PYQ Vault

Day 189: CBSE Class 12 Maths

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

  1. Question 1 (case study, 4 parts)

    Application of Derivatives. Asked once: 2023 (same type asked 4 times)

    In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should have a square base and a capacity of 250 m3\text{m}^3. The cost of land is ₹ 5,000 per square metre and cost of digging increases with depth and for the whole tank, it is ₹ 40,000 h2h^2, where h is the depth of the tank in metres. x is the side of the square base of the tank in metres.
    37 (i)
    Find the total cost C of digging the tank in terms of x.
    37 (ii)
    Find dCdx\frac{dC}{dx}.
    37 (iii) (a)
    Find the value of x for which cost C is minimum.
    37 (iii) (b)
    Check whether the cost function C(x) expressed in terms of x is increasing or not, where x > 0.

  2. Question 2

    Application of Derivatives. Asked once: 2023 (same type asked 4 times)

    21
    Find the interval in which the function f(x)=2x3−3xf(x) = 2x^3 - 3x is strictly increasing.

  3. Question 3

    Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)

    7
    For what value of k, the function given below is continuous at x=0x = 0 ? f(x)={4+x−2x,x≠0k,x=0f(x) = \begin{cases} \dfrac{\sqrt{4+x} - 2}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}

    Tap an option to check your answer.

  4. Question 4

    Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)

    7
    The value of constant c that makes the function f defined by f(x)={x2−c2,if x<4cx+20,if x≥4f(x) = \begin{cases} x^2 - c^2, & \text{if } x < 4 \\ cx + 20, & \text{if } x \geq 4 \end{cases} continuous for all real numbers is :

    Tap an option to check your answer.

  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)

    24 (b)
    Show that the function f(x)=∣x∣3f(x) = |x|^3 is differentiable at all points of its domain.