% of kerosene?