JEE Main 2009Annual, Paper 1MathematicsHardMatrices and Determinants245× since 2002Let a,b,ca, b, ca,b,c be such that b(a+c)≠0b\left( {a + c} \right) \ne 0b(a+c)=0 if ∣aa+1a−1−bb+1b−1cc−1c+1∣+∣a+1b+1c−1a−1b−1c+1(−1)n+2a(−1)n+1b(−1)nc∣=0\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} & {b + 1} & {b - 1} \cr c & {c - 1} & {c + 1} \cr } } \right| + \left| {\matrix{ {a + 1} & {b + 1} & {c - 1} \cr {a - 1} & {b - 1} & {c + 1} \cr {{{\left( { - 1} \right)}^{n + 2}}a} & {{{\left( { - 1} \right)}^{n + 1}}b} & {{{\left( { - 1} \right)}^n}c} \cr } } \right| = 0a−bca+1b+1c−1a−1b−1c+1+a+1a−1(−1)n+2ab+1b−1(−1)n+1bc−1c+1(−1)nc=0 then the value of nnn :AOption A. any even integerBOption B. any odd integerCOption C. any integerDOption D. zeroCheckSkip · show solution
