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Day 34: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Quadrilaterals. This type asked 3 times: CDS 1 2017, CDS 2 2018, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    74
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : P, Q, R and S are respectively the mid-points of sides AB, BC, CD, DA of a rhombus ABCD. These points are joined to form a quadrilateral PQRS. Is the quadrilateral cyclic ? Statement-I : ∠ABC=120∘\angle ABC = 120^\circ Statement-II : ∠BCD=60∘\angle BCD = 60^\circ Which one of the following is correct in respect of the above Question and the Statements ?

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  2. Question 2 (case study, 2 parts)

    Simple and Compound Interest. This type asked 3 times: CDS 1 2019, CDS 1 2022, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    For the next two (02) items that follow : A person borrows a sum of Rs. 16,000 on simple interest at the beginning of a year. After 4 months, Rs. 24,000 more is borrowed at a rate of interest double the previous one. At the end of the year, the total interest on both the loans is Rs. 4800.
    89
    What is the initial rate of interest per annum ?

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    90
    What is the ratio of the interest on the first loan to the interest on the second loan ?

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  3. Question 3

    Triangles. This type asked 3 times: CDS 2 2017, CDS 1 2018, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    49
    ABC is a triangle right-angled at B with sides BC=aBC = a, CA=bCA = b and AB=cAB = c. Let p be the length of the perpendicular from B to AC. Which of the following statements is/are correct ? I. p=aca2+c2p = \frac{ac}{\sqrt{a^2 + c^2}} II. pb=acpb = ac Select the answer using the code given below :

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  4. Question 4 (case study, 2 parts)

    Trigonometric Ratios and Identities. This type asked 3 times: CDS 2 2020, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    For the next two (02) items that follow : cosec⁡θ−sin⁡θ=p3\operatorname{cosec}\theta - \sin\theta = p^3 and sec⁡θ−cos⁡θ=q3\sec\theta - \cos\theta = q^3
    93
    What is tan⁡θ\tan\theta equal to ?

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    94
    What is p4q2+p2q4p^4q^2 + p^2q^4 equal to ?

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  5. Question 5

    Trigonometric Ratios and Identities. This type asked 3 times: CDS 2 2018, CDS 1 2022, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    41
    If cos⁡θ1−sin⁡θ+cos⁡θ1+sin⁡θ=4\frac{\cos\theta}{1 - \sin\theta} + \frac{\cos\theta}{1 + \sin\theta} = 4, then which one of the following is a value of (tan⁡2θ+cot⁡2θ)(\tan^2\theta + \cot^2\theta) ?

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