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Day 91: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 1 2025 (same type asked 6 times) See all 6 of this type

    28
    If cot⁡2θ−33cot⁡θ+6=0\cot^2\theta - 3\sqrt{3}\cot\theta + 6 = 0, where π6≤θ<π2\frac{\pi}{6} \le \theta < \frac{\pi}{2}, then what is a value of sin⁡θ+cos⁡2θ\sin\theta + \cos 2\theta ?

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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

    3
    If m:n=1:2m : n = 1 : 2 and p:q=3:4p : q = 3 : 4, then what is (2m+4p):(n+3q)(2m + 4p) : (n + 3q) equal to ?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 1 2023 (same type asked 6 times) See all 6 of this type

    14
    If the positive square root of (5+32)(5−32)(5 + 3\sqrt{2})(5 - 3\sqrt{2}) is α\alpha, then what is the positive square root of 8+2α8 + 2\alpha?

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  4. Question 4

    Averages. Asked once: CDS 2 2022 (same type asked 6 times) See all 6 of this type

    66
    If M is the mean of the first 100 even natural numbers, then what is the mean of the first 100 odd natural numbers ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2022 (same type asked 6 times) See all 6 of this type

    54
    If x=1+sin⁡θcos⁡θx = \frac{1 + \sin\theta}{\cos\theta}, then what is tan⁡θ+sec⁡θ−1tan⁡θ−sec⁡θ+1\frac{\tan\theta + \sec\theta - 1}{\tan\theta - \sec\theta + 1} equal to ?

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