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Day 165: CDS Maths

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

  1. Question 1

    Surds, Indices and Simplification. Asked once: CDS 1 2023 (same type asked 4 times) See all 4 of this type

    39
    If x=3+13−1x = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} and y=3−13+1y = \frac{\sqrt{3} - 1}{\sqrt{3} + 1}, then what is the value x3−y3x^3 - y^3 ?

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  2. Question 2

    Triangles. Asked once: CDS 2 2025 (same type asked 4 times) See all 4 of this type

    63
    ABCABC is a triangle right angled at BB. PP is the midpoint of ABAB and QQ is the midpoint of BCBC. Consider the following : I. AQ=73AQ = \sqrt{73} units II. CP=52CP = \sqrt{52} units Which of the above is/are required to determine the area of the triangle?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 2 2021 (same type asked 4 times) See all 4 of this type

    56
    If x=msec⁡A+ntan⁡Ax=m\sec A+n\tan A and y=mtan⁡A+nsec⁡Ay=m\tan A+n\sec A, then what is x2−y2x^2-y^2 equal to ?

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  4. Question 4

    Algebraic Identities and Simplification. Asked once: CDS 1 2021 (same type asked 4 times) See all 4 of this type

    17
    What is 8x1−x4−4xx2+1+x+1x−1−x−1x+1\frac{8x}{1 - x^4} - \frac{4x}{x^2 + 1} + \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} equal to?

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  5. Question 5

    Mensuration 2D. Asked once: CDS 1 2022 (same type asked 4 times) See all 4 of this type

    74
    ABCDABCD is a parallelogram with AB=15AB = 15 cm and AD=8AD = 8 cm. If θ\theta is the acute angle between ABAB and ADAD, then what is the area of the parallelogram in square cm?

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