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Day 228: CDS Maths

5 questions (10 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Heights and Distances. Asked once: CDS 2 2023

    Consider the following for the next two (02) items that follow : A flagstaff stands on the top of a vertical tower. The angle of elevation of the top of the flagstaff from a certain place on the same horizontal level with the base of the tower is found to be α\alpha. Advancing a distance d towards the tower in the same horizontal plane, the angle of elevation of the top of the flagstaff is observed to be β\beta and that of the top of the tower is observed to be γ\gamma. Let H be the height of the top of the flagstaff from the base of the tower and h be the height of the tower.
    31
    Which one of the following is correct ?

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    32
    Which one of the following is correct ?

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  2. Question 2

    Inequalities. Asked once: CDS 2 2025

    3
    Let pp and qq be natural numbers such that q>pq>p. What is the largest value of pp such that q2−5p−4q^2-5p-4 is negative?

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  3. Question 3 (case study, 5 parts)

    Linear Equations. Asked once: CDS 2 2023

    Consider the following for the next (05) items that follow : A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is 16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg.
    86
    What is D's age (in years) ?

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    87
    What is the average age (in years) of B, C, D, E and G ?

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    88
    What is the difference between the weights (in kg) of G and C ?

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    89
    What is the average weight (in kg) of A, B, C, D, E, F and G ?

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    90
    Consider the following statements : 1. The age of F cannot be determined due to insufficient data. 2. The average weight of D and F is equal to weight of E. 3. The weight difference is maximum for D and A. Which of the statements given above are correct ?

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  4. Question 4

    Lines, Angles and Polygons. Asked once: CDS 2 2020

    50
    What is the magnitude (in radian) of the interior angle of a regular pentagon ?

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  5. Question 5

    Logarithms. Asked once: CDS 2 2025

    38
    If x4+y4=14x2y2x^4 + y^4 = 14x^2y^2, then consider the following : I. log⁡10(x2+y2)=log⁡10x+log⁡10y+2log⁡102\log_{10}(x^2 + y^2) = \log_{10} x + \log_{10} y + 2\log_{10} 2 II. log⁡10(x2−y2)=log⁡10x+log⁡10y+log⁡102+0.5log⁡103\log_{10}(x^2 - y^2) = \log_{10} x + \log_{10} y + \log_{10} 2 + 0.5\log_{10} 3 Which of the above is/are correct?

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