PYQ Vault

Day 24: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    30 (b)
    Three vectors a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} satisfy the condition a⃗+b⃗+c⃗=0⃗\vec{a} + \vec{b} + \vec{c} = \vec{0}. Evaluate the quantity μ=a⃗⋅b⃗+b⃗⋅c⃗+c⃗⋅a⃗\mu = \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}, if ∣a⃗∣=3|\vec{a}| = 3, ∣b⃗∣=4|\vec{b}| = 4 and ∣c⃗∣=2|\vec{c}| = 2.

  2. Question 2

    Application of Integrals. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    12
    An ant is observed crawling on a sheet of paper along a straight line given by equation y=2x−4y = 2x - 4. Area of the surface covered by the ant bounded by y-axis, x-axis and x=1x = 1 is :

    Tap an option to check your answer.

  3. Question 3

    Differential Equations. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    34 (b)
    Find the general solution of the differential equation (x3−3xy2)dx=(y3−3x2y)dy\left(x^3 - 3xy^2\right) dx = \left(y^3 - 3x^2 y\right) dy.

  4. Question 4

    Differential Equations. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    27 (b)
    Find the particular solution of the differential equation dydx−3ycot⁡x=sin⁡2x\dfrac{dy}{dx} - 3y \cot x = \sin 2x, given that y=2y = 2 when x=π2x = \dfrac{\pi}{2}.

  5. Question 5

    Differential Equations. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    12
    The sum of the order and the degree of the differential equation y=xdydx+3[2−(dydx)2]y = x\dfrac{dy}{dx} + 3\left[2 - \left(\dfrac{dy}{dx}\right)^2\right] is :

    Tap an option to check your answer.