This is a question of CBSE Sample Paper - Class 12 - 2017/18.

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Question 13 If โˆ† = |โ– 8(1&๐‘Ž&๐‘Ž2@๐‘Ž&๐‘Ž2&1@๐‘Ž2&1&๐‘Ž)| = โˆ’4 Then find the value of |โ– 8(๐‘Ž3โˆ’1&0&๐‘Žโˆ’๐‘Ž4@0&๐‘Žโˆ’๐‘Ž4&๐‘Ž3โˆ’1@๐‘Žโˆ’๐‘Ž4&๐‘Ž3 โˆ’1&0)| Given |โ– 8(1&๐‘Ž&๐‘Ž2@๐‘Ž&๐‘Ž2&1@๐‘Ž2&1&๐‘Ž)| = โˆ’4 1 (a2 ร— a โ€“ 1 ร— 1) โ€“ a(a ร— a โ€“ a2 ร— 1) + a2 (a ร— 1 โ€“ a2 ร— a2) = โ€“ 4 1 (a3 โ€“ 1) โ€“ a(a2 โ€“ a2) + a2 (a โ€“ a4) = โ€“ 4 (a3 โ€“ 1) โ€“ a(0) + a2 (a โ€“ a4) = โ€“ 4 (a3 โ€“ 1) + a2 (a โ€“ a4) = โ€“ 4 (a3 โ€“ 1) + a2 ร— a(1 โ€“ a3) = โ€“ 4 (a3 โ€“ 1) + a3 (1 โ€“ a3) = โ€“ 4 (a3 โ€“ 1) โ€“ a3 (a3 โ€“ 1) = โ€“ 4 (a3 โ€“ 1)(1 โ€“ a3) = โ€“ 4 โ€“ (a3 โ€“ 1) (a3 โ€“ 1) = โ€“ 4 (a3 โ€“ 1) (a3 โ€“ 1) = 4 (a3 โ€“ 1)2 = 4 Now, we need to find |โ– 8(๐‘Ž3โˆ’1&0&๐‘Žโˆ’๐‘Ž4@0&๐‘Žโˆ’๐‘Ž4&๐‘Ž3โˆ’1@๐‘Žโˆ’๐‘Ž4&๐‘Ž3 โˆ’1&0)| = (๐‘Ž^3โˆ’1)[(๐‘Žโˆ’๐‘Ž^4 )ร—0โˆ’(๐‘Ž^3โˆ’1)(๐‘Ž^3โˆ’1)] โ€“ 0[0ร—0โˆ’(๐‘Žโˆ’๐‘Ž^4 )(๐‘Ž^3โˆ’1)] + (๐‘Žโˆ’๐‘Ž^4 )[0ร—(๐‘Ž^3โˆ’1)โˆ’(๐‘Žโˆ’๐‘Ž^4 )(๐‘Žโˆ’๐‘Ž^4 )] = (๐‘Ž^3โˆ’1)[0โˆ’(๐‘Ž^3โˆ’1)(๐‘Ž^3โˆ’1)] โ€“ 0 + (๐‘Žโˆ’๐‘Ž^4 )[0โˆ’(๐‘Žโˆ’๐‘Ž^4 )(๐‘Žโˆ’๐‘Ž^4 )] = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’(๐‘Žโˆ’๐‘Ž^4 )^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–(๐‘Ž(1โˆ’๐‘Ž^3)) ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 (1โˆ’๐‘Ž^3)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 ร—(โˆ’1)^3 (๐‘Ž^3โˆ’1)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 ร—(โˆ’1)^3 (๐‘Ž^3โˆ’1)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 ร—(โˆ’1) ร— (๐‘Ž^3โˆ’1)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3+ใ€–๐‘Ž^3 (๐‘Ž^3โˆ’1)ใ€—^3 = (๐‘Ž^3โˆ’1)^3 (โˆ’1+๐‘Ž^3) = (๐‘Ž^3โˆ’1)^3 (๐‘Ž^3โˆ’1) = (๐‘Ž^3โˆ’1)^4 = [(๐‘Ž^3โˆ’1)^2 ]^2 Putting (a3 โ€“ 1)2 = 4 from (1) = [4]^2 = 16 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 ร—(โˆ’1)^3 (๐‘Ž^3โˆ’1)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3โˆ’ใ€–๐‘Ž^3 ร—(โˆ’1) ร— (๐‘Ž^3โˆ’1)ใ€—^3 = โˆ’(๐‘Ž^3โˆ’1)^3+ใ€–๐‘Ž^3 (๐‘Ž^3โˆ’1)ใ€—^3 = (๐‘Ž^3โˆ’1)^3 (โˆ’1+๐‘Ž^3) = (๐‘Ž^3โˆ’1)^3 (๐‘Ž^3โˆ’1) = (๐‘Ž^3โˆ’1)^4 = [(๐‘Ž^3โˆ’1)^2 ]^2 Putting (a3 โ€“ 1)2 = 4 from (1) = [4]^2 = 16

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.