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Day 152: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2022 (same type asked 8 times) See all 8 of this type

    51
    If tan⁡θ=q2−p2p\tan\theta = \dfrac{\sqrt{q^2 - p^2}}{p}; 0<θ<90∘0 < \theta < 90^\circ, then what is sec⁡θ+cos⁡θ+2\sec\theta + \cos\theta + 2 equal to ?

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  2. Question 2

    Number System. Asked once: CDS 2 2024 (same type asked 8 times) See all 8 of this type

    73
    What is the remainder if we divide 3103^{10} by 7 ?

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  3. Question 3

    Averages. Asked once: CDS 2 2020 (same type asked 7 times) See all 7 of this type

    96
    The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 kg and that of girls is 40 kg. The number of boys exceeds the number of girls by

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  4. Question 4

    Polynomials. Asked once: CDS 2 2017 (same type asked 7 times) See all 7 of this type

    8
    The product of two non-zero expressions is (x+y+z)p3(x + y + z) p^3. If their HCF is p2p^2, then their LCM is

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  5. Question 5 (case study, 2 parts)

    Trigonometric Ratios and Identities. Asked once: CDS 2 2025 (same type asked 7 times) See all 7 of this type

    Let sin⁡θ+cos⁡θ=p\sin\theta + \cos\theta = p and sec⁡θ+cosec θ=q\sec\theta + \mathrm{cosec}\,\theta = q, where p≠1p \ne 1.
    49
    What is the relation between pp and qq?

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    50
    What is tan⁡θ+cot⁡θ\tan\theta + \cot\theta equal to?

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