CUET · MATHS · PYQ PAPER 2023

If the matrix \(A = \begin{bmatrix} 1 & -1 & 2 \\ 3 & 1 & -2 \\ 1 & 0 & 3 \end{bmatrix}\), the value of \(|\text{adj } A|\) is:

A 134
B 144
C 12
D 121

Verified Solution

Answer & Solution

Correct Answer

(B) 144

Step-by-step Solution

Detailed explanation

\(|A| = 1(3 - 0) - (-1)(9 - (-2)) + 2(0 - 1)\) \(|A| = 3 + 1(11) + 2(-1)\) \(|A| = 3 + 11 - 2 = 12\) \(|\text{adj } A| = |A|^{n-1}\) \(|\text{adj } A| = |A|^{3-1} = |A|^2\) \(|\text{adj } A| = (12)^2 = 144\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II (where \(c\) is an arbitrary constant)

List-I (Definite integral)	List-II (Value)
(A) \(\int_1^e \frac{\log x}{x} d x\)	(I) 4
(B) \(\int_{-2}^2 x^3\left(1-x^2\right) d x\)	(II) \(\frac{1}{2}\)
(C) \(\int_1^2 x d x\)	(III) \(0\)
(D) \(\int_{-2}^2\|x\| d x\)	(IV) \(\frac{3}{2}\)

Choose the correct answer from the options given below :

CUET 2025 Hard

Match List-I with List-II

Llst-I	Llst-(II)
(A) \(f(x)=[x]\)	(I) Continuous everywhere but not differentiable at \(x=-1\)
(B) \(f(x)=\|x-1\|\)	(II) Continuous everywhere except at all integral values
(C) \(f(x)=e^{\|x\|}\)	(III) Continuous everywhere but not differentiable at \(x=1\)
(D) \(f(x)=\|x+1\|\)	(IV) Continuous everywhere but not differentiable at \(x=0\)

Choose the correct answer from the options given below:

CUET 2025 Easy

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