PYQ Vault

Day 3: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    25 (a)
    Let two rods placed on the ground be represented by vectors 4i^−j^+3k^4\hat{i} - \hat{j} + 3\hat{k} and −2i^+j^−2k^-2\hat{i} + \hat{j} - 2\hat{k}. Find a vector representing a flag-post of height 5 m that has to be erected perpendicular to both the rods.

  2. Question 2

    Vector Algebra. Asked 3 times: 2024*, 2025, 2026* (* = numbers or wording changed that year)

    13
    If ∣a⃗∣=5|\vec{a}| = 5 and −2≤λ≤1-2 \leq \lambda \leq 1, then the sum of greatest and the smallest value of ∣λa⃗∣|\lambda \vec{a}| is

    Tap an option to check your answer.

  3. Question 3

    Differential Equations. Asked 3 times: 2023, 2024, 2025* (* = numbers or wording changed that year)

    16
    The order and degree of the differential equation (d2ydx2)2+(dydx)2=xsin⁡(dydx)\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x \sin\left(\frac{dy}{dx}\right) are :

    Tap an option to check your answer.

  4. Question 4

    Integrals. Asked 3 times: 2022*, 2024*, 2025 (* = numbers or wording changed that year)

    27 (a)
    Find : ∫2x(x2+3)(x2−5) dx\displaystyle\int \dfrac{2x}{(x^2 + 3)(x^2 - 5)}\ dx

  5. Question 5

    Linear Programming. Asked 3 times: 2023*, 2024*, 2025 (* = numbers or wording changed that year)

    29
    In the Linear Programming Problem (LPP), find the point/points giving maximum value for Z=5x+10yZ = 5x + 10y subject to constraints x+2y≤120x + 2y \le 120 x+y≥60x + y \ge 60 x−2y≥0x - 2y \ge 0 x, y≥0x,\ y \ge 0