Miscellaneous

Misc 1
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Misc 2

Misc 3 Important

Misc 4

Misc 5

Misc 6

Misc 7 Important

Misc 8 (MCQ)

Misc 9 (MCQ) Important

Matrices and Determinants - Formula Sheet and Summary Important

Question 1 Important Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 Deleted for CBSE Board 2024 Exams

Question 4 Important Deleted for CBSE Board 2024 Exams

Question 5 Important Deleted for CBSE Board 2024 Exams

Question 6 Important Deleted for CBSE Board 2024 Exams

Question 7 Deleted for CBSE Board 2024 Exams

Question 8 Deleted for CBSE Board 2024 Exams

Question 9 Important Deleted for CBSE Board 2024 Exams

Question 10 (MCQ) Important Deleted for CBSE Board 2024 Exams

Chapter 4 Class 12 Determinants

Serial order wise

Last updated at April 16, 2024 by Teachoo

Misc 1 Prove that determinant |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| is independent of ΞΈ. Let β = |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| β = x |β 8(βπ₯&1@1&π₯)| β sin ΞΈ |β 8(βsinβ‘ΞΈ&1@cosβ‘ΞΈ&π₯)| + cos ΞΈ |β 8(βsinβ‘ΞΈ&βπ₯@cosβ‘ΞΈ&1)| = x ( βx2 β 1) β sin ΞΈ ( βxsin ΞΈ β cos ΞΈ) + cos ΞΈ (βsin ΞΈ + x cos ΞΈ) = βx3 β x + x sinβ‘γ2 ΞΈγ + π¬π’π§β‘π cos ΞΈ β sin ΞΈ cos ΞΈ + x cos2 ΞΈ = βx3 β x + x sin2 ΞΈ + x cos2 ΞΈ = βx3 β x + x (sin2 ΞΈ + cos2 ΞΈ) = βx3 β x + x (1) = βx3 Hence β = βx3 Which has no ΞΈ term Thus, the determinant is independent of ΞΈ Hence Proved