PYQ Vault

Day 90: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 2026 (same type asked 2 times)

    5
    If sin⁡−1x+π=y\sin^{-1} x + \pi = y, then

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  2. Question 2

    Inverse Trigonometric Functions. Asked once: 2024 (same type asked 2 times)

    21
    Find value of k if sin⁡−1[ktan⁡(2cos⁡−132)]=π3\sin^{-1}\left[\mathrm{k}\tan\left(2\cos^{-1}\dfrac{\sqrt{3}}{2}\right)\right] = \dfrac{\pi}{3}.

  3. Question 3

    Matrices. Asked once: 2026 (same type asked 2 times)

    15
    If A=[12cos⁡x−sin⁡xsin⁡x12cos⁡x]A = \begin{bmatrix} \dfrac{1}{2}\cos x & -\sin x \\ \sin x & \dfrac{1}{2}\cos x \end{bmatrix} and A+A′=IA + A' = I, then value of x∈[−π2,π2]x \in \left[\dfrac{-\pi}{2}, \dfrac{\pi}{2}\right] is

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  4. Question 4

    Matrices. Asked once: 2026 (same type asked 2 times)

    5
    If a square matrix A is such that A2=AA^2 = A and (I−A)3=xA+I(I - A)^3 = xA + I, then value of x must be :

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  5. Question 5

    Matrices. Asked once: 2026 (same type asked 2 times)

    2
    A matrix B=[bij]m×mB = [b_{ij}]_{m \times m} is said to be a diagonal matrix, if :

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