PYQ Vault

Day 50: CBSE Class 12 Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Application of Derivatives. This type asked 2 times: 2023, 2026. This one: 2026

    A company produces cylindrical tumblers, open from the top. Since they want uniformity in the product, they fix the surface area of the tumblers produced. Based on the above information, answer the following questions : If for a tumbler, V is its volume, h the height and r the radius of the circular base, then :
    38 (i)
    Differentiate its volume with respect to radius of the base, where the surface area is constant.
    38 (ii)
    If the company wants to maximize the volume of each tumbler, then establish a relation between its height and the radius of the base.

  2. Question 2

    Application of Derivatives. This type asked 2 times: 2023, 2026. This one: 2026

    6
    If the distance travelled by a particle in t seconds is given by S=72t+3t2−t3S = 72t + 3t^2 - t^3, then time taken by the particle to come to rest is :

    Tap an option to check your answer.

  3. Question 3 (case study, 4 parts)

    Application of Integrals. This type asked 2 times: 2023, 2026. This one: 2026

    There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are A(0,4)A(0, 4), B(−2,0)B(-2, 0) and C(3,0)C(3, 0). Based on the above information, answer the following questions :
    38 (i)
    Write the equation of the boundary line AB of the park.
    38 (ii)
    Write the equation of the boundary line AC of the park.
    38 (iii) (a)
    Using integration, find the area of region OAC, in which children are allowed to play cricket, football.
    38 (iii) (b)
    Using integration, find the area of region AOB.

  4. Question 4

    Application of Integrals. This type asked 2 times: 2025, 2026. This one: 2026

    10
    Which of the following expressions will give the area of region bounded by the curve y=x2y = x^2 and line y=16y = 16 ?

    Tap an option to check your answer.

  5. Question 5

    Determinants. This type asked 2 times: 2023, 2026. This one: 2026

    17
    If A(adj A)=[202600020260002026]A(\text{adj } A) = \begin{bmatrix} 2026 & 0 & 0 \\ 0 & 2026 & 0 \\ 0 & 0 & 2026 \end{bmatrix}, then the value of ∣adj A∣|\text{adj } A| is equal to :

    Tap an option to check your answer.