Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202119 Aug 2021Evening ShiftMathematicsDeterminantsActual

Let a , b , c be such that ( b + c ) ≠ 0 and a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 + a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 - 1 n + 2 a - 1 n - 1 b - 1 n c = 0 Then the value of n is

Options

  1. AZero
  2. BAny even integer
  3. CAny odd integer
  4. DAny integer

Correct answer

C. Any odd integer

Step-by-step solution

a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 + a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 - 1 n + 2 a - 1 n - 1 b - 1 n c = 0 ⇒ a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 + - 1 n a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 a - b c = 0 ⇒ a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 + - 1 n a + 1 a - 1 a b + 1 b - 1 - b c - 1 c + 1 c = 0 ⇒ a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 + - 1 n a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 = 0 ⇒ ( 1 + - 1 n ) a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 = 0 Hence, n

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All AP EAMCET PYQs