PYQ Vault

Day 35: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. This type asked 4 times: 2022, 2023, 2025, 2026. This one: 2026

    21
    A vector a⃗\vec{a} of magnitude 14 has direction ratios <2,3,−6><2, 3, -6>. Find the projection of the vector a⃗\vec{a} on i^\hat{i}.
  2. Question 2

    Vector Algebra. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    14
    For any two vectors a⃗\vec{a} and b⃗\vec{b}, which of the following statements is always true ?

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  3. Question 3

    Application of Integrals. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    17
    The area of the region bounded by the curve y2=xy^2 = x between x=0x = 0 and x=1x = 1 is :

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  4. Question 4

    Differential Equations. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    28
    Find the particular solution of the differential equation dydx−yx+cosec⁡(yx)=0\dfrac{dy}{dx} - \dfrac{y}{x} + \operatorname{cosec}\left(\dfrac{y}{x}\right) = 0; given that y=0y = 0, when x=1x = 1.
  5. Question 5

    Integrals. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    12
    ∫012x5x2+1 dx\displaystyle\int_{0}^{1} \dfrac{2x}{5x^2 + 1}\ dx is equal to :

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