PYQ Vault

Day 1: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    22 (b)
    If y=Pcos⁡ux+Qsin⁡uxy = P \cos ux + Q \sin ux, show that d2ydx2+u2y=0\dfrac{d^2y}{dx^2} + u^2 y = 0.

  2. Question 2

    Determinants. Asked 4 times: 2023*, 2024, 2025, 2026 (* = numbers or wording changed that year)

    33 (a)
    If A=[021−2−1−21−10]A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix}, find A−1A^{-1} and use it to solve the following system of equations : −2y+z=7-2y + z = 7, 2x−y−z=82x - y - z = 8, x−2y=10x - 2y = 10

  3. Question 3

    Three Dimensional Geometry. Asked 4 times: 2022*, 2023*, 2025*, 2026 (* = numbers or wording changed that year)

    35
    Check whether the lines given by x−12=y−23=z−34\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} and x−45=y−12=z\frac{x - 4}{5} = \frac{y - 1}{2} = z are parallel or not. If parallel, find the distance between them, otherwise find their point of intersection, if the lines are intersecting.

  4. Question 4

    Application of Integrals. Asked 3 times: 2024, 2025, 2026

    33
    Using integration, find the area of the region bounded by the curve y=x∣x∣y = x|x|, x-axis, x=−2x = -2 and x=2x = 2.

  5. Question 5

    Differential Equations. Asked 3 times: 2023, 2024, 2026* (* = numbers or wording changed that year)

    4
    The general solution of the differential equation x dy−y dx=0x\,dy - y\,dx = 0 is

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