PYQ Vault

Day 26: CBSE Class 10 Maths

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

  1. Question 1

    Some Applications of Trigonometry. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    35 (a)
    The angle of elevation of an airborne helicopter from a point A on the ground is 45∘45^\circ. After a flight of 15 seconds, the angle of elevation of the helicopter changes to 30∘30^\circ. If the helicopter is flying at a constant height of 2000 m, find the speed of the helicopter. (Take 3=1⋅732\sqrt{3} = 1{\cdot}732)

  2. Question 2

    Some Applications of Trigonometry. Asked 2 times: 2024, 2025

    32 (b)
    The angles of depression of the top and the bottom of an 8 m tall building from the top of another multistoried building are 30∘30^\circ and 45∘45^\circ, respectively. Find the height of the multistoried building and the distance between the two buildings.

  3. Question 3

    Statistics. Asked 2 times: 2024, 2025

    35
    The following table shows the number of patients of different age group who were discharged from the hospital in a particular month :
    Age (in years)Number of Patients Discharged
    5-156
    15-2511
    25-3521
    35-4523
    45-5514
    55-655
    Total80
    Find the ‘mean’ and the ‘mode’ of the above data.

  4. Question 4

    Statistics. Asked 2 times: 2024, 2025

    15
    If the mean of 2,9,x+6,2x+3,5,10,52, 9, x + 6, 2x + 3, 5, 10, 5 is 7, then the value of x is :

    Tap an option to check your answer.

  5. Question 5 (case study, 4 parts)

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

    The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
    Rainfall (mm)No. of Sub-divisions
    200 – 4003
    400 – 6004
    600 – 8007
    800 – 10004
    1000 – 12003
    1200 – 14003
    Based on the information given above, answer the following questions :
    38 (i)
    Write the modal class.
    38 (ii) (a)
    Find the median of the given data.
    38 (ii) (b)
    Find the mean rainfall in the season.
    38 (iii)
    If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall ?