Let A be the area of the triangle with vertices (3, 8), (5, -1) and (k, 2), k Z (set of integers). If 2A = 75, then k is equal to: Option 1: -4 Option 2: 4 Option 3: 13 Option 4: -21

Answer: -4. Solution: 2A=, x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2), =, 3(-1-2)+5(2-8)+k(8+1), =, 9k-39, =75. So 9k-39=75 gives k=114/9, not an integer, while 9k-39=-75 gives k=-4.

Algebra

Matrices & Determinants

Medium

core

Let A be the area of the triangle with vertices (3, 8), (5, -1) and $(k, 2)$ , $k \in \mathbb{Z}$ (set of integers). If $2A = 75$ , then k is equal to:

-4

-21

✅ Correct Option: 1

$2A=|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

$=|3(-1-2)+5(2-8)+k(8+1)|=|9k-39|=75$ .

So $9k-39=75$ gives $k=\frac{114}{9}$ , not an integer, while $9k-39=-75$ gives $k=-4$ .

2026: 18 May Shift 2

If matrix $A=\begin{bmatrix} 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 \end{bmatrix}$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$16$
B.	Minor of $a_{23}$	II.	$27$
C.	Cofactor of $a_{32}$	III.	$19$
D.	If $a_{23}$ is interchanged with $a_{32}$ , then $\vert A \vert$	IV.	$2$

Choose the correct answer from the options given below:

2025: 13 May Shift 1

The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a

(A) Null matrix

(B) Unit matrix

(D) Skew-symmetric matrix

Choose the correct answer from the options given below:

2026: 12 May Shift 2

The matrix which is both symmetric and skew-symmetric, is a:

2025: 22 May Shift 2

Let A and B be 3×3 matrices such that $A \neq B$ . If $A^3 = B^3$ and $A^2B = B^2A$ , then the determinant of $A^2 + B^2$ is:

2022: 7 Aug Shift 2

Match List - I with List - II.

	List - I		List - II
(A)	$A = \begin{bmatrix} 6 & 9 \\ 2 & 3 \end{bmatrix}$ , $B = \begin{bmatrix} 2 & 6 & 0 \\ 7 & 9 & 8 \end{bmatrix}$ , AB will be	(I)	$\begin{bmatrix} 75 & 117 & 72 \\ 35 & 39 & 24 \end{bmatrix}$
(B)	$P = \begin{bmatrix} 8 & 45 & 30 \\ 17 & 19 & 5 \end{bmatrix}$ , $Q = \begin{bmatrix} 67 & 72 & 42 \\ 8 & 30 & 19 \end{bmatrix}$ , P+Q will be	(II)	$\begin{bmatrix} 75 & 117 & 72 \\ 25 & 39 & 24 \end{bmatrix}$
(C)	$\begin{bmatrix} 85 & 42 & 69 \\ 73 & 42 & 50 \end{bmatrix} - \begin{bmatrix} 10 & -75 & -3 \\ 38 & 3 & 26 \end{bmatrix}$	(III)	$\begin{bmatrix} 75 & 117 & 72 \\ 25 & 49 & 24 \end{bmatrix}$
(D)	$2 \begin{bmatrix} 34 & 36 & 30 \\ 12 & 18 & 20 \end{bmatrix} + \begin{bmatrix} 7 & 55 & 12 \\ 1 & 13 & -16 \end{bmatrix}$	(IV)	$\begin{bmatrix} 75 & 127 & 72 \\ 25 & 49 & 24 \end{bmatrix}$

Choose the correct answer from the options given below :

2026: 14 May Shift 2

If A is a 3x3 matrix then:

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj A\vert$	I.	$\vert A\vert^{-1}$
B.	$\vert A.adj A\vert$	II.	$\vert A\vert$
C.	$\vert A^{-1}\vert$	III.	$\vert A\vert^2$
D.	$\vert A^{-1}.adj A\vert$	IV.	$\vert A\vert^3$

Choose the correct answer from the options given below:

Let A be the area of the triangle with vertices (3, 8), (5, -1) and (k,2)(k, 2)(k,2), k∈Zk \in \mathbb{Z}k∈Z (set of integers). If 2A=752A = 752A=75, then k is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let A be the area of the triangle with vertices (3, 8), (5, -1) and $(k, 2)$ , $k \in \mathbb{Z}$ (set of integers). If $2A = 75$ , then k is equal to: