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Day 51: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked 2 times: CDS 1 2020, CDS 1 2024 See all 2 times it was asked

    52
    If sin⁡θ−cos⁡θ+1sin⁡θ+cos⁡θ−1=psec⁡θ+qtan⁡θ\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = p\sec\theta + q\tan\theta, where 0<θ<π20 < \theta < \frac{\pi}{2}, then what is p+qp + q equal to ?

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  2. Question 2

    Percentage, Profit and Loss. Asked 2 times: CDS 1 2018*, CDS 2 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    79
    A person bought an article and sold it at a profit of 20%. Had he bought it at 20% less, what would have been the profit percentage if the selling price had been the same ?

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  3. Question 3

    Number System. Asked 2 times: CDS 1 2018*, CDS 1 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    2
    What is the largest power of 10 that divides the product 29×28×27×…2×129 \times 28 \times 27 \times \ldots 2 \times 1?

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  4. Question 4

    Polynomials. Asked 2 times: CDS 2 2020, CDS 1 2023 See all 2 times it was asked

    43
    Consider the following statements in respect of the polynomial 1−x−xn+xn+11 - x - x^n + x^{n+1}, where nn is a natural number : 1. It is divisible by 1−2x+x21 - 2x + x^2. 2. It is divisible by 1−xn1 - x^n. Which of the statements given above is/are correct ?

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  5. Question 5

    Ratio, Proportion and Variation. Asked 2 times: CDS 2 2016*, CDS 1 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    6
    A, B, C, D and E enter into a business. They invest money in the ratio 2 : 3 : 4 : 5 : 6. However, the time invested by them is in the ratio 6 : 5 : 4 : 3 : 2. If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit?

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