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Day 115: CDS Maths

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

  1. Question 1

    Triangles. Asked once: CDS 1 2018 (same type asked 3 times) See all 3 of this type

    65
    ABC is a triangle right angled at C with BC = a and AC = b. If p is the length of the perpendicular from C on AB, then which one of the following is correct ?

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  2. Question 2 (case study, 2 parts)

    Trigonometric Ratios and Identities. Asked once: CDS 2 2025 (same type asked 3 times) See all 3 of this type

    Let cosec θ−sin⁡θ=p\mathrm{cosec}\,\theta - \sin\theta = p and sec⁡θ−cos⁡θ=q\sec\theta - \cos\theta = q.
    43
    What is (psin⁡θ+qcos⁡θ)(p\sin\theta + q\cos\theta) equal to?

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    44
    What is p2q2(p2+q2+3)p^2q^2(p^2 + q^2 + 3) equal to?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    60
    If cos⁡θcosec⁡θ+1+cos⁡θcosec⁡θ−1=2\dfrac{\cos\theta}{\operatorname{cosec}\theta + 1} + \dfrac{\cos\theta}{\operatorname{cosec}\theta - 1} = 2 where 0<θ<90∘0 < \theta < 90^\circ, then what is the value of sin⁡4θ+cos⁡4θ\sin^4\theta + \cos^4\theta?

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  4. Question 4

    Algebraic Identities and Simplification. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    26
    If a+b=2,1a+1b=2a + b = 2,\quad \frac{1}{a} + \frac{1}{b} = 2 then what is the value of a3+b3a^3 + b^3 ?

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  5. Question 5

    Circles. Asked once: CDS 1 2025 (same type asked 3 times) See all 3 of this type

    12
    C is the centre of a circle of radius 20 cm. AB is a chord of length 32 cm. E is a point on AB such that CE = 13 cm. What is AE×EBAE \times EB equal to ?

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