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Day 63: CDS Maths

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

  1. Question 1

    Quadrilaterals. This type asked 2 times: CDS 2 2025, CDS 2 2026. This one: CDS 2 2026 See all 2 of this type

    78
    ABCD is a parallelogram with ∠ABC=150∘\angle ABC = 150^\circ and the sides have integer values. If the area of the parallelogram is 17.5 cm2\text{cm}^2, then consider the following statements : I. It is possible to have a perimeter equal to 24 cm. II. It is possible to have a perimeter equal to 72 cm. Which of the statements given above is/are correct ?

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  2. Question 2

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

    39
    If sin⁡4x+cos⁡4x=1\sin^4 x + \cos^4 x = 1, where 0≤x≤π20 \le x \le \frac{\pi}{2}, then what is sin⁡x⋅cos⁡x\sin x \cdot \cos x equal to ?

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  3. Question 3

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

    40
    If 3cos⁡θ+4sin⁡θ=43\cos\theta + 4\sin\theta = 4, where 0≤θ<π20 \le \theta < \frac{\pi}{2}, then what is 4cos⁡θ+3sin⁡θ4\cos\theta + 3\sin\theta equal to ?

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  4. Question 4

    Algebraic Identities and Simplification. This type asked 2 times: CDS 2 2019, CDS 1 2026. This one: CDS 1 2026 See all 2 of this type

    3
    If a2b2+c2=b2c2+a2=c2a2+b2\frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a4+b4+c4a^4 + b^4 + c^4 equal to ?

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  5. Question 5

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

    52
    Let O be the centre of a circle. Let A, B and C lie on the circle such that ∠ABC=153∘\angle ABC = 153^\circ. What is the value of ∠AOC\angle AOC ?

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