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Day 37: CDS Maths

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

  1. Question 1

    Quadratic Equations. This type asked 3 times: CDS 2 2017, CDS 1 2019, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    80
    The equations x2+px+q=0x^2 + px + q = 0 and x2+qx+p=0x^2 + qx + p = 0 (p≠q)(p \ne q) have a common root. What is the value of (p+q)(p + q) ?

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  2. Question 2

    Ratio, Proportion and Variation. This type asked 3 times: CDS 1 2018, CDS 1 2021, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    10
    A mixture of 100 L contains kerosene and turpentine oil in the ratio 3 : 2. What is the minimum quantity of kerosene in litres (whole number) that should be mixed in the mixture so that the resulting mixture has 20% of kerosene ?

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  3. Question 3

    Triangles. This type asked 3 times: CDS 1 2017, CDS 2 2018, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    18
    The measure of an angle formed by the bisectors of the angles A and C of the triangle ABC is 130∘130^\circ. What is the measure of the angle B ?

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  4. Question 4

    Algebraic Identities and Simplification. This type asked 3 times: CDS 2 2019, CDS 1 2024, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    33
    What is the minimum value of (a8+a4+1)(b8+b4+1)a4b4\dfrac{(a^8 + a^4 + 1)(b^8 + b^4 + 1)}{a^4 b^4}, where a>0a > 0, b>0b > 0 ?

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  5. Question 5

    Number System. This type asked 3 times: CDS 1 2019, CDS 2 2019, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    96
    The number 199 can be written as m2−n2m^2 - n^2, where mm, nn are natural numbers (m>n)(m > n). What is the value of mnmn ?

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