PYQ Vault

Day 96: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2025 (same type asked 2 times)

    35 (a)
    Show that the area of a parallelogram whose diagonals are represented by a⃗\vec{a} and b⃗\vec{b} is given by 12∣a⃗×b⃗∣\frac{1}{2}|\vec{a} \times \vec{b}|. Also find the area of a parallelogram whose diagonals are 2i^−j^+k^2\hat{i} - \hat{j} + \hat{k} and i^+3j^−k^\hat{i} + 3\hat{j} - \hat{k}.

  2. Question 2

    Vector Algebra. Asked once: 2025 (same type asked 2 times)

    30 (a)
    If a⃗+b⃗+c⃗=0⃗\vec{a} + \vec{b} + \vec{c} = \vec{0} such that ∣a⃗∣=3|\vec{a}| = 3, ∣b⃗∣=5|\vec{b}| = 5, ∣c⃗∣=7|\vec{c}| = 7, then find the angle between a⃗\vec{a} and b⃗\vec{b}.

  3. Question 3

    Continuity and Differentiability. Asked once: 2023 (same type asked 2 times)

    25 (b)
    If f(x)={ax+b;0<x≤12x2−x;1<x<2f(x) = \begin{cases} ax + b & ; \quad 0 < x \le 1 \\ 2x^2 - x & ; \quad 1 < x < 2 \end{cases} is a differentiable function in (0, 2), then find the values of a and b.

  4. Question 4

    Determinants. Asked once: 2024 (same type asked 2 times)

    32 (a)
    If A=[12−320−3120]\mathrm{A} = \begin{bmatrix} 1 & 2 & -3 \\ 2 & 0 & -3 \\ 1 & 2 & 0 \end{bmatrix}, then find A−1\mathrm{A}^{-1} and hence solve the following system of equations : x+2y−3z=1x + 2\mathrm{y} - 3\mathrm{z} = 1 2x−3z=22x - 3\mathrm{z} = 2 x+2y=3x + 2\mathrm{y} = 3

  5. Question 5

    Differential Equations. Asked once: 2023 (same type asked 2 times)

    13
    The number of solutions of the differential equation dydx=y+1x−1\dfrac{dy}{dx} = \dfrac{y + 1}{x - 1}, when y(1)=2y(1) = 2, is :

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