Day 226: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

Question 1 (case study, 2 parts)
Statistics. Asked once: CDS 2 2025
For the following two (02) items : The following data represent the distance covered (in metres) by two groups of athletic children. It is known that the median distance in the first group is 20.8 metres while the mean distance in the second group is 17.3 metres. Some frequencies in both the groups are missing :
Distance Class First Group Second Group
0-5 $u$ $3u$
5-10 $v$ $2v$
10-15 11 40
15-20 52 50
20-25 75 30
25-30 22 28
97 $u$
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98 $v$
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Question 2
Surds, Indices and Simplification. Asked once: CDS 2 2026
19 $(\sqrt{2} + \sqrt{3} + \sqrt{5})(\sqrt{2} + \sqrt{3} - \sqrt{5})(\sqrt{2} - \sqrt{3} + \sqrt{5})(-\sqrt{2} + \sqrt{3} + \sqrt{5})$
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Question 3
Time and Work. Asked once: CDS 1 2024
59 $p number of men can finish a piece of work in q days. If there are 50% more men, then the work will be finished 12 days earlier. What is the value of q ?$
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Question 4
Time, Speed and Distance. Asked once: CDS 1 2026
17 $Without stoppages, a train travels at an average speed of 60 km/h and with stoppages it covers the same distance at an average speed of 48 km/h. How many minutes per hour does the train stop ?$
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Question 5
Triangles. Asked once: CDS 2 2026
67 $\angle ABC = 120^\circ$
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Question 1 (case study, 2 parts)