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Day 315: CDS Maths

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

  1. Question 1

    Number System. Asked once: CDS 1 2023

    17
    It is given that 5 does not divide n−1n - 1, n and n+1n + 1, where n is a positive integer. Which one of the following is correct?

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  2. Question 2

    Quadratic Equations. Asked once: CDS 1 2018

    15
    If α\alpha and β\beta are the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0, then what is the value of the expression (α+1)(β+1)(\alpha + 1)(\beta + 1)?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 1 2017

    43
    What is the value of 4121253\sqrt[3]{4\frac{12}{125}} ?

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  4. Question 4

    Triangles. Asked once: CDS 1 2022

    79
    In a triangle ABCABC, AB=ACAB = AC and BCBC is produced to DD such that ∠ACD=x\angle ACD = x, then what is ∠BAC\angle BAC equal to?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2022

    56
    If sin⁡θ+cos⁡θsin⁡θ−cos⁡θ=5\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 5, where 0<θ<π20 < \theta < \frac{\pi}{2}, θ≠π4\theta \ne \frac{\pi}{4}, then what is the value of 2sin⁡θ+3cos⁡θ3sin⁡θ−2cos⁡θ\frac{2\sin\theta + 3\cos\theta}{3\sin\theta - 2\cos\theta} ?

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