Question 2 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 2 If for three matrices 𝐴=[𝑎_𝑖𝑗 ]_(𝑚×4)," " B=[𝑏_𝑖𝑗 ]_(𝑛×3) and C=[𝑐_𝑖𝑗 ]_(𝑝×𝑞) products 𝐴𝐵 and 𝐴𝐶 both are defined and are square matrices of same order, then value of 𝑚,𝑛,𝑝 and 𝑞 are: (A) 𝑚=𝑞=3 and 𝑛=𝑝=4 (B) 𝑚=2,𝑞=3 and 𝑛=𝑝=4 (C) 𝑚=𝑞=4 and 𝑛=𝑝=3 (D) 𝑚=4,𝑝=2 and 𝑛=𝑞=3 Let’s check both AB and AC separately For AB Order of A is m × 4 Order of B is n × 3 AB = [𝑎_𝑖𝑗 ]_(m × 4) [𝑏_𝑖𝑗 ]_(𝑛×3) This is possible only if n = 4 And, order of AB is m × 3 Since AB is square matrix Both m and 3 should be equal ∴ m = 3 For AC Order of A is m × 4 Order of C is p × q AB = [𝑎_𝑖𝑗 ]_(m × 4) [𝑐_𝑖𝑗 ]_(𝑝×𝑞) This is possible only if p = 4 And, order of AC is m × q i.e. 3 × q Since AB is square matrix Both 3 and q should be equal ∴ q = 3 Thus, m = q = 3 n = p = 4 So, the correct answer is (A)