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Day 180: CDS Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    76
    If 2ycos⁡θ=xsin⁡θ2y\cos\theta = x\sin\theta and 2xsec⁡θ−ycosec⁡θ=32x\sec\theta - y\operatorname{cosec}\theta = 3, then what is x2+4y2x^2 + 4y^2 equal to ?

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  2. Question 2

    Trigonometric Ratios and Identities. Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    81
    If tan⁡2x+1tan⁡2x=2\tan^2 x + \frac{1}{\tan^2 x} = 2 and 0∘<x<90∘0^\circ < x < 90^\circ, then what is the value of xx ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    42
    If a square of side xx and an equilateral triangle of side yy are inscribed in a circle, then what is the ratio of xx to yy ?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    43
    The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm2616\ \text{cm}^2, what is the volume of the cylinder ?

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  5. Question 5

    Time and Work. Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    17
    AA can do 50% more work than BB in the same time. BB alone can do a piece of work in 30 hours. BB starts working and had already worked for 12 hours when AA joins him. How many hours should BB and AA work together to complete the remaining work ?

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