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Day 68: CDS Maths

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

  1. Question 1

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

    36
    The difference between the two acute angles in a right-angled triangle is π12\dfrac{\pi}{12} radian. One of the acute angles of the triangle is

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  2. Question 2

    Algebraic Identities and Simplification. This type asked 2 times: CDS 2 2023, CDS 1 2025. This one: CDS 1 2025 See all 2 of this type

    75
    If 2s=a+b+c2s = a + b + c, then what is s (s−a) (s−b) (s−c)[1s−a+1s−b+1s−c−1s]s\,(s - a)\,(s - b)\,(s - c)\left[\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} - \frac{1}{s}\right] equal to ?

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  3. Question 3

    Algebraic Identities and Simplification. This type asked 2 times: CDS 2 2023, CDS 1 2025. This one: CDS 1 2025 See all 2 of this type

    40
    If x, y, z are real numbers such that x+y+z=10x + y + z = 10 and xy+yz+zx=18xy + yz + zx = 18, then what is the value of x3+y3+z3−3xyzx^3 + y^3 + z^3 - 3xyz ?

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  4. Question 4 (case study, 2 parts)

    Mensuration 2D. This type asked 2 times: CDS 1 2021, CDS 1 2025. This one: CDS 1 2025 See all 2 of this type

    Consider the following for the next two (02) items that follow : ABC is a triangle right-angled at B. The perimeter of the triangle is 24 cm and the difference between the sum of the perpendicular sides and the hypotenuse is 4 cm.
    53
    What is the area of the triangle ABC ?

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    54
    A circle is inscribed in the triangle. What is its radius ?

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  5. Question 5 (case study, 2 parts)

    Mensuration 3D. This type asked 2 times: CDS 2 2022, CDS 1 2025. This one: CDS 1 2025 See all 2 of this type

    The sides of an open box are 0.5 cm thick and bottom is 1 cm thick. The internal length, breadth and depth are respectively 14 cm, 10 cm and 8 cm. It is completely filled with water.
    63
    If the material weighs 2000 kg per cubic metre, then what is the weight of the material used in the construction of the box ?

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    64
    If water weighs 1000 kg per cubic metre, then what is the weight of the box with water ?

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