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Day 32: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. This type asked 3 times: CDS 1 2021, CDS 1 2025, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    50
    If p=sec⁡θ+tan⁡θp = \sec\theta + \tan\theta and q=cosec⁡θ−cot⁡θq = \operatorname{cosec}\theta - \cot\theta, then what is (p−q−pq)(p - q - pq) equal to ?

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  2. Question 2

    Inequalities. This type asked 3 times: CDS 1 2022, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    76
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is rnr^n less than 1, where r is a real number and n is a natural number ? Statement-I : 0<r2<10 < r^2 < 1 Statement-II : 0<r3<20 < r^3 < 2 Which one of the following is correct in respect of the above Question and the Statements ?

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  3. Question 3

    Linear Equations. This type asked 3 times: CDS 1 2017, CDS 2 2021, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    10
    For what integral value of k, the system of equations kx−5y+6=0kx - 5y + 6 = 0 and 4(k−1)y−12x+3=04(k - 1)y - 12x + 3 = 0 has no solution ?

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  4. Question 4

    Mensuration 3D. This type asked 3 times: CDS 1 2021, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    61
    The diameter of a copper solid sphere is 6 cm. The sphere is melted and recast into a wire. If the diameter of the wire is 0.5 cm, then what is the length of the wire ?

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  5. Question 5

    Number System. This type asked 3 times: CDS 1 2023, CDS 1 2024, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    26
    What is the greatest possible speed at which a person can walk 13.3 km and 20.9 km so that the time (in hours) required in each case is a whole number ?

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