Question 40 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

Given that A = [8(α β γ -α )] and A ² = 3I, then :

(a) 1 + 𝛼 ² + 𝛽𝛾 = 0 (b) 1 − 𝛼 ² − 𝛽𝛾 = 0

(c) 3 − 𝛼 ² − 𝛽𝛾 = 0 (d) 3 + 𝛼 ² + 𝛽𝛾 = 0

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Transcript

Question 40 Given that A = [■8(𝛼&𝛽@𝛾&−𝛼 )] and A2 = 3I, then : a) 1 + 𝛼2 + 𝛽𝛾 = 0 b) 1 − 𝛼2 − 𝛽𝛾 = 0 c) 3 − 𝛼2 − 𝛽𝛾 = 0 d) 3 + 𝛼2 + 𝛽𝛾 = 0 Given A2 = 3I [■8(𝛼&𝛽@𝛾&−𝛼)] [■8(𝛼&𝛽@𝛾&−𝛼)] = 3I [■8(𝛼(𝛼)+𝛽(𝛾)&𝛼(𝛽)+𝛽(−𝛼)@𝛾(𝛼)+(−𝛼)𝛾&𝛾(𝛽)+(−𝛼)(−𝛼))] = 3 [■8(1&0@0&1)] [■8(𝜶^𝟐+𝜷𝜸&𝟎@𝟎&𝜶^𝟐+𝜷𝜸)] = [■8(𝟑&𝟎@𝟎&𝟑)] Thus, 𝜶^𝟐⤶7+𝜷𝜸 = 3 0 = 3 − 𝛼^2−𝛽𝛾 3 − 𝛼2 − 𝛽𝛾 = 0 So, the correct answer is (C)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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