Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Determinants

NDA 2012 · Mathematics · Determinants

If the matrix [ array ccc α & 2 & 2 -3 & 0 & 4 1 & -1 & 1 array ]...

If the matrix \left[α22−3041−11\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}$\right] is not invertible, then :$

Options

  1. Aα=−5\alpha=-5
  2. Bα=5\alpha=5
  3. Cα=0\alpha=0
  4. Dα=1\alpha=1

Correct answer

A. α=−5\alpha=-5

Step-by-step solution

\left[α22−3041−11\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}\right]=0\begin{aligned} & \Rightarrow \alpha(0+4)-2(-3-4)+2(3-0)=0 \\ & \Rightarrow \quad 4 \alpha+14+6=0\end{aligned}$⇒4α=−20α=−5\Rightarrow \quad 4 \alpha=-20\alpha=-5.$
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