Q236 / 269 · NDA 2025 (Phase 1) · Mathematics
Consider the following for the two (02) items that follow:
Let $f = \{(1, 1), (2, 4), (3, 7), (4, 10)\}$.
If $f(x) = px + q$, then what is the value of $(p + q)$?
Let $f = \{(1, 1), (2, 4), (3, 7), (4, 10)\}$.
If $f(x) = px + q$, then what is the value of $(p + q)$?
- A$-1$
- B$0$
- Correct answerC$1$
- D$5$
Solution
Given $f(x) = px + q$.
From the given set of points, we have $f(1) = 1$.
Substituting $x = 1$ in the function, we get:
$p(1) + q = 1$
$p + q = 1$
Alternatively, using $f(2) = 4$, we get $2p + q = 4$. Solving $p + q = 1$ and $2p + q = 4$ gives $p = 3$ and $q = -2$.
Thus, $p + q = 3 - 2 = 1$.
Answer: $1$
From the given set of points, we have $f(1) = 1$.
Substituting $x = 1$ in the function, we get:
$p(1) + q = 1$
$p + q = 1$
Alternatively, using $f(2) = 4$, we get $2p + q = 4$. Solving $p + q = 1$ and $2p + q = 4$ gives $p = 3$ and $q = -2$.
Thus, $p + q = 3 - 2 = 1$.
Answer: $1$
Hence, the correct answer is option: 'C'.