PYQ Vault

Day 30: CBSE Class 12 Maths

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

  1. Question 1

    Inverse Trigonometric Functions. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    34
    Find the domain of g(x)=cos⁡−1(x2−1)g(x) = \cos^{-1}(x^2 - 1). Hence, find the value of xx for which g(x)=π3g(x) = \dfrac{\pi}{3}. Also, write the range of cos⁡−1x\cos^{-1} x other than its principal branch.

  2. Question 2

    Inverse Trigonometric Functions. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    25 (b)
    Evaluate : sin⁡(tan⁡−1(−3)−sec⁡−12)\sin \left( \tan^{-1} \left( -\sqrt{3} \right) - \sec^{-1} 2 \right)

  3. Question 3

    Inverse Trigonometric Functions. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    3
    For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined ?

    Tap an option to check your answer.

  4. Question 4

    Linear Programming. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    35
    Solve the following Linear Programming Problem graphically : Maximise Z=12x+18yZ = 12x + 18y subject to the constraints x+y≤1200x + y \le 1200 x−2y≥0x - 2y \ge 0 x+3y≥600x + 3y \ge 600 x≥0, y≥0x \ge 0,\ y \ge 0

  5. Question 5

    Linear Programming. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    29
    Solve the following Linear Programming Problem graphically : Minimize Z=20x+10yZ = 20x + 10y subject to x+2y≤40x + 2y \leq 40 3x+y≥303x + y \geq 30 4x+3y≥604x + 3y \geq 60 x,y≥0x, y \geq 0