NDA 1 2025 Maths, question 76

Topic: Differential calculus

Passage · Q75 to Q76

Let $(x + y)^{p + q} = x^{p}y^{q}$ , where $p$ , $q$ are positive integers.

Q76

If $p + q = 10$ , then what is $\frac{dy}{dx}$ equal to?

Solution.

Answer: (a) $y/x$

From question 75, $\frac{dy}{dx} = \frac{y}{x}$ for any positive integers $p, q$ .
So with $p + q = 10$ the derivative is still $y/x$ .

Trap: The value 10 is a distraction; it does not change the derivative, so (c) and (d), which use 10 as a power, are wrong.