PYQ Vault

Day 9: CBSE Class 10 Maths

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

  1. Question 1

    Some Applications of Trigonometry. Asked 3 times: 2022*, 2023*, 2024 (* = numbers or wording changed that year)

    34
    From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are 30∘30^\circ and 45∘45^\circ respectively. Find the height of the opposite house. (Use 3=1⋅732\sqrt{3} = 1{\cdot}732)

  2. Question 2

    Some Applications of Trigonometry. Asked 3 times: 2022*, 2023*, 2024 (* = numbers or wording changed that year)

    34
    From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be 30∘30^\circ and 60∘60^\circ. If the line joining the ships passes through the foot of the light house, find the distance between the ships. (Use 3=1.73\sqrt{3} = 1.73)

  3. Question 3

    Areas Related to Circles. Asked 2 times: 2023, 2026* (* = numbers or wording changed that year)

    31
    A chord of a circle, of radius 14 cm, subtends an angle of 60∘60^\circ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

  4. Question 4

    Areas Related to Circles. Asked 2 times: 2023, 2026

    15
    The area of a semicircle of diameter ‘d’ is :

    Tap an option to check your answer.

  5. Question 5 (case study, 4 parts)

    Areas Related to Circles. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure. Based on the above information, answer the following questions :
    38 (i)
    What is the radius of circle ?
    38 (ii)
    What is the circumference of the brooch ?
    38 (iii) (a)
    What is the total length of silver wire required ?
    38 (iii) (b)
    What is the area of each sector of the brooch ?