PYQ Vault

Day 129: CBSE Class 10 Maths

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

  1. Question 1

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

    8
    Which of the following is a quadratic polynomial with zeroes 53\dfrac{5}{3} and 0 ?

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  2. Question 2

    Polynomials. Asked once: 2025 (same type asked 3 times)

    10
    Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is :

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  3. Question 3 (case study, 4 parts)

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

    In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by h=20t−16t2h = 20t - 16t^2. Based on the above, answer the following questions :
    38 (i)
    Find zeroes of polynomial p(t)=20t−16t2p(t) = 20t - 16t^2.
    38 (ii)
    Which of the following types of graph represents p(t)p(t) ? (a) Graph (a) as printed - a downward-opening curve starting at O that rises and comes back to the time axis at 5/4; see the attached figure. (b) Graph (b) as printed - a downward-opening curve starting at O whose highest point is above 5/4 (dashed line), meeting the time axis beyond 5/4; see the attached figure. (c) Graph (c) as printed - an upward-opening curve through O and 5/4 that dips below the time axis between them; see the attached figure. (d) Graph (d) as printed - a downward-opening curve that starts below the time axis and touches it at 5/4; see the attached figure.
    38 (iii) (a)
    What would be the value of h at t=32t = \dfrac{3}{2} ? Interpret the result.
    38 (iii) (b)
    How much distance has the dolphin covered before hitting the water level again ?

  4. Question 4

    Polynomials. Asked once: 2025 (same type asked 3 times)

    21 (b)
    If α\alpha and β\beta are zeroes of the polynomial p(x)=x2−2x−1p(x) = x^2 - 2x - 1, then find the value of 12α+12β+3αβ\dfrac{1}{2\alpha} + \dfrac{1}{2\beta} + 3\alpha\beta.

  5. Question 5

    Probability. Asked once: 2025 (same type asked 3 times)

    24
    From a pack of 52 cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find the probability that the card so drawn is (i) a face card. (ii) a card of red colour.