Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of (ABC) = 3 sq. units, then the value of k is: Option 1: ± 3 Option 2: ± 2 Option 3: ± 6 Option 4: ± 4

Answer: ± 2. Solution: Using the determinant formula, area = 1/2, 1(0-0) - 3(0-k) + 1(0-0), = (3, k, )/2. Setting this equal to 3 gives, k, = 2, so k = ± 2.

Algebra

Matrices & Determinants

Easy

core

Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of $\Delta(ABC) = 3$ sq. units, then the value of k is:

$\pm 3$

$\pm 2$

$\pm 6$

$\pm 4$

✅ Correct Option: 2

Using the determinant formula, area $= \frac{1}{2}|1(0-0) - 3(0-k) + 1(0-0)| = \frac{3|k|}{2}$ . Setting this equal to 3 gives $|k| = 2$ , so $k = \pm 2$ .

2026: 18 May Shift 1

Consider the system of equation $x+y+3z=8$ , $2x+y+bz=24$ , $x+ay+3z=10$ , then which of the following statements are True?

(A) The system of equations has a unique solution if $a=2, b=3$

(B) The system of equations is inconsistent if $a=1, b \in R$ be any real number.

(D) The system of equations has a unique solution if $a=4$ and $b=3$ .

Choose the correct answer from the options given below:

2025: 13 May Shift 2

If A is an invertible matrix of order 3 and the determinant of A is 9, then the determinant of $A^{-1}$ is:

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
A is given matrix	$\left\vert \text{adj}(\text{adj}A) \right\vert$
(A) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 3$	(I) $3$
(B) Order of A $= 3 \times 3$ and $\left\vert A \right\vert = 2$	(II) $1$
(C) Order of A $= 4 \times 4$ and $\left\vert A \right\vert = 1$	(III) $16$
(D) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 4$	(IV) $4$

Choose the correct answer from the options given below:

2026: 19 May Shift 1

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ , $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ , then the value of k so that $A^2 = 8A + kI$ is

2025: 13 May Shift 1

If $M = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$ and $N = [7 \quad 1 \quad -4]$ , then $(MN)^T$ will be equal to:

2022: 10 Aug Shift 1

The linear equation involving $x$ and $y$ are written in matrix form as:

Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of Δ(ABC)=3\Delta(ABC) = 3Δ(ABC)=3 sq. units, then the value of k is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of $\Delta(ABC) = 3$ sq. units, then the value of k is: