Question
Consider the following for the three (03) items that follow: Let p = 2 - and q = - 2 . What is ^2 equal to?
NDA
Mathematics
Trigonometric Ratios & Identities
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. pq p+q
- B. p+2q p
- C. p p+2q
- D. p 2p+q
Answer
C. p p+2q
Step-by-step solution
Given p = 2 - p = 2 2 - = 2 - 2 2 p = (2 - ) 2 = 2 = 2 Also given q = - 2 q = - 2 2 = 2 - 2 2 q = (2 - ) 2 = 2 = 1 2 Dividing p by q, we get: p q = 2 2 = 2 Using the formula 2 = 2 1 - ^2 : p q = ( 2 1 - ^2 ) = 2 ^2 1 - ^2 p(1 - ^2 ) = 2q ^2 p - p ^2 = 2q ^2 p = ^2 (p + 2q) ^2 = p p + 2q Answer: p p+2q
Related: Mathematics — Trigonometric Ratios & Identities · All PYQ Banks