CUET · MATHS · PYQ PAPER 2025
Let A be a non-singular square matrix of order 3 and |adj A| = 5 then |A| is equal to
- A \(\pm \sqrt{5}\)
- B 5
- C 25
- D 125
Answer & Solution
Correct Answer
(A) \(\pm \sqrt{5}\)
Step-by-step Solution
Detailed explanation
\( |adj A| = |A|^{n-1} \) \( 5 = |A|^{3-1} \) \( 5 = |A|^2 \) \( |A| = \pm \sqrt{5} \)
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 maximum value of the determinant of the matrix \(\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin x & 1 \\ 1+\cos x & 1 & 1\end{array}\right]\)
(where \(x\) is real) is :CUET 2025 Hard - The matrix \(X\) in the equation \(A X=B\), such that \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) is given byCUET 2025 Medium
- Match List-l with List-ll
Choose the correct answer from the options given below :List-I List-II (A) Integrating factor of \(x d y-\left(y+x^2\right) d x=0\) (I) \(x^2\) (B) Integrating factor of \(x d y+\left(2 y+x^2\right) d x=0\) (II) \(x^3\) (C) Integrating factor of \(\left(3 y-x^2\right) d x+x d y=0\) (III) \(x\) (D) Integrating factor of \(\left(y+3 x^2\right) d x+x d y=0\) (IV) \(\frac{1}{x}\) CUET 2025 Medium - Let A be a square matrix of order n, then which of the following are TRUE?
(A) \(|\operatorname{adj} A|=|A|^{n-1}\)
(B) \(|A \cdot \operatorname{adj} A|=|A|^n\)
(C) A. (adj A) = |A|
(D) |KA| = K|A|
(E) \(\left|A^{-1}\right|=\frac{1}{|A|},|A| \neq 0\)
Choose the correct answert from the option given below :CUET 2025 Medium - The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:CUET 2025 Medium
- The random variable X can take only the values 0, 1, 2. Given that \(P(X = 0) = P(X = 1) = p\) and \(E(X^2) = E(X) + 1\), then the value of p is:CUET 2023 Medium
More PYQs from CUET
- The angle between \(x\) axis and the vector \(\hat{i}+\hat{j}+\hat{k}\) is :CUET 2023 Medium
- If charge is moving parallel to uniform magnetic field, its path will be:CUET 2023 Easy
- Answer the question on the basis of passage given below :
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under laboratory conditions, but microbes do it easily. Ammonia forms a large number of complexes with transition metals. Hybridisation easily explains the ease of sigma donation capability of NH₃ and PH₃. Phosphine is an inflammable gas, and it is prepared from white phosphorus.
Which of the following is the correct statement?CUET 2023 Hard - A parallel plate capacitor with plates of area A, held a distance d apart, has a capacitance C. A thin silver foil of negligible thickness and the same area is inserted at mid-point between the plates. The capacitance becomesCUET 2025 Medium
- Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to :CUET 2024 Easy
- Who proposed the concept 'saltation' in evolution?CUET 2023 Easy