Introduction to Linear Polynomials: CBSE Class 9 Mathematics practice questions

B. $6p + 8q + 2$

$p$ green boxes hold $6p$ markers and $q$ yellow boxes hold $8q$ erasers. Adding the 2 free erasers gives $6p + 8q + 2$. $8p + 6q + 2$ swaps the box sizes, $6p + 8q$ forgets the free erasers, and $14pq + 2$ wrongly multiplies the two kinds of boxes together.

C. $0$

Writing every power in turn gives $4z^3 + 5z^2 + 0z - 11$, so the coefficient of $z$ is 0: there is no $z$ term at all. $4$ is the coefficient of $z^3$, $5$ is the coefficient of $z^2$, and $-11$ is the constant term, not a coefficient of $z$.

A. 14 coins of ₹5 and 28 coins of ₹2

With $n$ coins of ₹5 and $2n$ coins of ₹2, the value is $5n + 2(2n) = 9n = 126$, so $n = 14$: 14 coins of ₹5 and 28 coins of ₹2 (₹70 + ₹56 = ₹126). Swapping them gives ₹168. 18 and 36 come from $5n + 2n = 126$ (forgot that there are $2n$ two-rupee coins), and 42 and 84 come from counting coins, $n + 2n = 126$, instead of rupees.