Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2022MathematicsDeterminantsActual

If ₁= | array lll 1 & p & q 1 & q & r 1 & r & p array | and ₂= | array lll 1 & 1 & 1 q & r & p r & p & q array | where p q r , then ₁+ ₂ is

Options

  1. A0
  2. Balways positive
  3. Calways negative
  4. Dpositive if p, q, r are positive else negative

Correct answer

C. always negative

Step-by-step solution

aligned & ₁^1= | array lll 1 & 1 & 1 p & q & r q & r & p array |= | array lll 1 & 1 & 1 q & r & p r & p & q array | [ array l Applying c₁ c₂ c₂ c₃ array ] & ₁^1= ₁= ₂ & ₁+ ₂=2 ₂=2 | array lll 1 & 1 & 1 q & r & p r & p & q array | aligned [Applying c₂ c₂-c₁ and c₃ c₃-c₁ ] aligned & ₁^1= | array lll 1 & 1 & 1 p & q & r q & r & p array |= | array lll 1 & 1 & 1 q & r & p r & p & q array | [ array l Applying c₁ c₂ c₂ c₃ array ] & ₁^1= ₁= ₂ & ₁+ ₂=2 ₂=2 | array lll 1 & 1 & 1 q & r & p r & p & q array | aligned [Applying

Practice Determinants on Quantrex Academy →

More from Determinants

Let p=(x+y+z) and q=xyz . If vmatrix x & 1 & 1 1 & y & 1 1 & 1 & z vmatrix is positive, then which one of the following is correct ? 2026Let f(x)= vmatrix 3x^2 & x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix where q is any constant, then what is d^2 dx^2 (f(x) ) at x=0 equal to ? 2026If M= bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix , then what is the value of |M| ,| adj M| ? 2026If vmatrix a-b & p-q & x-y b-c & q-r & y-z c-a & r-p & z-x vmatrix =k vmatrix a & b & c p & q & r x & y & z vmatrix , then what is the value of k ? 2026If A is a square matrix such that |A|=-2 , then |AA^ T | , where A^ T is the transpose of A , is equal to 2026The system of equations 2x - 3y - 5 = 0 , 15y - 10x + 50 = 0 2025The value of the determinant vmatrix a & b & c l & m & n p & q & r vmatrix is equal to 2025If a , b , c are the sides of a triangle ABC and p is the perimeter of the triangle, then what is vmatrix p+c & a & b c & p+a & b c & a & p+b vmatrix equal to? 2025 Full Determinants list All NDA PYQs