# Misc 17 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 17 Choose the correct answer. If a, b, c, are in A.P., then the determinant +2 +3 +2 +3 +4 +2 +4 +5 +2 is A. 0 B. 1 C. x D. 2x Since a, b & c are in A.P Then b a = c b b a c + b = 0 2b a c = 0 Solving x+2 x+3 x+2a x+3 x+4 x+2b x+4 x+5 x+2c Multiplying and dividing 2 = 2 2 x+2 x+3 x+2a x+3 x+4 x+2b x+4 x+5 x+2c Multiplying R2 by 2 = 1 2 +2 +3 +2 ( +3) ( +4) ( +2 ) +4 +5 +2 = 1 2 +2 +3 +2 2 +6 2 +8 2 +4 +4 +5 +2 Applying R2 R2 R1 R3 = 1 2 +2 +3 +2 2 +6 +2 ( +4 ) 2 +8 +3 ( +5) 2 +4 +2 ( +2 ) +4 +5 +2 = 1 2 +2 +3 +2 2 +6 2 4 2 +8 3 5 2 +4 2 2 +4 +5 +2 = 1 2 +2 +3 +2 0 0 4 2 2 +4 +5 +2 = 1 2 +2 +3 +2 0 0 2( ) +4 +5 +2 = 1 2 +2 +3 +2 0 0 2( ) +4 +5 +2 = 1 2 +2 +3 +2 0 0 0 +4 +5 +2 If any row as column of determinant are zero, then value of determinant is also zero. = 1 2 0 = 0 Thus, the value of determinant is 0 Correct Answer is A Misc. 17(Method 2) Choose the correct answer. If a, b, c, are in A.P., then the determinant x+2 x+3 x+2a x+3 x+4 x+2b x+4 x+5 x+2c is A. 0 B. 1 C. x D. 2x We need to find value of x+2 x+3 x+2a x+3 x+4 x+2b x+4 x+5 x+2c Since a, b & c are in A.P Then a b = c b b + b = c + a 2b = a + c Consider +2 +3 +2 +3 +4 +2 +4 +5 +2 Applying R1 R1 + R3 2R2 = +2 + +4 2( +3) +3 + +5 2( +4) +2 + +2 2( +2 ) +3 +4 +2 +4 +5 +2 = +2+ +4 2 6 +3+ +5 2 8 +2 + +2 2 4 +3 +4 +2 +4 +5 +2 = 2 2 +6 6 2 2 +8 8 2 2 +2 +2 4 +3 +4 +2 +4 +5 +2 = 0 0 0+2( + 2 ) +3 +4 +2 +4 +5 +2 = 0 0 2( 2 ) +3 +4 +2 +4 +5 +2 = 0 0 0 +3 +4 +2 +4 +5 +2 If any row as column of determinant are zero, then value of determinant is also zero. = 0 Hence, value of determinant is 0 Correct Answer is A

Chapter 4 Class 12 Determinants

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.