Question
For the following two (02) items: Let (2x + 3y) = 1 2 and (3x + 2y) = 3 2 , where - How many values does (y - x) 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 A = 2x + 3y and B = 3x + 2y. We are given A = 1 2 with - The possible values for A are 3 and - 3 . We are also given B = 3 2 with - The possible values for B are 6 and - 6 . We need to find the number of values of (y - x). Observe that A - B = (2x + 3y) - (3x + 2y) = y - x. The possible values for A - B are: 3 - 6 = 6 3 - (- 6 ) = 2 - 3 - 6 = - 2 - 3 - (- 6 ) = - 6 Since all four values are distinct, (y - x) has four values.
Related: Mathematics — Trigonometric Equations · All PYQ Banks