CUET · MATHS · PYQ PAPER 2025
Let \(A=\left[a_{i j}\right]\) be a square matrix, where \(a_{i j}=\left\{\begin{array}{ll}0, & \text { when } i=j \\ 1, & \text { otherwise }\end{array}\right.\)
If \(|\operatorname{adj} A|=|A|^2\), then which of the following statements are correct?
(A) A is a skew-symmetric matrix.
(B) A is a non-singular matrix.
(C) A is a square matrix of order 4.
(D) A is a symmetric matrix.
Choose the correct answer from the options given below :
- A (A), (B) and (C) only
- B (B) and (D) only
- C (A) and (C) only
- D (B), (C) and (D) only
Answer & Solution
Correct Answer
(D) (B), (C) and (D) only
Step-by-step Solution
Detailed explanation
\(|\operatorname{adj} A|=|A|^{n-1}\) \(|A|^{n-1}=|A|^2\) If \(|A|=0\), then \(n-1=0 \implies n=1\). For \(n=1\), \(A=[0]\), \(|\operatorname{adj} A|=1\), \(|A|^2=0\). \(1=0\) is false. Thus, \(|A| \ne 0\). Therefore, \(n-1=2 \implies n=3\). This means (C) "A is a square matrix…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The area bounded by \(y^2=x, y=5\) and the \(y\)-axis is:CUET 2023 Easy
- The inverse of the matrix \(\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]\) is:CUET 2023 Easy
- Mr. X wishes to purchase a flat for Rs. \(44,65,000\) with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years.
If the bank charges \(6 \%\) per annum compounded monthly, the EMI is :
[Given: \((1.005)^{300}=4.465\)]CUET 2025 Hard - A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A isCUET 2025 Hard
- If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \(\vec{a}+\sqrt{3 b}\) to be a unit vector is given by :CUET 2023 Hard
- Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:CUET 2025 Hard
More PYQs from CUET
- In a step down Transformer :CUET 2023 Hard
- For the objective function \(z=p x+q y\), where \(p, q>0\) the corner points of the feasible region determined by the system of linear constraints are \((0,10),(5,5),(15,15)\) and \((0,20)\), condition on \(p\) and \(q\) so that maximum of \(z\) occurs at both the points \((15,15)\) and \((0,20)\) is :CUET 2023 Medium
- When two independent small samples of sizes \(n_1\) and \(n_2\) with means \(\bar{x}_1\) and \(\bar{x}_2\) respectively are drawn from populations with identical population variances, the test-statistic is computed as :CUET 2025 Medium
- A solution of 2.5 g of ethanoic acid in 75 g of benzene is prepared. What is the molar mass of ethanoic acid, moles of ethanoic acid, mass of benzene and molality of ethanoic acid?
(A) \(0.556 \text{ mol } kg^{-1}\)
(B) \(0.0417 \text{ mol}\)
(C) \(60 \text{ g } mol^{-1}\)
(D) \(0.075 \text{ kg}\)
Choose the correct answer from the options given below:CUET 2025 Medium - Match List-I and List-II
List-I List-II A. Phosphine I. Catches fire in air B. Chlorine water II. Smoke screen C. White phosphorus III. Crown structure D. Sulphur monoclinic and rhombic IV. Bleaching agent
Choose the correct answer from the options given below:CUET 2023 Easy - At some instant, the current in the circuit shown below is 1 A, and it is decreasing at a rate of \( 10^2 \text{ A/s} \). The value of the potential difference \( (V_P - V_Q) \) at that instant is:
CUET 2025 Easy