Day 273: CDS Maths

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

Question 1
Lines, Angles and Polygons. Asked once: CDS 2 2017
79 $Consider the following statements in respect of three straight lines A, B and C on a plane : 1. If A and C are parallel and B and C are parallel; then A and B are parallel. 2. If A is perpendicular to C and B is perpendicular to C; then A and B are parallel. 3. If the acute angle between A and C is equal to the acute angle between B and C; then A and B are parallel. Which of the above statements are correct ?$
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Question 2
Logarithms. Asked once: CDS 1 2019
58 $\log_{10} 1995 = 3.3000$
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Question 3 (case study, 3 parts)
Mensuration 2D. Asked once: CDS 1 2024
Consider the following for the next three (03) items that follow : Consider two identical semicircles and one circle inscribed in a rectangle of length 10 cm as shown in the figure given below. (Take $\pi = 3.14$ and $\sqrt{2} = 1.4$ ).
91 $What is the area of triangle EOF ?$
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92 $What is the area of trapezium AEFB ?$
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93 $What is the area of the shaded region ?$
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Question 4
Mensuration 3D. Asked once: CDS 1 2023
59 $A solid cube is cut into two cuboids of equal volume. What is the ratio of total surface area of the given cube to that of one of the cuboids ?$
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Question 5
Number System. Asked once: CDS 1 2025
85 $Consider the following statements in respect of prime numbers p and q : I. Their LCM is always an odd number. II. Sum of their LCM and HCF is always an even number. Which of the statements given above is/are correct ?$
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Question 1

Question 2

Question 3 (case study, 3 parts)

Question 4

Question 5