CDS 2 2025 Maths Question Paper (14-Sep-2025)

Question 1

Let $p(x)$ be a polynomial. When $p(x)$ is divided by $(x-1)$, it leaves 2 as the remainder. When $p(x)$ is divided by $(x-2)$, it leaves 1 as the remainder. What is the remainder when $p(x)$ is divided by $(x - 1)(x-2)$?

Accepted Answer

$3-x$

Answer

3

Answer

-3

Answer

$3-2x$

Question 2

Consider the following in respect of a positive real number $x$ : I. $x+\frac{1}{x} >1$ II. $x+\frac{1}{x} > 2$ III. $(x+\frac{1}{x})^2 > 9$ Which of the above are correct?

Accepted Answer

I, II and III

Answer

I and II only

Answer

II and III only

Answer

I and III only

Question 3

Let $p$ and $q$ be natural numbers such that $q > p$. What is the largest value of $p$ such that $q^2 - 5p-4$ is negative?

Accepted Answer

3

Answer

4

Answer

5

Answer

6

Question 4

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?

Accepted Answer

One

Answer

Two

Answer

Three

Answer

None

Question 5

If $(x + 1)(x + p)(x^2 + p^2) = x^4 - 1$, then what is the value of $p$?

Accepted Answer

-1

Answer

0

Answer

1

Answer

Cannot be determined

CDS 2 2025 Maths Question Paper (14-Sep-2025)

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