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Day 90: CDS Maths

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

  1. Question 1

    Quadratic Equations. Asked once: CDS 2 2024 (same type asked 6 times) See all 6 of this type

    20
    If pp and qq are the roots of the equation x2−sin⁡2θ x−cos⁡2θ=0x^2 - \sin^2\theta\,x - \cos^2\theta = 0, then what is the minimum value of p2+q2p^2 + q^2 ?

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  2. Question 2

    Time and Work. Asked once: CDS 2 2020 (same type asked 6 times) See all 6 of this type

    18
    If xx men working xx hours per day can do xx units of work in xx days, then yy men working yy hours per day in yy days would be able to do kk units of work. What is the value of kk ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 2 2023 (same type asked 6 times) See all 6 of this type

    55
    Two equal arcs of different circles C1C_1 and C2C_2 subtend angles of 60∘60^\circ and 75∘75^\circ respectively, at the centres. What is the ratio of the radius of C1C_1 to the radius of C2C_2 ?

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  4. Question 4

    Mensuration 2D. Asked once: CDS 1 2022 (same type asked 6 times) See all 6 of this type

    76
    The diagonal of a square is 12212\sqrt{2} cm and the area of an equilateral triangle is 64364\sqrt{3} square cm. Which of the following statements is/are correct? 1. The square and the triangle have the same perimeter. 2. Four times the area of the square is equal to 333\sqrt{3} times the area of the triangle. Select the correct answer using the code given below.

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  5. Question 5 (case study, 2 parts)

    Triangles. Asked once: CDS 1 2025 (same type asked 6 times) See all 6 of this type

    ABC is a triangle right-angled at A. Further, AB = 8 cm, BC = 10 cm. D is the point on BC such that AD is perpendicular to BC.
    65
    What is AD equal to ?

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    66
    What is ratio of area of triangle ADC to area of triangle ADB ?

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