PYQ Vault

Day 34: CBSE Class 10 Maths

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

  1. Question 1

    Surface Areas and Volumes. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    32
    From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.

  2. Question 2

    Arithmetic Progressions. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    27 (b)
    The sum of first n terms of an A.P. is 2n2+13n2n^2 + 13n. Find its nthn^{\text{th}} term and hence 10th10^{\text{th}} term.

  3. Question 3

    Circles. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    4
    In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that ∠SQT=55∘\angle SQT = 55^\circ. The m ∠QPS\angle QPS is

    Tap an option to check your answer.

  4. Question 4 (case study, 4 parts)

    Surface Areas and Volumes. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm ×\times 12 cm ×\times 17 cm.
    37 (i)
    Find the surface area of the bulb.
    37 (ii)
    What could be the maximum diameter of the bulb if at least 1 cm space is left from each side ?
    37 (iii) (a)
    Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges.
    37 (iii) (b)
    Find the space available inside the lamp.

  5. Question 5

    Areas Related to Circles. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2025

    29
    The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.