UPSC NDA I 2025 Mathematics Paper

Given,
The function is f={(1,1),(2,4),(3,7),(4,10)}, and we are also given that the function is f(x)=px+q, where p and q are constants.
Using the points f(1)=1 and f(2)=4, we create the following system of equations:
- From f(1)=1, we have p(1)+q=1, so p+q=1
- From f(2)=4, we have p(2)+q=4, so 2p+q=4
Subtract Equation 1 from Equation 2:
(2p+q)−(p+q)=4−1
p=3
Now, substitute p=3 into Equation 1:
3+q=1
q=−2
p+q=3+(−2)=1
∴ The value of p+q is 1.