Algebra

Matrices & Determinants

Easy

common

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$

$\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

✅ Correct Option: 1

Both rows of the matrix are identical, so the determinant is $0$ .

Alternatively, $\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2} = 0$ .

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The number of possible matrices of order 3x3 with each entry 1 or 0	(I) $2^4$
(B) The number of possible matrices of order 2x3 with each entry 1 or 0	(II) $2^9$
(C) The number of possible matrices of order 2x3 with each entry 0,1,2	(III) $2^6$
(D) The number of possible matrices of order 2x2 with each entry 1 or 0	(IV) $3^6$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) A square matrix $P$ is said to be non-singular if	(I) $\vert P\vert = 0$
(B) A square matrix $P$ is said to be singular if	(II) $P P^T$ is symmetric
(C) If a matrix $P$ is both symmetric and skew-symmetric, then	(III) $\vert P\vert \neq 0$
(D) If $P$ is a square matrix, then	(IV) $P$ is a null matrix

Choose the correct answer from the options given below:

2025: 21 May Shift 1

The system of equations

$x + ky = 0$

$3x + 5y = 0$

has infinitely many solutions, then k is equal to

2026: 30 May Shift 1

If $A=\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x)=x^2-2x-3$ , then $f(A)$ is equal to

2025: 16 May Shift 1

If A is an invertible symmetric matrix, then A⁻¹ is

2025: 26 May Shift 2

If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is

The value of ∣3/21/23/21/2∣\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}​3​/23​/2​1/21/2​​

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$