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Day 46: CDS Maths

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

  1. Question 1

    Mensuration 3D. This type asked 3 times: CDS 2 2016, CDS 1 2018, CDS 2 2018. This one: CDS 2 2018 See all 3 of this type

    73
    Walls (excluding roofs and floors) of 5 identical rooms having length, breadth and height 6 m, 4 m and 2.5 m respectively are to be painted. Out of five rooms, two rooms have one square window each having a side of 2.5 m. Paints are available only in cans of 1 litre; and 1 litre of paint can be used for painting 20 square metres. The number of cans required for painting is

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  2. Question 2

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

    24
    The remainder when 3x3−2x2y−13xy2+10y33x^3 - 2x^2y - 13xy^2 + 10y^3 is divided by (x−2y)(x - 2y) is equal to

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  3. Question 3

    Statistics. Asked 2 times: CDS 2 2020*, CDS 2 2026 (* = numbers or wording changed that year) See all 2 times it was asked

    95
    If the heights (in cm) of 9 students of a class are 150, 165, 145, 149, 150, 147, 152, 144 and 148, then what is the algebraic sum of the heights measured from their arithmetic mean ?

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  4. Question 4

    Trigonometric Ratios and Identities. Asked 2 times: CDS 2 2018*, CDS 2 2026 (* = numbers or wording changed that year) See all 2 times it was asked

    41
    If cot⁡θ+cos⁡θ=m\cot\theta + \cos\theta = m, cot⁡θ−cos⁡θ=n\cot\theta - \cos\theta = n, where 0<θ<π20 < \theta < \frac{\pi}{2}, then what is m2−n2mn\frac{m^2 - n^2}{\sqrt{mn}} equal to ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked 2 times: CDS 2 2022*, CDS 2 2026 (* = numbers or wording changed that year) See all 2 times it was asked

    42
    If 1cosec⁡θ+cot⁡θ−1sin⁡θ=p\frac{1}{\operatorname{cosec}\theta + \cot\theta} - \frac{1}{\sin\theta} = p, then what is 1sin⁡θ−1cosec⁡θ−cot⁡θ\frac{1}{\sin\theta} - \frac{1}{\operatorname{cosec}\theta - \cot\theta} equal to ?

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