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Day 321: CDS Maths

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

  1. Question 1

    Mensuration 3D. Asked once: CDS 1 2019

    69
    A right circular cone has height 8 cm. If the radius of its base is 6 cm, then what is its total surface area ?

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  2. Question 2

    Number System. Asked once: CDS 1 2022

    22
    Let p=22n+2+mp = 2^{2n+2} + m and q=24n−mq = 2^{4n} - m (where nn is even natural number). What should be the least value of mm such that pp as well as qq is divisible by 5?

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  3. Question 3

    Quadratic Equations. Asked once: CDS 2 2016

    2
    If λ\lambda is an integer and α\alpha, β\beta are the roots of 4x2−16x+λ4=04x^2 - 16x + \frac{\lambda}{4} = 0 such that 1<α<21 < \alpha < 2 and 2<β<32 < \beta < 3, then how many values can λ\lambda take ?

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  4. Question 4

    Triangles. Asked once: CDS 2 2020

    85
    AD is the median of the triangle ABC. If P is any point on AD, then which one of the following is correct ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2021

    48
    What is sin⁡3θ+cos⁡3θsin⁡θ+cos⁡θ+sin⁡3θ−cos⁡3θsin⁡θ−cos⁡θ\dfrac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}+\dfrac{\sin^3\theta-\cos^3\theta}{\sin\theta-\cos\theta} equal to ?

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