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Day 155: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2023 (same type asked 6 times) See all 6 of this type

    26
    What is the value of sin⁡θ+cos⁡θ\sin\theta + \cos\theta, if θ\theta satisfies the equation cot⁡2θ−(3+1)cot⁡θ+3=0\cot^2\theta - (\sqrt{3} + 1)\cot\theta + \sqrt{3} = 0; 0<θ<π40 < \theta < \dfrac{\pi}{4} ?

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  2. Question 2

    Ratio, Proportion and Variation. Asked once: CDS 1 2024 (same type asked 6 times) See all 6 of this type

    1
    If a:b:c:d=4:3:2:1a : b : c : d = \sqrt{4} : \sqrt{3} : \sqrt{2} : \sqrt{1}, then what is the value of (−a2+b2+c2+d2)(a2−b2+c2−d2)\frac{(-a^2 + b^2 + c^2 + d^2)}{(a^2 - b^2 + c^2 - d^2)} ?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 2 2016 (same type asked 6 times) See all 6 of this type

    3
    What is 62+72+82+92+1027+43−4+23\frac{6^2 + 7^2 + 8^2 + 9^2 + 10^2}{\sqrt{7 + 4\sqrt{3}} - \sqrt{4 + 2\sqrt{3}}} equal to ?

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  4. Question 4

    Averages. Asked once: CDS 2 2020 (same type asked 6 times) See all 6 of this type

    98
    The mean of five observations xx, x+2x + 2, x+4x + 4, x+6x + 6, x+8x + 8 is mm. What is the mean of the first three observations ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022 (same type asked 6 times) See all 6 of this type

    46
    If x=1−cos⁡θ+sin⁡θ1+sin⁡θx = \frac{1 - \cos\theta + \sin\theta}{1 + \sin\theta} then what is sin⁡θ+cos⁡θ−1cos⁡θ\frac{\sin\theta + \cos\theta - 1}{\cos\theta} equal to?

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