PYQ Vault

Day 120: CBSE Class 10 Maths

5 questions (11 parts). Try each one first, then open its answer.

  1. Question 1

    Circles. Asked once: 2025 (same type asked 5 times)

    7
    In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠NML=30∘\angle NML = 30^\circ, then ∠RLM\angle RLM is :

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  2. Question 2 (case study, 4 parts)

    Surface Areas and Volumes. Asked once: 2025 (same type asked 5 times)

    A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood – two small ones on the ends and one larger in the centre to create a perfect tool. The baker loved the rolling pin, as it rolled out the smoothest dough for breads and pastries. The length of the bigger cylindrical part is 12 cm and diameter is 7 cm and the length of each smaller cylindrical part is 5 cm and diameter is 2⋅12{\cdot}1 cm. Based on the above information, answer the following questions :
    38 (i)
    Find the volume of the bigger cylindrical part.
    38 (ii)
    Find the curved surface area of the bigger cylindrical part.
    38 (iii) (a)
    Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.
    38 (iii) (b)
    Find the sum of the curved surface areas of the two identical smaller cylindrical parts.

  3. Question 3

    Areas Related to Circles. Asked once: 2023 (same type asked 4 times)

    2
    What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90∘90^\circ ?

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  4. Question 4

    Areas Related to Circles. Asked once: 2025 (same type asked 4 times)

    29
    A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding minor segment. [Use π=3⋅14\pi = 3{\cdot}14]

  5. Question 5 (case study, 4 parts)

    Arithmetic Progressions. Asked once: 2025 (same type asked 4 times)

    Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are installed at equal intervals on the way to provide support to the cables on which car moves. The distance of first pole from base point is 200 m and subsequent poles are installed at equal interval of 150 m. Further, the distance of last pole from the top is 300 m. Based on above information, answer the following questions using Arithmetic Progression :
    37 (i)
    Find the distance of 10th10^{\text{th}} pole from the base.
    37 (ii)
    Find the distance between 15th15^{\text{th}} pole and 25th25^{\text{th}} pole.
    37 (iii) (a)
    Find the time taken by cable car to reach 15th15^{\text{th}} pole from the top if it is moving at the speed of 5m/sec and coming from top.
    37 (iii) (b)
    Find the total number of poles installed along the entire journey.