PYQ Vault

Day 93: CBSE Class 12 Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    32 (b)
    Sum of two numbers is 5. If the sum of the cubes of these numbers is least, then find the sum of the squares of these numbers.

  2. Question 2

    Application of Derivatives. Asked once: 2024 (same type asked 2 times)

    33 (b)
    The perimeter of a rectangular metallic sheet is 300 cm. It is rolled along one of its sides to form a cylinder. Find the dimensions of the rectangular sheet so that volume of cylinder so formed is maximum.

  3. Question 3 (case study, 2 parts)

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    Sooraj's father wants to construct a rectangular garden using a brick wall on one side of the garden and wire fencing for the other three sides as shown in the figure. He has 200 metres of fencing wire. Based on the above information, answer the following questions :
    38 (i)
    Let 'x' metres denote the length of the side of the garden perpendicular to the brick wall and 'y' metres denote the length of the side parallel to the brick wall. Determine the relation representing the total length of fencing wire and also write A(x), the area of the garden.
    38 (ii)
    Determine the maximum value of A(x).

  4. Question 4 (case study, 2 parts)

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    The use of electric vehicles will curb air pollution in the long run. The use of electric vehicles is increasing every year and estimated electric vehicles in use at any time t is given by the function V : V(t)=15t3−52t2+25t−2V(t) = \frac{1}{5}t^3 - \frac{5}{2}t^2 + 25t - 2 where t represents the time and t = 1, 2, 3.... corresponds to year 2001, 2002, 2003, ....... respectively. Based on the above information, answer the following questions :
    38 (i)
    Can the above function be used to estimate number of vehicles in the year 2000 ? Justify.
    38 (ii)
    Prove that the function V(t) is an increasing function.

  5. Question 5

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    23
    If equal sides of an isosceles triangle with fixed base 10 cm are increasing at the rate of 4 cm/sec, how fast is the area of triangle increasing at an instant when all sides become equal ?