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Miscellaneous

Misc 1

Misc. 2 Important Deleted for CBSE Board 2023 Exams

Misc 3

Misc 4

Misc 5 You are here

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important Deleted for CBSE Board 2023 Exams

Misc 12 Important Deleted for CBSE Board 2023 Exams

Misc. 13 Deleted for CBSE Board 2023 Exams

Misc 14 Deleted for CBSE Board 2023 Exams

Misc. 15 Important Deleted for CBSE Board 2023 Exams

Misc. 16 Important

Misc 17 (MCQ) Important Deleted for CBSE Board 2023 Exams

Misc 18 (MCQ)

Misc 19 (MCQ) Important

Matrices and Determinants - Formula Sheet and Summary Important

Chapter 4 Class 12 Determinants

Serial order wise

Last updated at May 29, 2018 by Teachoo

Misc 5 Solve the equations 𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 = 0, a ≠ 0 Solving ∆ = 𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Applying R1 → R1 + R2 + R3 = 𝑥+𝑎+𝑥+𝑥𝑥+𝑥+𝑎+𝑥𝑥+𝑥+𝑥+𝑎𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 = 𝟑𝒙+𝒂𝟑𝒙+𝒂𝟑𝒙+𝒂𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Taking (3x + a) common from R1 = (3x + a) 111𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Applying C2 → C2 – C1 = (3x + a) 1𝟏−𝟏1𝑥𝑥+𝑎−𝑥𝑥𝑥𝑥−𝑥𝑥+𝑎 = (3x+ a) 1𝟎1𝑥𝑎𝑥𝑥0𝑥+𝑎 Applying C3 →C3 – C1 = (3x + a) 10𝟏−𝟏𝑥𝑎𝑥−𝑥𝑥0𝑥+𝑎−𝑥 = (3x + a) 10𝟎𝑥𝑎0𝑥0𝑎 = (3x+ a) 1 𝑎00𝑎−0 𝑥0𝑥0+0 𝑥𝑎𝑥0 = (3x+ a) 1 𝑎00𝑎−0+0 = (3x+ a) (1(a2 – 0) – 0 + 0) = (3x+ a) (a2) ∴ ∆ = (3x+ a) (a2) Given ∆ = 0 ∴ (3x + a) a2 = 0