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State PCS PYQPrelims 2023

BPSC – Combined Competitive Examination · Question 150

Four branches of a company are at M, N, O and P. M is 4 km north of N; P is 2 km south of O; N is 1 km south-east of O. What is the distance between M and P?

  1. 5.34 km
  2. 6.74 km
  3. 28.5 km
  4. None of the above
Show answer & explanation

Answer: (A) 5.34 km

Explanation

Horizontal gap = 1/√2 ≈ 0.707 km; vertical gap = 4 − 0.707 + 2 = 5.293 km; distance ≈ 5.34 km.

  • (A) Correct

    Correct: with O at origin, N = (0.707, −0.707), M = (0.707, 3.293), P = (0, −2); MP = √(0.5 + 28.02) ≈ 5.34 km.

  • (B) Incorrect

    Wrong: too large.

  • (C) Incorrect

    Wrong: this is roughly MP², not MP.

  • (D) Incorrect

    Wrong: 5.34 km is correct.