Question
For the following two (02) items: Let (2x + 3y) = 1 2 and (3x + 2y) = 3 2 , where - How many values does (x + y) have?
NDA
Mathematics
Trigonometric Equations
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. Two
- B. Three
- C. Four
- D. More than four
Answer
C. Four
Step-by-step solution
Let 2x + 3y = u and 3x + 2y = v. Given u = 1 2 and - Given v = 3 2 and - Adding the two equations, we get u + v = 5(x + y) x + y = u + v 5 . The possible values of u + v are: 3 + 6 = 2 3 - 6 = 6 - 3 + 6 = - 6 - 3 - 6 = - 2 Since all four values of u + v are distinct, there are exactly four distinct values for x + y.
Related: Mathematics — Trigonometric Equations · All PYQ Banks