PYQ Vault

Day 83: CBSE Class 10 Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 2024 (same type asked 3 times)

    31
    In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the digits is 36. Find the number.

  2. Question 2 (case study, 4 parts)

    Some Applications of Trigonometry. Asked once: 2025 (same type asked 3 times)

    The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is 80380\sqrt{3} m away from the base of the Statue is found to be 60∘60^\circ. Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be 30∘30^\circ and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :
    38 (i)
    Represent the Situation – I with the help of a diagram.
    38 (ii)
    Represent the Situation – II with the help of a diagram.
    38 (iii) (a)
    Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation – I.
    38 (iii) (b)
    Find the horizontal distance of point B (Situation – II) from the Statue and the value of tan⁡α\tan\alpha, where α\alpha is the angle of elevation of top of base of the Statue from point B.

  3. Question 3

    Surface Areas and Volumes. Asked once: 2023 (same type asked 3 times)

    34
    A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.

  4. Question 4

    Surface Areas and Volumes. Asked once: 2023 (same type asked 3 times)

    9
    Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes ?

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  5. Question 5

    Arithmetic Progressions. Asked once: 2024 (same type asked 3 times)

    11
    The number of terms in the A.P. 3,6,9,12,…,1113, 6, 9, 12, \ldots, 111 is :

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