GATE Mechanical 2023 | GA Question: 7

Question

Consider the following inequalities
$$
\begin{aligned}
& p^2-4 q<4 \\
& 3 p+2 q<6
\end{aligned}
$$
where $p$ and $q$ are positive integers.

The value of $(p+q)$ is __________.

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

Given P and Q are Positive integers.

Let p , q=1,Then Inequality becomes

i)1-4<4 is True

ii)3+2<6 is True

Then  Ans might be p + q=1+1=2

Lets take p=1,q=2;

i)1-8<4 is True

ii)3+4<6 is False

Let take p=2,q=1;

i)4-4<4 is True

ii}6+2<6 is False

Hence p=q=1 is Right Choice to select

Therefore, answer is option A.