PYQ Vault

Day 153: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    27
    If y=(tan⁡−1x)2\mathrm{y} = (\tan^{-1}x)^2, show that (x2+1)2d2ydx2+2x(x2+1)dydx=2(x^2 + 1)^2\dfrac{\mathrm{d}^2\mathrm{y}}{\mathrm{d}x^2} + 2x(x^2 + 1)\dfrac{\mathrm{d}\mathrm{y}}{\mathrm{d}x} = 2.

  2. Question 2

    Determinants. Asked once: 2024 (same type asked 3 times)

    3
    If A is a square matrix of order 3 such that the value of ∣adj⋅A∣=8\left|\mathrm{adj}{\cdot}\mathrm{A}\right| = 8, then the value of ∣AT∣\left|\mathrm{A}^{\mathrm{T}}\right| is :

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  3. Question 3

    Determinants. Asked once: 2025 (same type asked 3 times)

    6
    If A is a square matrix of order 3 such that det(A) = 9, then det⁡(9 A−1)\det(9\,A^{-1}) is equal to

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  4. Question 4

    Differential Equations. Asked once: 2022 (same type asked 3 times)

    2
    Find the general solution of the differential equation : log⁡(dydx)=ax+by\log \left( \dfrac{dy}{dx} \right) = ax + by.

  5. Question 5

    Integrals. Asked once: 2024 (same type asked 3 times)

    12
    If f(x) is an odd function, then ∫−π2π2f(x)cos⁡3x  dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} f(x) \cos^3 x \; dx equals :

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