Algebra

Matrices & Determinants

Medium

core

The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is

(a + b + c)

(a - b)(b - c)(c - a)

$a^2 + b^2 + c^2$

✅ Correct Option: 1

Apply $C_3 \to C_3 + C_2$ . Column 3 becomes $(a+b+c, a+b+c, a+b+c)^T$ . Factor out $(a+b+c)$ , leaving column 3 with all 1s, identical to column 1. A determinant with two equal columns is 0.

2025: 14 May Shift 1

If $A = \begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$ , then $|adj A|$ is equal to

2025: 22 May Shift 1

Let A be a non-singular square matrix of order 3 and $|adj A| = 5$ then $|A|$ is equal to

2025: 14 May Shift 2

If A is a square matrix of order 3 such that $|A| = 3$ , then $|adj(adj A)|$ is equal to:

2025: 15 May Shift 1

If $A = \begin{bmatrix} -2 \\ -1 \\ -4 \end{bmatrix}$ , $B = [-1 \quad 2 \quad 3]$ , then the value of $A'B'$ is

2026: 21 May Shift 2

If $\begin{vmatrix}x-2 & 2x-3 & 3x-4\\x-4 & 2x-9 & 3x-16\\x-8 & 2x-27 & 3x-64\end{vmatrix} = 0$ then the value of x is:

2022: 25 May Shift 1

If the matrix $A = \begin{bmatrix} 0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0 \end{bmatrix}$ is skew-symmetric, then :

The value of ∣1ab+c1bc+a1ca+b∣\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}​111​abc​b+cc+aa+b​​ is

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is