PYQ Vault

Day 78: CBSE Class 12 Maths

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

  1. Question 1

    Determinants. Asked once: 2026 (same type asked 3 times)

    5
    For a square matrix A, (3A)−1=(3A)^{-1} =

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  2. Question 2

    Determinants. Asked once: 2024 (same type asked 3 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : For matrix A=[1cos⁡θ1−cos⁡θ1cos⁡θ−1−cos⁡θ1]A = \begin{bmatrix} 1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1 \end{bmatrix}, where θ∈[0,2π]\theta \in [0, 2\pi], ∣A∣∈[2,4]|A| \in [2, 4]. Reason (R) : cos⁡θ∈[−1,1]\cos \theta \in [-1, 1], ∀θ∈[0,2π]\forall \theta \in [0, 2\pi].

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  3. Question 3

    Differential Equations. Asked once: 2025 (same type asked 3 times)

    4
    Which of the following is not a homogeneous function of xx and yy ?

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  4. Question 4

    Differential Equations. Asked once: 2026 (same type asked 3 times)

    11
    The integrating factor of differential equation Rdxdy+Px=QR \frac{dx}{dy} + Px = Q where P, Q, R are functions of y is

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  5. Question 5

    Inverse Trigonometric Functions. Asked once: 2026 (same type asked 3 times)

    21
    Evaluate sin⁡[tan⁡−1tan⁡(3π4)]\sin\left[\tan^{-1}\tan\left(\dfrac{3\pi}{4}\right)\right].