PYQ Vault

Day 87: CBSE Class 12 Maths

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

  1. Question 1

    Probability. Asked once: 2023 (same type asked 3 times)

    35 (a)
    In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 35\dfrac{3}{5} be the probability that he knows the answer and 25\dfrac{2}{5} be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 13\dfrac{1}{3}. What is the probability that the student knows the answer, given that he answered it correctly ?

  2. Question 2 (case study, 2 parts)

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

    A store has been selling calculators at ₹ 350 each. A market survey indicates that a reduction in price (p) of calculator increases the number of units (xx) sold. The relation between the price and quantity sold is given by the demand function p=450−12xp = 450 - \dfrac{1}{2}x. Based on the above information, answer the following questions :
    36 (i)
    Determine the number of units (xx) that should be sold to maximise the revenue R(x)=x p(x)R(x) = x\,p(x). Also, verify the result.
    36 (ii)
    What rebate in price of calculator should the store give to maximise the revenue ?

  3. Question 3 (case study, 4 parts)

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

    Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The piston moves inside the cylinder bore The cylinder bore in the form of circular cylinder open at the top is to be made from a metal sheet of area 75π75\pi cm2^2. Based on the above information, answer the following questions :
    36 (i)
    If the radius of cylinder is r cm and height is h cm, then write the volume V of cylinder in terms of radius r.
    36 (ii)
    Find dVdr\frac{dV}{dr}.
    36 (iii)(a)
    Find the radius of cylinder when its volume is maximum.
    36 (iii)(b)
    For maximum volume, h > r. State true or false and justify.

  4. Question 4

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

    24
    Find the point on the curve y2=8xy^2 = 8x for which the abscissa and ordinate change at the same rate.

  5. Question 5

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

    34
    Find the area of the region bounded by the lines y = 4x + 5, x + y = 5 and 4y = x + 5, using integration.