PYQ Vault

Day 45: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    2
    The function f(x)=x2−4x+6f(x) = x^2 - 4x + 6 is increasing in the interval

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  2. Question 2

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    22
    Find the values of 'a' for which f(x)=x2−2ax+bf(x) = x^2 - 2ax + b is an increasing function for x>0x > 0.

  3. Question 3

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

    33
    A woman discovered a scratch along a straight line on a circular table top of radius 8 cm. She divided the table top into 4 equal quadrants and discovered the scratch passing through the origin inclined at an angle π4\dfrac{\pi}{4} anticlockwise along the positive direction of x-axis. Find the area of the region enclosed by the x-axis, the scratch and the circular table top in the first quadrant, using integration.

  4. Question 4

    Application of Integrals. This type asked 3 times: 2022, 2024, 2025. This one: 2025

    32
    Sketch a graph of y=x2y = x^2. Using integration, find the area of the region bounded by y=9y = 9, x=0x = 0 and y=x2y = x^2.

  5. Question 5

    Continuity and Differentiability. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    9
    If f(x)={[x], x∈R}f(x) = \{[x],\ x \in R\} is the greatest integer function, then the correct statement is :

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