CUET UG 2025 — Mathematics Algebra

2025mcqmedium

If $A = \begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}$ , $B = \begin{bmatrix} 2 & 3 \\ y & 3 \end{bmatrix}$ and $C = \begin{bmatrix} z & 1 \\ 8 & 2 \end{bmatrix}$ are singular matrices then:

(A) $x > y$

(B) $y > z$

(D) $x \neq y \neq z$

Choose the correct answer from the options given below:

Official previous-year question

Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
(A) and (B) only
B
(B) and (C) only
C
(C) and (D) only
D
(D) only

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Solution

A singular matrix has determinant equal to 0.

For matrix $A = \begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}$ :

$\det(A) = (x)(4) - (3)(2) = 0$

$4x - 6 = 0$

$4x = 6$

$x = \frac{6}{4} = 1.5$

For matrix $B = \begin{bmatrix} 2 & 3 \\ y & 3 \end{bmatrix}$ :

$\det(B) = (2)(3) - (3)(y) = 0$

$6 - 3y = 0$

$3y = 6$

$y = 2$

For matrix $C = \begin{bmatrix} z & 1 \\ 8 & 2 \end{bmatrix}$ :

$\det(C) = (z)(2) - (1)(8) = 0$

$2z - 8 = 0$

$2z = 8$

$z = 4$

With $x = 1.5$ , $y = 2$ , and $z = 4$ :

(A) $x > y$ : Is $1.5 > 2$ ? False

(B) $y > z$ : Is $2 > 4$ ? False

(D) $x \neq y \neq z$ : Are $1.5$ , $2$ , and $4$ all different? True

Both (C) and (D) are correct.

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Solution

A singular matrix has determinant equal to 0.

For matrix $A = \begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}$ :

$\det(A) = (x)(4) - (3)(2) = 0$

$4x - 6 = 0$

$4x = 6$

$x = \frac{6}{4} = 1.5$

For matrix $B = \begin{bmatrix} 2 & 3 \\ y & 3 \end{bmatrix}$ :

$\det(B) = (2)(3) - (3)(y) = 0$

$6 - 3y = 0$

$3y = 6$

$y = 2$

For matrix $C = \begin{bmatrix} z & 1 \\ 8 & 2 \end{bmatrix}$ :

$\det(C) = (z)(2) - (1)(8) = 0$

$2z - 8 = 0$

$2z = 8$

$z = 4$

With $x = 1.5$ , $y = 2$ , and $z = 4$ :

(A) $x > y$ : Is $1.5 > 2$ ? False

(B) $y > z$ : Is $2 > 4$ ? False

(D) $x \neq y \neq z$ : Are $1.5$ , $2$ , and $4$ all different? True

Both (C) and (D) are correct.

CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

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CUET UG Algebra in other years

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Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

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Keep practicing Algebra

CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra