PYQ Vault

Day 120: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    22
    Find the values of 'a' for which f(x)=3sin⁡x−cos⁡x−2ax+bf(x) = \sqrt{3} \sin x - \cos x - 2ax + b is decreasing on R\mathbb{R}.

  2. Question 2

    Application of Integrals. Asked once: 2022 (same type asked 3 times)

    12
    Using integration, find the area of the region bounded by the curves x2+y2=4x^2 + y^2 = 4, x=3 yx = \sqrt{3}\, y and xx-axis lying in the first quadrant.

  3. Question 3

    Application of Integrals. Asked once: 2025 (same type asked 3 times)

    33
    Use integration to find the area of the region enclosed by curve y=−x2y = -x^2 and the straight lines x=−3x = -3, x=2x = 2 and y=0y = 0. Sketch a rough figure to illustrate the bounded region.

  4. Question 4

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    4
    The number of points of discontinuity of f(x)={∣x∣+3,if x≤−3−2x,if −3<x<36x+2,if x≥3f(x) = \begin{cases} |x| + 3, & \text{if } x \le -3 \\ -2x, & \text{if } -3 < x < 3 \\ 6x + 2, & \text{if } x \ge 3 \end{cases} is :

    Tap an option to check your answer.

  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    28 (a)
    If y=(log⁡x)2y = (\log x)^2, prove that x2y′′+xy′=2x^2 y'' + x y' = 2.