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NDA 2026 · PYQ · Straight Lines · medium

What is the angle made by the line L with positive direction of y-axis?

  1. A.30°
  2. B.45°
  3. C.60°✓ Correct
  4. D.90°

Explanation

Line L: x + √3 y + 3√3 = 0 has slope m = −1/√3, so it makes an angle of 150° with positive x-axis (tan⁻¹(−1/√3) in second quadrant). The angle with positive y-axis = 150° − 90° = 60°. Alternatively, if a line makes angle θ with x-axis, it makes angle (90° − θ) or (θ − 90°) with y-axis. Here the inclination is 150°, so angle with positive y-axis = 60°.
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