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Day 116: CDS Maths

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

  1. Question 1

    Mensuration 3D. Asked once: CDS 1 2019 (same type asked 3 times) See all 3 of this type

    53
    A right circular cylinder has a diameter of 20 cm and its curved surface area is 1000 cm2\text{cm}^2. What is the volume of the cylinder ?

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  2. Question 2

    Mensuration 3D. Asked once: CDS 2 2024 (same type asked 3 times) See all 3 of this type

    87
    A cone, a hemisphere and a cylinder stand on equal base of radius rr and have the same height. If the sum of volumes of cone, the hemisphere and the cylinder is equal to volume of a sphere of radius RR, then what is R3r3\frac{R^3}{r^3} equal to ?

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  3. Question 3 (case study, 2 parts)

    Quadratic Equations. Asked once: CDS 2 2023 (same type asked 3 times) See all 3 of this type

    A quadratic equation is given by (a+b+c)x2−(2a+2b)x+(a+b−c)=0(a + b + c)x^2 - (2a + 2b)x + (a + b - c) = 0; where a, b and c are real and distinct.
    49
    What are the roots of the equation ?

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    50
    Consider the following statements : 1. One of the roots of the equation is always less than 1 if a, b and c are all positive. 2. One of the roots of the equation is always negative if a, b and c are all negative. Which of the statements given above is/are correct ?

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  4. Question 4

    Statistics. Asked once: CDS 2 2025 (same type asked 3 times) See all 3 of this type

    91
    Which measure of central tendency is least affected by the presence of extreme observations in the data?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2022 (same type asked 3 times) See all 3 of this type

    60
    What is (1+sin⁡θcos⁡θ)2+(cos⁡θ1+sin⁡θ)2−2\sqrt{\left(\frac{1 + \sin\theta}{\cos\theta}\right)^2 + \left(\frac{\cos\theta}{1 + \sin\theta}\right)^2 - 2} equal to, where 0<θ<π20 < \theta < \frac{\pi}{2} ?

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