Suppose R is the region bounded by the two curves Y = x and Y = 2x -1 shown in the following diagram: Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If is the total number of regions generated by

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Q: 58 (CAPF/2016)
Suppose R is the region bounded by the two curves Y = x and Y = 2x -1 shown in the following diagram: Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If ҮҠis the total number of regions generated by these lines, then :

question_subject: 

Geography

question_exam: 

CAPF

stats: 

0,1,6,2,2,2,1

keywords: 

{'regions': [0, 0, 1, 2], 'distinct lines': [0, 0, 0, 1], 'region': [0, 0, 0, 1], 'lines': [2, 0, 3, 6], 'following diagram': [0, 0, 1, 1], 'total number': [0, 0, 3, 0], 'parts': [6, 2, 8, 19]}

The correct answer is option 1, ҮҠ can be 4 but not 3.

Let`s analyze each option:

Option 1: ҮҠ can be 4 but not 3.

This option means that ҮҠ can take a maximum value of 4, but it cannot be 3. In other words, when two distinct lines are drawn, they can create a maximum of 4 regions, but they cannot create only 3 regions.

Option 2: ҮҠ can be 4 but not 5.

This option means that ҮҠ can take a maximum value of 4, but it cannot be 5. However, this is incorrect because when two distinct lines are drawn, they can create a maximum of 4 regions, but they cannot create 5 regions. Therefore, this option is incorrect.

Option 3: ҮҠ can be 5 but not 6.

This option means that ҮҠ can take a maximum value of 5, but it cannot be 6. However, when two distinct lines are drawn, they can create a maximum of 4 regions, so it is not possible for ҮҠ