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A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, ⋯ , rn-1 such that r < r2 < r3 < ⋯ rn-1 concentric with the circle C. If pm = rm+1 /rm, then which one of the following is correct?​
  • a)
    p increases as m increases
  • b)
    p decreases as m increases
  • c)
    p remains constant as m increases
  • d)
    p increases for some values of m as m increases and then decreases thereafter
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A region of area A bounded by a circle C is divided into n regions, ea...
Area of (m + 1)th region = π (rm+12 – rm2)
⇒ πrm2 [(rm+1/rm)2 – 1]
⇒ πrm2 × (pm2 – 1)
Since area of all the region is constant
pm2 – 1 ∝ 1/rm2
So as m increases rm increases, ∴ pdecreases with the m
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Most Upvoted Answer
A region of area A bounded by a circle C is divided into n regions, ea...


Explanation:

Given Information:
- The region of area A is bounded by a circle C.
- The region is divided into n regions, each of area A/n.
- Circles of radii r1, r2, r3, ..., rn-1 are drawn concentric with circle C such that r1 < r2="" />< r3="" />< ...="" />< />

Calculation of pm:
- pm = rm+1 / rm where m is an integer.

Analysis:
- As the radius of the circles increases (m increases), the area of each divided region decreases.
- Since the area of each region is proportional to the square of the radius, pm will decrease as m increases.
- This is because the increase in the denominator (rm) will be greater than the increase in the numerator (rm+1), resulting in a decrease in the value of pm.

Conclusion:
- Therefore, the correct option is p decreases as m increases.
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A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, , rn-1such that r < r2< r3< rn-1concentric with the circle C. If pm= rm+1/rm, then which one of the following is correct?a)p increases as m increasesb)p decreases as m increasesc)p remains constant as m increasesd)p increases for some values of m as m increases and then decreases thereafterCorrect answer is option 'B'. Can you explain this answer?
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A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, , rn-1such that r < r2< r3< rn-1concentric with the circle C. If pm= rm+1/rm, then which one of the following is correct?a)p increases as m increasesb)p decreases as m increasesc)p remains constant as m increasesd)p increases for some values of m as m increases and then decreases thereafterCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, , rn-1such that r < r2< r3< rn-1concentric with the circle C. If pm= rm+1/rm, then which one of the following is correct?a)p increases as m increasesb)p decreases as m increasesc)p remains constant as m increasesd)p increases for some values of m as m increases and then decreases thereafterCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, , rn-1such that r < r2< r3< rn-1concentric with the circle C. If pm= rm+1/rm, then which one of the following is correct?a)p increases as m increasesb)p decreases as m increasesc)p remains constant as m increasesd)p increases for some values of m as m increases and then decreases thereafterCorrect answer is option 'B'. Can you explain this answer?.
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