2025 · Q29
Which of the following equations is/are possible? I. (x+y)²4xy, where x, y are positive unequal real quantities. II. 1/x, where x is a positive real quantity. Select the correct answer using the code given below :
Elementary MathematicsTrigonometry
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Statement (I) asserts sin²θ = (x+y)²/(4xy) with x, y positive and unequal; by AM–GM, (x+y)² > 4xy strictly when x ≠ y, so the right side exceeds 1 while sin²θ ≤ 1 — no such θ exists. Statement (II) asserts sinθ + cosθ = x for a positive real x, but sinθ + cosθ ≤ √2, so for any x > √2 the equation has no solution. Hence neither equation is possible, option (d).