PYQ Vault

Day 148: 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)

    26 (a)
    If x=ecos⁡3tx = e^{\cos 3t} and y=esin⁡3ty = e^{\sin 3t}, prove that dydx=−ylog⁡xxlog⁡y\dfrac{dy}{dx} = -\dfrac{y \log x}{x \log y}.

  2. Question 2

    Continuity and Differentiability. Asked once: 2025 (same type asked 3 times)

    32 (b)
    If x=a(cos⁡θ+log⁡tan⁡θ2)x = a\left(\cos\theta + \log\tan\frac{\theta}{2}\right) and y=sin⁡θy = \sin\theta, then find d2ydx2\frac{d^2y}{dx^2} at θ=π4\theta = \frac{\pi}{4}.

  3. Question 3

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

    34
    Use the product of matrices [12−332−22−11][012−77−7−75−4]\begin{bmatrix} 1 & 2 & -3 \\ 3 & 2 & -2 \\ 2 & -1 & 1 \end{bmatrix}\begin{bmatrix} 0 & 1 & 2 \\ -7 & 7 & -7 \\ -7 & 5 & -4 \end{bmatrix} to solve the following system of equations : x+2y−3z=6x + 2y - 3z = 6 3x+2y−2z=33x + 2y - 2z = 3 2x−y+z=22x - y + z = 2

  4. Question 4

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

    3
    Let A=[abcd]A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} be a square matrix such that adj A = A. Then, (a+b+c+d)(a + b + c + d) is equal to :

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  5. Question 5

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

    16
    The integrating factor of the differential equation dydx+ytan⁡x−sec⁡x=0\frac{dy}{dx} + y \tan x - \sec x = 0 is :

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