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Day 310: CDS Maths

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

  1. Question 1

    Mensuration 3D. Asked once: CDS 1 2020

    74
    The thickness of a cylinder is 1 foot, the inner radius of the cylinder is 3 feet and height is 7 feet. To paint the inner surface it requires one litre of a particular colour. How much quantity of the same colour is required to paint all the surfaces of the cylinder ?

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  2. Question 2

    Number System. Asked once: CDS 1 2024

    19
    When the number (12345678910111213 ... 99100) is divided by 16, what will be the remainder ?

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  3. Question 3

    Quadratic Equations. Asked once: CDS 2 2018

    9
    If α\alpha and β\beta are two real numbers such that α+β=−qp\alpha + \beta = -\frac{q}{p} and αβ=rp\alpha\beta = \frac{r}{p}, where 1<p<q<r1 < p < q < r, then which one of the following is the greatest ?

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  4. Question 4

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

    19
    If 9x 3y=21879^x \, 3^y = 2187 and 23x 22y−4xy=02^{3x} \, 2^{2y} - 4^{xy} = 0, then what can be the value of (x+y)(x + y) ?

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  5. Question 5

    Triangles. Asked once: CDS 2 2022

    68
    In a triangle ABC, ∠A=2θ\angle A = 2\theta, ∠B=∠C=4θ\angle B = \angle C = 4\theta and θ\theta satisfies 4sin⁡2θ+2sin⁡θ−1=04\sin^2\theta + 2\sin\theta - 1 = 0. What is the ratio of BC to AB ?

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