PYQ Vault

Day 37: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    6
    If a line makes angles of 3π4,π3\dfrac{3\pi}{4}, \dfrac{\pi}{3} and θ\theta with the positive directions of xx, y and z-axis respectively, then θ\theta is

    Tap an option to check your answer.

  2. Question 2

    Application of Derivatives. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    9
    Absolute minimum value of f(x)=(x−2)2+5f(x) = (x - 2)^2 + 5 in the interval [−3, 2][-3,\ 2] is :

    Tap an option to check your answer.

  3. Question 3

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    32 (a)
    Find the sub-interval of (0,π2)\left(0, \dfrac{\pi}{2}\right) in which f(x)=log⁡(sin⁡x+cos⁡x)f(x) = \log (\sin x + \cos x) is increasing and decreasing.

  4. Question 4

    Application of Derivatives. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    23
    Determine the interval(s) in which f(x)=x3+3xf(x) = \dfrac{x}{3} + \dfrac{3}{x}, x≠0x \ne 0 is increasing.

  5. Question 5

    Application of Derivatives. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    33 (a)
    Find the sub intervals in which f(x)=cot⁡−1(sin⁡x+cos⁡x)f(x) = \cot^{-1}(\sin x + \cos x), x∈(0,π)x \in (0, \pi) is increasing and decreasing.