Sarkari RiseLogin
NDA 2026 · PYQ · Matrices and Determinants · easy

If M_k = [[k, k−1],[k−1, k]], where k is a positive integer, then |M₁| + |M₂| + |M₃| + ... + |M₅₀| is equal to

Answer

The correct answer is C: 2500. |M_k| = k² − (k−1)² = 2k − 1. So sum = Σ(2k−1) for k=1 to 50 = 2·(50·51/2) − 50 = 2550 − 50 = 2500.

  1. A.50
  2. B.1250
  3. C.2500✓ Correct
  4. D.5000

Explanation

|M_k| = k² − (k−1)² = 2k − 1. So sum = Σ(2k−1) for k=1 to 50 = 2·(50·51/2) − 50 = 2550 − 50 = 2500.
💡 Practice unlimited NDA PYQs + AI-tracked progress on each topic. Sign up free →

More Matrices and Determinants questions

Want more NDA practice?

Free daily 10-Q quiz · adaptive mocks · 49,000+ practice questions (19,000+ verified PYQs) · AI doubt solver in Hindi + English

Sign up freeMore Matrices and Determinants practice