AfterBoards Logo
Skip to main contentSkip to solution

CUET Mathematics 2025 PYQs30 May Shift 2. Free, no login required.

Algebra

past year questions, CUET Mathematics 2025 30 May Shift 2

Matrices & Determinants

past year questions, Algebra, CUET Mathematics 2025 30 May Shift 2

Medium

core

The value of ∣265240219240225198219198181∣\begin{vmatrix}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix} is

Solution

✅ Correct Option: 3

The given determinant is:

∣265240219240225198219198181∣\begin{vmatrix}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix}

A determinant equals zero when the rows (or columns) are linearly dependent, meaning one row can be expressed as a combination of other rows.

Applying R₁ → R₁ - R₂:

∣265−240240−225219−198240225198219198181∣\begin{vmatrix}265-240 & 240-225 & 219-198 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix}

=∣251521240225198219198181∣= \begin{vmatrix}25 & 15 & 21 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix}

Applying R₂ → R₂ - R₃:

∣251521240−219225−198198−181219198181∣\begin{vmatrix}25 & 15 & 21 \\ 240-219 & 225-198 & 198-181 \\ 219 & 198 & 181\end{vmatrix}

=∣251521212717219198181∣= \begin{vmatrix}25 & 15 & 21 \\ 21 & 27 & 17 \\ 219 & 198 & 181\end{vmatrix}

Applying R₁ → R₁ - R₂:

∣25−2115−2721−17212717219198181∣\begin{vmatrix}25-21 & 15-27 & 21-17 \\ 21 & 27 & 17 \\ 219 & 198 & 181\end{vmatrix}

=∣4−124212717219198181∣= \begin{vmatrix}4 & -12 & 4 \\ 21 & 27 & 17 \\ 219 & 198 & 181\end{vmatrix}

The first row can be written as 4(1,−3,1)4(1, -3, 1). Continuing this process reveals that the rows are linearly dependent.

Therefore, the value of the determinant is 00.

Related questions:

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−1A^{-1} is:

2026: 18 May Shift 2

If A=[10−15]A=\begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix} and I is indentity matrix of order 2, then which of following statements are TRUE?

A. A2−6A−mI=0A^2-6A-mI=0 if m=−5m=-5.

B. A2−6A+mI=0A^2-6A+mI=0 if m=−5m=-5.

C. AA is a non-singular matrix.

D. A2=AA^2=A

Choose the correct answer from the options given below:

2026: 29 May Shift 2

If ∣x218x∣=∣62186∣\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}, then x equals:

2026: 15 May Shift 1

The value of ∣xx+1x−1x∣\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix} is:

2023: 23 May Shift 3

If x,yx, y & zz are non zero real numbers, the inverse of matrix A=[x000y000z]A = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix} is :

2025: 3 June Shift 1

If A=[5632]A = \begin{bmatrix} 5 & 6 \\ 3 & 2 \end{bmatrix} then which of the following is correct?

(A) ∣A∣|A| is positive

(B) ∣adj A∣=−8|adj\ A| = -8

(C) Cofactor of 3 is 6

(D) ∣2A∣=−32|2A| = -32

Choose the correct answer from the options given below:

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question

CUET Mathematics Past Year Questions (Topic-Wise)