CDS 2026 Mathematics Medium Questions

Let $XYZ$ be a 3-digit number and the difference between $XYZ$ and $ZYX$ is equal to $PQR$. Is $(P+R)$ equal to $Q$?
Statement-I : $P=3$
Statement-II : $R=6$
Which one of the following is correct in respect of the above Question and the Statements?

Is $r^n$ less than $1$, where $r$ is a real number and $n$ is a natural number ?

Statement-I : $0<r^2<1$

Statement-II : $0<r^3<2$

LCM of three numbers $p,q$ and $r$ $(p>q>r>0)$ is $30$ and their HCF is $5$. What is the product of the three numbers?
Statement-I : $p=15$
Statement-II : $q=10$
Which one of the following is correct in respect of the above Question and the Statements?

Consider the following statements :

I. Two consecutive natural numbers are always co-prime.

II. If $m$ and $n$ are relatively prime, then $m\times n$ is always even.

Which of the statements given above is/are correct ?

Let $P=N^2$ where $N$ is an odd integer. What is the remainder when $P$ is divided by 8 ?

If the HCF of $p$ and $q$ ($p>q$) is $G$, then which of the following statements is/are correct?

I. HCF of $p$ and $(p+q)$ is $G$

II. HCF of $p$ and $(p-q)$ is $G$

Let the area of the largest possible square inscribed in a circle of unit radius be $x$. Let the area of the largest possible circle inscribed in a square of unit side length be $y$. What is the relation between $x$ and $y$?

All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E ?

Let $P=5^5\times 15^{15}\times 25^{25}\times 35^{35}$ and $Q=10^{10}\times 20^{20}\times 30^{30}\times 40^{40}$. What is the number of consecutive zeros at the end of the sum $(P+Q)$?

What is the LCM of $3.6$, $0.009$, $0.27$?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question :

$ABCD$ is a parallelogram with $\angle ABC=60^{\circ }$. If the area of the parallelogram is $7\sqrt{3}$ square units, then what is the perimeter of the parallelogram?

Statement-I :

The lengths of the sides $AB$ and $DA$ are prime numbers.

Statement-II :

The lengths of the sides are natural numbers each greater than 1 unit.

Which one of the following is correct in respect of the above Question and the Statements?

A number $N$ is such that when divided by 4, 6, 7 or 9, it leaves 3 as remainder. What is the smallest 4-digit number that satisfies this property?

Let $x$ and $y$ be natural numbers, each less than 20, such that $x$, $y$, $x+y$ and $x-y$ are prime numbers. How many such combinations of $(x,y,x+y,x-y)$ are possible?

Let $N$ be the greatest number that will divide $600$, $631$ and $724$, leaving the same remainder. What is the value of $N$?

At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be $\frac{5}{6}$. On walking $70\mathrm{m}$ towards the tower, the tangent of the angle of elevation of the top of the tower is found to be $\frac{9}{8}$. What is the height of the tower ?

Let $p$ and $q$ be two natural numbers such that $(p+q{)}^{p+q}$ is divisible by 512. What is the least value of $(p+q)$?

Is $p^2+q^2$ always a composite number, where $p$ and $q$ are different prime numbers?

Statement-I : $(p-q)$ is an odd integer

Statement-II : $(p+q)$ is an odd integer

Which one of the following is correct in respect of the above Question and the Statements?

ABCD is a quadrilateral with sides $AB=9$ cm, $BC=40$ cm, $CD=28$ cm and $DA=15$ cm and one of the diagonals $AC=41$ cm. Which of the following statements is/are correct?
I. The vertices $A,B,C$ and $D$ of the quadrilateral lie on a circle.
II. The area of triangle $ACD$ is $126{\text{cm}}^2$.
Select the answer using the code given below:

What is the digit at hundreds place of the number $(25{)}^{10}$?

If $x=2+2^{1/2}+2^{3/2}$, then what is $x^2-4x-10$ equal to?