PYQ Vault

Day 27: CBSE Class 10 Maths

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

  1. Question 1

    Statistics. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    2
    The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four observations is 18, then the fourth observation is :

    Tap an option to check your answer.

  2. Question 2

    Statistics. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    35
    Find the missing frequency ‘f’ in the following table, if the mean of the given data is 18. Hence find the mode.
    Daily AllowanceNumber of Children
    11 – 137
    13 – 156
    15 – 179
    17 – 1913
    19 – 21f
    21 – 235
    23 – 254

  3. Question 3

    Surface Areas and Volumes. Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)

    32
    A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. Also, find the surface area of the toy. (Take π=3⋅14\pi = 3{\cdot}14)

  4. Question 4

    Surface Areas and Volumes. Asked 2 times: 2023, 2025

    30
    A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains 140821 m3\dfrac{1408}{21}\,\text{m}^3 of air, find the height of the cylindrical part. (Use π=227\pi = \dfrac{22}{7}).

  5. Question 5

    Triangles. Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)

    33 (b)
    In ΔABC\Delta ABC, if AD⊥BCAD \perp BC and AD2=BD×DCAD^2 = BD \times DC, then prove that ∠BAC=90∘\angle BAC = 90^\circ.