PYQ Vault

Day 13: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    25
    For the curve y=5x−2x3y = 5x - 2x^3, if x increases at the rate of 2 units/s, then how fast is the slope of the curve changing when x=2x = 2 ?

  2. Question 2

    Application of Integrals. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    33
    Using integration, find the area of the ellipse x2a2+y2b2=1\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 bounded between the lines x=−a2x = -\dfrac{a}{2} to x=a2x = \dfrac{a}{2}.

  3. Question 3

    Continuity and Differentiability. Asked 2 times: 2023, 2025

    8
    If f(x)={sin⁡2axx2,if x≠01,if x=0f(x) = \begin{cases} \dfrac{\sin^2 ax}{x^2}, & \text{if } x \ne 0 \\ 1, & \text{if } x = 0 \end{cases} is continuous at x=0x = 0, then the value of 'a' is :

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  4. Question 4

    Continuity and Differentiability. Asked 2 times: 2024, 2025

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : f(x)={xsin⁡1x,x≠00,x=0f(x) = \begin{cases} x \sin \dfrac{1}{x}, & x \ne 0 \\ 0, & x = 0 \end{cases} is continuous at x=0x = 0. Reason (R) : When x→0x \to 0, sin⁡1x\sin \dfrac{1}{x} is a finite value between −1-1 and 11.

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  5. Question 5

    Continuity and Differentiability. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    5
    If f(x)=∣x∣+∣x−1∣f(x) = |x| + |x - 1|, then which of the following is correct ?

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