PYQ Vault

Day 231: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked once: 2023 (same type asked 3 times)

    27 (b)
    If y=tan⁡x+sec⁡xy = \tan x + \sec x, then prove that d2ydx2=cos⁡x(1−sin⁡x)2\dfrac{d^2y}{dx^2} = \dfrac{\cos x}{(1 - \sin x)^2}.

  2. Question 2

    Determinants. Asked once: 2023 (same type asked 3 times)

    4
    If ∣A∣=∣kA∣|A| = |kA|, where A is a square matrix of order 2, then sum of all possible values of k is

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  3. Question 3

    Integrals. Asked once: 2023 (same type asked 3 times)

    4
    If ∫02πcos⁡2x dx=k∫0π/2cos⁡2x dx\int\limits_{0}^{2\pi} \cos^2 x \, dx = k \int\limits_{0}^{\pi/2} \cos^2 x \, dx, then the value of k is

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  4. Question 4

    Integrals. Asked once: 2023 (same type asked 3 times)

    16
    ∫e−x(x+1x2) dx\int e^{-x} \left( \frac{x+1}{x^2} \right) \, dx is equal to :

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  5. Question 5

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

    3 (a)
    If ddx[F(x)]=sec⁡4xcosec⁡4x\frac{d}{dx}[F(x)] = \frac{\sec^4 x}{\operatorname{cosec}^4 x} and F(π4)=π4F\left(\frac{\pi}{4}\right) = \frac{\pi}{4}, then find F(x)F(x).