PYQ Vault

Day 115: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 4 parts)

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

    Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹ 160. From the same shop, Vikram buys 2 pens, 1 bag and 3 instrument boxes and pays a sum of ₹ 190. Also Ankur buys 1 pen, 2 bags and 4 instrument boxes and pays a sum of ₹ 250. Based on the above information, answer the following questions :
    37 (i)
    Convert the given above situation into a matrix equation of the form AX = B.
    37 (ii)
    Find ∣A∣|A|.
    37 (iii) (a)
    Find A−1A^{-1}.
    37 (iii) (b)
    Determine P=A2−5AP = A^2 - 5A.

  2. Question 2

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

    32 (b)
    Find the product of the matrices [12−32323−3−4]\begin{bmatrix} 1 & 2 & -3 \\ 2 & 3 & 2 \\ 3 & -3 & -4 \end{bmatrix} and [−61713145−8−159−1]\begin{bmatrix} -6 & 17 & 13 \\ 14 & 5 & -8 \\ -15 & 9 & -1 \end{bmatrix} and hence solve the system of linear equations : x+2y−3z=−4x + 2\mathrm{y} - 3\mathrm{z} = -4 2x+3y+2z=22x + 3\mathrm{y} + 2\mathrm{z} = 2 3x−3y−4z=113x - 3\mathrm{y} - 4\mathrm{z} = 11

  3. Question 3

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

    15
    If A and B are invertible matrices, then which of the following is not correct ?

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  4. Question 4

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

    26
    Show that the determinant ∣xsin⁡θcos⁡θ−sin⁡θ−x1cos⁡θ1x∣\begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix} is independent of θ\theta.

  5. Question 5

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

    7
    The differential equation dydx=F(x,y)\dfrac{dy}{dx} = F(x, y) will not be a homogeneous differential equation, if F(x, y) is :

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