Exams › JEE Main › Maths

An ordered pair (α, β) for which the system of linear equations (1 + α)x + βy + z = 2 αx + (1 + β)y + z = 3 αx + βy + 2z = 2 has a unique solution is:

1. (-3, 1)
2. (1, -3)
3. (-4, 2)
4. (2, 4)

Correct answer: (2, 4)

Solution

The ordered pair (2, 4) ensures that the determinant of the coefficient matrix of the system is non-zero, which is a requirement for the system to have a unique solution. This means that the equations are linearly independent and intersect at a single point.

Related JEE Main Maths questions

• In a triangle $ABC$, if the determinant $\begin{vmatrix}\sin A & \sin^2 A\\ \sin B & \sin^2 B\\ \sin C & \sin^2 C\end{vmatrix}=0$, then the triangle must be
• If $[\,\cdot\,]$ represents the greatest integer less than or equal to a real number, and $-1\le x<0$, $0\le y<1$, $1\le z<2$, then the determinant \[ \begin{vmatrix} [x] & [y] & [z] \\ [x+1] & [y+1] & [z] \\ [x] & [y] & [z]+1 \end{vmatrix} \] is equal to:
• Let $x$, $y$, and $z$ be complex numbers. If $\Delta$ denotes the determinant of the matrix \[ \begin{bmatrix} 0 & -y & -z\\ y & 0 & -x\\ z & x & 0 \end{bmatrix}, \] then $\Delta$ is
• For the linear system \[ \begin{aligned} x_1+2x_2+3x_3&=6\\ x_1+3x_2+5x_3&=9\\ 2x_1+5x_2+ax_3&=b \end{aligned} \] if it is consistent and admits infinitely many solutions, then which statement must be true?
• For which value(s) of $x$ does the determinant of the matrix \[ \begin{vmatrix} 1 & x-3 & (x-3)^2\\ 1 & x-4 & (x-4)^2\\ 1 & x-5 & (x-5)^2 \end{vmatrix} \] become zero?
• Let $\Delta_r$ denote the determinant \[ \Delta_r=\begin{vmatrix} \binom{m}{r} & 1 & 1\\ m^2-1 & 2^m & m+1\\ \sin^2(m^2) & \sin^2(m) & \sin^2(m+1) \end{vmatrix}. \] Then the value of $\sum_{r=0}^{m} \Delta_r$ is

⚔️ Practice JEE Main Maths free + battle 1v1 →