

Miscellaneous
Misc. 2 Important Deleted for CBSE Board 2022 Exams
Misc 3
Misc 4 Deleted for CBSE Board 2022 Exams
Misc 5
Misc 6 Important Deleted for CBSE Board 2022 Exams
Misc 7 Important
Misc 8
Misc 9
Misc 10
Misc 11 Important Deleted for CBSE Board 2022 Exams
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Misc. 13 Deleted for CBSE Board 2022 Exams
Misc 14 Deleted for CBSE Board 2022 Exams You are here
Misc. 15 Important Deleted for CBSE Board 2022 Exams
Misc. 16 Important
Misc 17 (MCQ) Important Deleted for CBSE Board 2022 Exams
Misc 18 (MCQ)
Misc 19 (MCQ) Important
Matrices and Determinants - Formula Sheet and Summary Important
Misc 14 Using properties of determinants, prove that: 11+p1+p+q23+2p4+3p+2q36+3p10+6p+3q = 1 Taking L.H.S 11+p1+p+q23+2p4+3p+2q36+3p10+6p+3q Applying R2→ R2 – 2R1 = 11+p1+p+q𝟐−𝟐(𝟏)3+2p−2(1+p)4+3𝑝+2𝑝−2(1+𝑝+𝑞)36+3p−210+6p+3q = 11+p1+p+q𝟎12+𝑝36+3p10+6p+3q Applying R3→ R3 – 3R2 = 11+p1+p+q012+p𝟑−𝟑(𝟏)6+3𝑝−3(1+𝑝)10+6𝑝+3𝑞−3(1+𝑝+𝑞) = 11+p1+p+q012+p𝟎37+3𝑝 Expanding determinant along C1 = 1 12+p37+3p – 0 1+𝑝2+p37+3p + 0 1+𝑝1+p+q12+p = 1 12+p37+3p – 0 + 0 = 1 (7 + 3p – 3 (2 + p)) = 7 + 3p – 6 – 3p = 1 = R.H.S Hence Proved