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Let A = …, where 0 ≤ θ ≤ 2π. Then which of the following are true? (A) |A| = 2 + 2 sin^2 θ (B) |A| = 2 + sin^2 θ (C) minimum value of |A| is 1 (D)…

CUET UG 2025 — Mathematics Algebra

2025mcqhard

Let A=[1sin⁡θ1−sin⁡θ1sin⁡θ−1−sin⁡θ1]A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}A=​1−sinθ−1​sinθ1−sinθ​1sinθ1​​, where 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π. Then which of the following are true?

(A) ∣A∣=2+2sin⁡2θ|A| = 2 + 2 \sin^{2} \theta∣A∣=2+2sin2θ

(B) ∣A∣=2+sin⁡2θ|A| = 2 + \sin^{2} \theta∣A∣=2+sin2θ

(C) minimum value of ∣A∣|A|∣A∣ is 111

(D) maximum value of ∣A∣|A|∣A∣ is 444

Choose the correct answer from the options given below:

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A) and (D) only

  2. B

    (A), (B) and (C) only

  3. C

    (B), (C) and (D) only

  4. D

    (C) and (D) only

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