PYQ Vault

Day 196: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2023 (same type asked 4 times)

    10
    Projection of vector 2i^+3j^2\hat{i} + 3\hat{j} on the vector 3i^−2j^3\hat{i} - 2\hat{j} is

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  2. Question 2

    Vector Algebra. Asked once: 2024 (same type asked 4 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : For any non-zero unit vector a⃗\vec{a}, a⃗⋅(−a⃗)=(−a⃗)⋅a⃗=−1\vec{a} \cdot (-\vec{a}) = (-\vec{a}) \cdot \vec{a} = -1. Reason (R) : Angle between a⃗\vec{a} and (−a⃗)(-\vec{a}) is π2\dfrac{\pi}{2}.

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  3. Question 3

    Application of Integrals. Asked once: 2023 (same type asked 4 times)

    33
    Using integration, find the area of the region bounded by the parabola y2=4axy^2 = 4ax and its latus rectum.

  4. Question 4

    Differential Equations. Asked once: 2022 (same type asked 4 times)

    10
    Find the particular solution of the differential equation xdydx+xcos⁡2(yx)=yx\frac{dy}{dx} + x\cos^2\left(\frac{y}{x}\right) = y; given that when x=1x = 1, y=π4y = \frac{\pi}{4}.

  5. Question 5

    Integrals. Asked once: 2024 (same type asked 4 times)

    27 (a)
    Evaluate : ∫−222−x2+x dx\displaystyle\int_{-2}^{2} \sqrt{\dfrac{2 - x}{2 + x}}\, dx