If vmatrix 1 & -2 & 5 \\ 2 & & -1 \\ 0 & 4 & 2 vmatrix = 86, the sum of the values of is: Option 1: 4 Option 2: -4 Option 3: 1 Option 4: -1

Answer: -4. Solution: Expanding along the first row gives (2^2+4) + 2(4) + 5(8) = 2^2 + 8 + 44. Setting this equal to 86 gives ^2 + 4 - 21 = 0, whose roots sum to -4.

Algebra

Matrices & Determinants

Medium

core

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$ , the sum of the values of $\lambda$ is:

-4

-1

✅ Correct Option: 2

Expanding along the first row gives $(2\lambda^2+4) + 2(4\lambda) + 5(8) = 2\lambda^2 + 8\lambda + 44$ . Setting this equal to $86$ gives $\lambda^2 + 4\lambda - 21 = 0$ , whose roots sum to $-4$ .

2026: 25 May Shift 1

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. If A is an invertible square matrix then $\lvert A^{-1}\rvert =$	I. $\dfrac{1}{\lvert A\rvert}(\mathrm{adj}\,A)$
B. For every square matrix (adj A) A =	II. $\dfrac{1}{\lvert A\rvert}$
C. For a square matrix A, if $\lvert A\rvert \neq 0$ , then $A^{-1} =$	III. $B^{-1}A^{-1}$
D. If A and B are invertible matrices, then $(AB)^{-1} =$	IV. $\lvert A\rvert.I$ , where I is the identity matrix of same order as A

Choose the correct answer from the options given below:

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
Matrix A	$\left\vert \text{adj } A \right\vert^2$
(A) $\begin{bmatrix} 3 & 7 \\ 2 & 8 \end{bmatrix}$	(I) $121$
(B) $\begin{bmatrix} 5 & -1 \\ 2 & 4 \end{bmatrix}$	(II) $144$
(C) $\begin{bmatrix} 3 & 6 \\ 5 & 14 \end{bmatrix}$	(III) $484$
(D) $\begin{bmatrix} 7 & 5 \\ 2 & 3 \end{bmatrix}$	(IV) $100$

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to

2026: 30 May Shift 1

The value of $\begin{vmatrix}1 & \log_ba\\\log_ab & 1\end{vmatrix}$ is:

2026: 29 May Shift 1

Which of the following are correct?

(A) If $A=\begin{bmatrix}7 & 5 \\ 4 & 3\end{bmatrix}$ , then $A^{-1}=\begin{bmatrix}3 & -5 \\ -4 & 7\end{bmatrix}$

(B) If $A=\begin{bmatrix}3 & 5 \\ 6 & 10\end{bmatrix}$ , then $A$ is a non-singular matrix

(D) If $A=\begin{bmatrix}6 & x \\ y & 0\end{bmatrix}$ and $A=A^T$ , then $x=y$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

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

If ∣1−252λ−1042λ∣=86\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86​120​−2λ4​5−12λ​​=86, the sum of the values of λ\lambdaλ is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$ , the sum of the values of $\lambda$ is: