PYQ Vault

Day 33: CBSE Class 10 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Surface Areas and Volumes. Asked 2 times: 2023*, 2024 (* = numbers or wording changed that year)

    35
    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5⋅85{\cdot}8 cm and its base is of radius 2⋅12{\cdot}1 cm, find the total surface area of the article.

  2. Question 2

    Circles. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    33 (a)
    A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area ΔABC=90 cm2\Delta ABC = 90\,\text{cm}^2.

  3. Question 3

    Some Applications of Trigonometry. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    35 (a)
    The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60∘60^\circ and the angle of elevation of the top of the second tower from the foot of the first tower is 30∘30^\circ. Find the distance between the two towers and also the height of the other tower.

  4. Question 4

    Some Applications of Trigonometry. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    35
    An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60∘60^\circ and 45∘45^\circ respectively. Find the vertical distance between the aeroplanes at that instant. Also, find the distance of first plane from the point of observation. (Take 3=1.73\sqrt{3} = 1.73)

  5. Question 5

    Statistics. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    32
    The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’.
    Class Interval0 – 1515 – 3030 – 4545 – 6060 – 7575 – 90Total
    Frequency67a1510b51