Comprehension

Consider the following for the two (02) items that follow: 

 Let (x+y)p+q=xpyq, where p,q are positive integers.

If p+q=10, then what is  equal to?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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Calculation:

Given,

and .

Differentiate both sides with respect to implicitly:

Left side:

Right side (product rule):

Rearrange to collect terms and use

.

After cancellation of the common factor , you obtain:

∴ 

Hence, the correct answer is Option 1. 

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