If vmatrix 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 vmatrix + vmatrix 3 & 2 \\ 4 & 5 vmatrix = 0, then the value of x is Option 1: -2/3 Option 2: -7/3 Option 3: -4/3 Option 4: -5/3

Answer: -7/3. Solution: Take x common from the second row: the third-order determinant becomes xvmatrix2&3&2\\1&1&1\\4&9&1vmatrix=3x. The second-order determinant is 15-8=7. So 3x+7=0 and x=-73.

Algebra

Matrices & Determinants

Medium

applied

If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + \begin{vmatrix} 3 & 2 \\ 4 & 5 \end{vmatrix} = 0$ , then the value of $x$ is

-2/3

-7/3

-4/3

-5/3

✅ Correct Option: 2

Take $x$ common from the second row: the third-order determinant becomes $x\begin{vmatrix}2&3&2\\1&1&1\\4&9&1\end{vmatrix}=3x$ . The second-order determinant is $15-8=7$ . So $3x+7=0$ and $x=-\frac73$ .

2026: 29 May Shift 2

If A is a skew symmetric matrix, then $A^2$ is a

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$ , then $k$ is	(I) $0$
(B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is	(II) $3$
(C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$	(III) $8$
(D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$ , then the minor of the element $a_{23}$ is	(IV) $7$

Choose the correct answer from the options given below :

2026: 22 May Shift 2

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$ , where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

2025: 3 June Shift 1

The value of $\begin{vmatrix} x & x+y & x+y+z \\ 2x & 3x+2y & 4x+3y+2z \\ 3x & 6x+3y & 10x+6y+3z \end{vmatrix}$ is

2022: 30 Aug Shift 1

If $0 < x < \pi$ and the matrix $\begin{bmatrix} 4\sin x & -1 \\ -3 & \sin x \end{bmatrix}$ is singular, then the values of $x$ are :

2025: 13 May Shift 2

For what value of k, the following system of equations has infinitely many solutions?

$x + 2y = 5, 3x + ky = 15$

If ∣232xxx491∣+∣3245∣=0\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + \begin{vmatrix} 3 & 2 \\ 4 & 5 \end{vmatrix} = 0​2x4​3x9​2x1​​+​34​25​​=0, then the value of xxx is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + \begin{vmatrix} 3 & 2 \\ 4 & 5 \end{vmatrix} = 0$ , then the value of $x$ is