PYQ Vault

Day 18: CBSE Class 10 Maths

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

  1. Question 1 (case study, 4 parts)

    Some Applications of Trigonometry. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is 30∘30^\circ and the angle of elevation of the top of section ‘A’ is 60∘60^\circ. Based on the above information, answer the following questions :
    37 (i)
    Find the length of the wire from the point ‘O’ to the top of section ‘B’.
    37 (ii)
    Find the length of the wire from the point ‘O’ to the top of section ‘A’.
    37 (iii) (a)
    Find the distance AB.
    37 (iii) (b)
    Find the area of ΔOPB\Delta OPB.

  2. Question 2

    Some Applications of Trigonometry. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    9
    The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle of 30∘30^\circ with the ground. The height of the kite above the ground is :

    Tap an option to check your answer.

  3. Question 3

    Statistics. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    34
    The monthly expenditure on fruits in 200 families of a Housing Society is given below. Find the value of xx and also find the mode and mean expenditure on fruits.
    Monthly Expenditure (in ₹)No. of Families
    1000-150024
    1500-200040
    2000-250033
    2500-300028
    3000-3500xx
    3500-400022
    4000-450016
    4500-50007

  4. Question 4

    Surface Areas and Volumes. Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm2160\,\text{cm}^2. Reason (R) : The surface area of a cuboid of dimensions l×b×hl \times b \times h is (lb+bh+hl)(lb + bh + hl).

    Tap an option to check your answer.

  5. Question 5

    Surface Areas and Volumes. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    16
    The total surface area of a solid hemisphere of diameter ‘2d2d’ is :

    Tap an option to check your answer.