SSC CGL Exam > SSC CGL Questions > are in HP, then which of the following is/are...
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are in HP, then which of the following is/are correct?1. a, b, c are in AP
2. (b + c)2, (c + a)2, (a + b)2 are in GP. Select the correct answer using the code given below.
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
are in HP, then which of the following is/are correct?1. a, b, c are i...
Concept:
- If a, b and c are three terms in GP then b2 = ab and vice-versa
- If three terms a, b, c are in HP, then
and vice-versa - When three quantities are in AP, the middle one is called as the arithmetic mean of the other two.
- If a, b and c are three terms in AP then
- and vice-versa
- If a, b and c are in A.P then 1/a, 1/b, 1/c are in H.P and vice-versa
Calculation:
(b + c), (c + a) and (a + b) are in A.P
⇒ 2(c + a) = b + c + a + b
⇒ 2c + 2a = 2b + a + c -----(i)
⇒ 2c + 2a - 2b - a - c = 0
⇒ 2b = c + a
So, a, b, c are in AP
Now, Let (b + c)2, (c + a)2, (a + b)2 are in GP
(c + a)2 = √[(b + c).(a + b)]2
⇒ c2 + a2 + 2ac = (b + c).(a + b)
⇒ c2 + a2 + 2ac = ab + b2 + ac + bc
⇒ c2 + a2 - b2 + ac - ab - bc = 0
From here we are unable to check the relation between a, b and c
So, Our assumption was wrong
So, (b + c)2, (c + a)2, (a + b)2 are not in GP.
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are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?.
are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2are in GP. Select the correct answer using the code given below.a)1 onlyb)2onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?.
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