PYQ Vault

Day 40: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    30
    If (sin⁡x)y=ycos⁡x(\sin x)^y = y^{\cos x}, then find dydx\dfrac{dy}{dx}.

  2. Question 2 (case study, 4 parts)

    Determinants. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length. On the basis of the above information, answer the following questions :
    37 (i)
    Write the equations representing the various dimensions and express them as the matrix equation AX=BAX = B.
    37 (ii)
    Find if A−1A^{-1} exists. Justify your answer.
    37 (iii) (a)
    Find A−1A^{-1}.
    37 (iii) (b)
    Find A2+7 IA^2 + 7\,I.

  3. Question 3

    Determinants. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    32 (a)
    If P=[1−10234012]P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} and Q=[22−4−42−42−15]Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{bmatrix}, find (QP) and hence solve the following system of equations using matrices : x−y=3x - y = 3, 2x+3y+4z=172x + 3y + 4z = 17, y+2z=7y + 2z = 7

  4. Question 4

    Determinants. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    5
    If A is a non-singular matrix, then which of the following is not true ?

    Tap an option to check your answer.

  5. Question 5

    Determinants. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    32 (b)
    Obtain the value of Δ=∣1+x1111+y1111+z∣\Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} in terms of xx, y and z. Further, if Δ=0\Delta = 0 and xx, y, z are non-zero real numbers, prove that x−1+y−1+z−1=−1x^{-1} + y^{-1} + z^{-1} = -1.