Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Determinants

NDA 2019 · Mathematics · Determinants

What are the values of x that satisfy the equation | array lll x &...

What are the values of xx that satisfy the equation \left|x022x21111\begin{array}{lll} x & 0 & 2 \\ 2 x & 2 & 1 \\ 1 & 1 & 1 \end{array}\right|+\left|3x02x221011\begin{array}{lll} 3 x & 0 & 2 \\ x^2 & 2 & 1 \\ 0 & 1 & 1 \end{array}\right|=0 ?

Options

  1. A−2±3-2 \pm \sqrt{3}
  2. B−1±3-1 \pm \sqrt{3}
  3. C−1±6-1 \pm \sqrt{6}
  4. D−2±6-2 \pm \sqrt{6}

Correct answer

D. −2±6-2 \pm \sqrt{6}

Step-by-step solution

On expanding both the determinantswegetdeterminants we get[n(1)+2(2x−2)]+[3x+2x2]=0=2x2+8x−4=0⇒x2+4x−2=0⇒x=−2±6\begin{aligned} & {[n(1)+2(2 x-2)]+\left[3 x+2 x^2\right]=0} \\ & =2 x^2+8 x-4=0 \\ & \Rightarrow x^2+4 x-2=0 \\ & \Rightarrow x=-2 \pm \sqrt{6} \end{aligned}$$
Practice Determinants on Quantrex Academy →

More from Determinants

Let p=(x+y+z) and q=xyz . If vmatrix x and 1 and 1 1 and y and 1 1 and 1 and z vmatrix is… NDA 2026Let f(x)= vmatrix 3x^2 and x and - x 6 and -1 and 0 q and q^2 and q^3 vmatrix where q is… NDA 2026If M= bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix , then what is the value of… NDA 2026If vmatrix a-b and p-q and x-y b-c and q-r and y-z c-a and r-p and z-x vmatrix =k vmatrix… NDA 2026If A is a square matrix such that |A|=-2 , then |AA^ T | , where A^ T is the transpose of… NDA 2026The system of equations 2x - 3y - 5 = 0 , 15y - 10x + 50 = 0 NDA 2025The value of the determinant vmatrix a and b and c l and m and n p and q and r vmatrix is… NDA 2025If a , b , c are the sides of a triangle ABC and p is the perimeter of the triangle, then… NDA 2025Consider the following statements: Statement-I: If X is an n × n matrix, then (mX) = m^n… NDA 2025If Δ = vmatrix a and b and c d and e and f g and h and i vmatrix and A , B , C , D , G… NDA 2025If A^2 + B^2 + C^2 = 0 , then what is the value of vmatrix 1 and C and B C and 1 and A B… NDA 2025Consider the following statements in respect of the determinant Δ = vmatrix k(k+2) and… NDA 2025If vmatrix 2 & 3+i & -1 3-i & 0 & i-1 -1 & -1-i & 1 vmatrix = A + iB where i = -1 , then… NDA 2025Consider the following in respect of a non-singular matrix M : I. |M^2| = |M|^2 II. |M| =… NDA 2025In obtaining the solution of the system of equations x + y + z = 7 , x + 2y + 3z = 16 and… NDA 2025If Z=(1)/(3)| array ccc i & 2 i & 1 2 i & 3 i & 2 3 & 1 & 3 array |=x+i y ; i= -1 then… NDA 2024 Full Determinants list Determinants JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs