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Day 96: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Circles. Asked once: CDS 2 2023 (same type asked 5 times) See all 5 of this type

    Two parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart.
    35
    What is the diameter of the circle ?

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    36
    If the chord AB subtends an angle α\alpha and chord CD subtends an angle β\beta at the centre O, then what is the value of tan⁡(β2)−tan⁡(α2)\tan\left(\frac{\beta}{2}\right) - \tan\left(\frac{\alpha}{2}\right) ?

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  2. Question 2

    Heights and Distances. Asked once: CDS 2 2024 (same type asked 5 times) See all 5 of this type

    18
    From a point XX on a bridge across a river, the angles of depression of two points PP and QQ on the banks on opposite side of the river are α\alpha and β\beta respectively. If the point XX is at a height hh above the surface of the river, what is the width of the river if α\alpha and β\beta are complementary ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 1 2022 (same type asked 5 times) See all 5 of this type

    70
    A tall cylindrical container with circular base of radius 18 cm contains a good quantity of water. Metal balls each of radius 0.9 cm are immersed in it. How many balls are required to raise the water level by 3 cm?

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  4. Question 4

    Number System. Asked once: CDS 1 2022 (same type asked 5 times) See all 5 of this type

    21
    275+31327^5 + 3^{13} is divisible by

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  5. Question 5

    Number System. Asked once: CDS 1 2022 (same type asked 5 times) See all 5 of this type

    34
    Consider the following statements : 1. The sum of the cubes of three consecutive natural numbers is divisible by 9. 2. Every even power of every odd number (>1> 1) when divided by 8 gives 1 as remainder. Which of the above statements is/are correct?

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