PYQ Vault

Day 58: CBSE Class 10 Maths

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

  1. Question 1

    Quadratic Equations. This type asked 2 times: 2025, 2026. This one: 2026

    33 (b)
    The area of a right-angled triangle is 600 cm2600\,\text{cm}^2. If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

  2. Question 2

    Quadratic Equations. This type asked 2 times: 2024, 2026. This one: 2026

    29
    Find two consecutive negative integers, sum of whose squares is 481.

  3. Question 3

    Some Applications of Trigonometry. This type asked 2 times: 2025, 2026. This one: 2026

    17
    A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60∘60^\circ. If AB=53AB = 5\sqrt{3} m, then length of the wire is

    Tap an option to check your answer.

  4. Question 4

    Some Applications of Trigonometry. This type asked 2 times: 2022, 2026. This one: 2026

    35
    A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30∘30^\circ. Another boy standing on the roof of a 20 m high building, finds the angle of elevation of same kite to be 45∘45^\circ. If both the boys are on opposite sides of the kite, find the distance of the first boy from the base of the building. Also, find the height of the kite from the ground. (Use 3=1⋅73\sqrt{3} = 1{\cdot}73)

  5. Question 5 (case study, 4 parts)

    Some Applications of Trigonometry. This type asked 2 times: 2025, 2026. This one: 2026

    Tejas is standing at the top of a building and observes a car at an angle of depression of 30∘30^\circ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to 60∘60^\circ, and at that moment, the car is 25 m away from the building. Based on the information given above, answer the following questions :
    37 (i)
    What is the height of the building ?
    37 (ii)
    What is the distance between the two positions of the car ?
    37 (iii) (a)
    What would be the total time taken by the car to reach the foot of the building from the starting point ?
    37 (iii) (b)
    What is the distance of the observer from the car when it makes an angle of 60∘60^\circ ?