Question 1 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

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Question 1 If for a square matrix 𝐴,□( ) 𝐴.( adj 𝐴)=[■(2025&0&0@0&2025&0@0&0&2025)], then the value of |𝐴|+|𝑎𝑑𝑗𝐴| is equal to: (A) 1 (B) 2025+1 (C) (2025)^2+45 (D) 2025+(2025)^2Given 𝐴.( adj 𝐴)=[■(2025&0&0@0&2025&0@0&0&2025)] Taking 2025 common 𝐴.( adj 𝐴)=2025[■(1&0&0@0&1&0@0&0&1)] 𝑨.( adj 𝑨)=𝟐𝟎𝟐𝟓𝑰 And, we know that 𝑨.( adj 𝑨)=|𝑨|𝑰 Thus, |𝑨| = 2025 Finding |adj (A)| |adj (A)| = |A|n − 1 Where n is the order of matrix Since I is of order 3 × 3, therefore n = 3 Thus, |adj (A)| = |A|3− 1 = |A|2 = (2025)2 Now, |𝐴|+|𝑎𝑑𝑗𝐴| = 2025 + (2025)2 So, the correct answer is (D)

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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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