Question
Consider the following for the three (03) items that follow: Let p = 2 - and q = - 2 . What is (p + q) equal to?
NDA
Mathematics
Trigonometric Ratios & Identities
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 4
- B. 4
- C. 2 4
- D. 2 4
Answer
D. 2 4
Step-by-step solution
Given p = 2 - and q = - 2 . Simplifying p: p = 2 2 - = 2 - 2 2 = (2 - ) 2 = 2 Simplifying q: q = - 2 2 = 2 - 2 2 = (2 - ) 2 = 2 = 1 2 Now, adding p and q: p + q = 2 + 1 2 Using 2 = 2 : p + q = 2 + 1 2 p + q = 2 ^2 + 2 2 2 Using the identity 2 = 1 - 2 ^2 in the numerator and 2 = 2 in the denominator: p + q = 2 ^2 + (1 - 2 ^2 ) 2 2 p + q = 1 2 2 Multiplying and dividing by 2: p + q = 2 2 2 2 = 2 4 p + q = 2 4 Answer: 2 4
Related: Mathematics — Trigonometric Ratios & Identities · All PYQ Banks