Day 130: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

Question 1
Time and Work. Asked once: CDS 1 2024 (same type asked 2 times) See all 2 of this type
20 $A, B, C, D can complete a work in 3, 6, 9, 12 hours respectively. Further, only one person can work at a time in each hour and nobody can work for two consecutive hours. It is not necessary to engage all. What is the minimum number of hours that they will take to finish the work ?$
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Question 2 (case study, 2 parts)
Triangles. Asked once: CDS 2 2021 (same type asked 2 times) See all 2 of this type
Consider the following for the next two (02) items that follow : $ABC$ is triangle in which $AB = AC$ and $D$ is any point on $BC$ .
84 $Which one of the following is correct ?$
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85 $AD = 5$
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Question 3 (case study, 2 parts)
Trigonometric Ratios and Identities. Asked once: CDS 2 2025 (same type asked 2 times) See all 2 of this type
Let $p\sin^2\alpha + q\cos^2\alpha = m$ , $q\sin^2\beta + p\cos^2\beta = n$ ; $p \ne m, n$ and $q \ne m, n$ .
41 $\left(\dfrac{\tan\alpha}{\tan\beta}\right)^2$
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42 $\alpha$
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Question 4
Lines, Angles and Polygons. Asked once: CDS 2 2018 (same type asked 2 times) See all 2 of this type
87 $\angle AOC = 5 \angle AOD$
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Question 5
Logarithms. Asked once: CDS 2 2022 (same type asked 2 times) See all 2 of this type
24 $\log_{10}\left[995 + \sqrt{x^2 - 12x + 60}\right] = 3$
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Question 1

Question 2 (case study, 2 parts)

Question 3 (case study, 2 parts)

Question 4

Question 5