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Day 219: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2018 (same type asked 8 times) See all 8 of this type

    61
    If cos⁡θ=15\cos \theta = \frac{1}{\sqrt{5}}, where 0<θ<π20 < \theta < \frac{\pi}{2}, then 2tan⁡θ1−tan⁡2θ\frac{2 \tan \theta}{1 - \tan^2 \theta} is equal to

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  2. Question 2

    Number System. Asked once: CDS 1 2021 (same type asked 8 times) See all 8 of this type

    2
    What is the remainder when 210000002^{1000000} is divided by 7?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 2 2016 (same type asked 7 times) See all 7 of this type

    71
    If sin⁡θ+cos⁡θ=72\sin\theta + \cos\theta = \frac{\sqrt{7}}{2}, then what is sin⁡θ−cos⁡θ\sin\theta - \cos\theta equal to ?

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  4. Question 4

    Number System. Asked once: CDS 2 2019 (same type asked 7 times) See all 7 of this type

    50
    The expression 52n−23n5^{2n} - 2^{3n} has a factor

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2016 (same type asked 6 times) See all 6 of this type

    75
    What is the value of cosec⁡268∘+sec⁡256∘−cot⁡234∘−tan⁡222∘\operatorname{cosec}^2 68^\circ + \sec^2 56^\circ - \cot^2 34^\circ - \tan^2 22^\circ ?

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