PYQ Vault

Day 47: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    11
    ∫x+5(x+6)2 ex dx\displaystyle\int \dfrac{x + 5}{(x + 6)^2}\, e^x\, dx is equal to :

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  2. Question 2

    Integrals. This type asked 3 times: 2022, 2023, 2025. This one: 2025

    12
    ∫e9log⁡x−e8log⁡xe6log⁡x−e5log⁡x dx\displaystyle\int \dfrac{e^{9\log x} - e^{8\log x}}{e^{6\log x} - e^{5\log x}}\, dx is equal to :

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  3. Question 3

    Inverse Trigonometric Functions. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : Set of values of sec⁡−1(32)\sec^{-1}\left(\dfrac{\sqrt{3}}{2}\right) is a null set. Reason (R) : sec⁡−1x\sec^{-1} x is defined for x∈R−(−1, 1)x \in R - (-1,\ 1).

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  4. Question 4

    Matrices. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    3
    What is the total number of possible matrices of order 3×33 \times 3 with each entry as 2\sqrt{2} or 3\sqrt{3} ?

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  5. Question 5

    Matrices. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    7
    If [2x−13x0y2−1]=[x+312035]\begin{bmatrix} 2x - 1 & 3x \\ 0 & y^2 - 1 \end{bmatrix} = \begin{bmatrix} x + 3 & 12 \\ 0 & 35 \end{bmatrix}, then the value of (x−y)(x - y) is :

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