PYQ Vault

Day 88: CBSE Class 10 Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 2025 (same type asked 2 times)

    32 (a)
    There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.

  2. Question 2

    Quadratic Equations. Asked once: 2024 (same type asked 2 times)

    28
    Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three integers.

  3. Question 3

    Some Applications of Trigonometry. Asked once: 2025 (same type asked 2 times)

    10
    A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of 60∘60^\circ with the ground, the height of the pole is :

    Tap an option to check your answer.

  4. Question 4

    Some Applications of Trigonometry. Asked once: 2026 (same type asked 2 times)

    34
    A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30∘30^\circ. From the bottom of the same building, the angle of elevation of kite is 45∘45^\circ. Find the length of the string and height of roof from the ground. (Use 3=1.73\sqrt{3} = 1.73)

  5. Question 5 (case study, 4 parts)

    Some Applications of Trigonometry. Asked once: 2025 (same type asked 2 times)

    A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be 30∘30^\circ at a particular instant. Based on above information, answer the following questions :
    38 (i)
    Represent the above situation with the help of a diagram.
    38 (ii)
    Find the distance between the ambulance and the site of accident (P) at the particular instant. (Use 3=1.73\sqrt{3} = 1.73)
    38 (iii) (a)
    Find the time (in seconds) in which the angle of depression changes from 30∘30^\circ to 45∘45^\circ.
    38 (iii) (b)
    How long (in seconds) will the ambulance take to reach point P from a point T on the highway such that angle of depression of the ambulance at T is 60∘60^\circ from the drone ?