CA Foundation Exam > CA Foundation Questions > 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 ...
Start Learning for Free
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None?
Most Upvoted Answer
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) ...
Solution:
Given, (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P.
Let, (c - a) ^ 2 = (b - c) ^ 2 + d^2 ...(1) [as given in A.P.]
To prove: (b - c) , (c - a) ,(a - b) are in A.P.
Proof:
From equation (1), we get
(c - a) ^ 2 - (b - c) ^ 2 = d^2
On simplifying, we get
(c ^ 2 + a ^ 2 - 2ac) - (b ^ 2 + c ^ 2 - 2bc) = d^2
2c ^ 2 - 2ac - 2b ^ 2 + 2bc = d^2
c ^ 2 - ac - b ^ 2 + bc = d^2 / 2 ...(2)
Now, (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P.
Thus, (c - a) ^ 2 - (b - c) ^ 2 = (a - b) ^ 2 - (c - a) ^ 2
On simplifying, we get
2ac - 2bc = 2ab - 2ac
ac - bc = ab - ac
c(a + c) = b(a + c)
c = b [∵ a ≠ c]
Therefore, (b - c) = 0
Hence, (b - c) , (c - a) ,(a - b) are in A.P.
Therefore, the correct option is (a) A.P.
Given, (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P.
Let, (c - a) ^ 2 = (b - c) ^ 2 + d^2 ...(1) [as given in A.P.]
To prove: (b - c) , (c - a) ,(a - b) are in A.P.
Proof:
From equation (1), we get
(c - a) ^ 2 - (b - c) ^ 2 = d^2
On simplifying, we get
(c ^ 2 + a ^ 2 - 2ac) - (b ^ 2 + c ^ 2 - 2bc) = d^2
2c ^ 2 - 2ac - 2b ^ 2 + 2bc = d^2
c ^ 2 - ac - b ^ 2 + bc = d^2 / 2 ...(2)
Now, (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P.
Thus, (c - a) ^ 2 - (b - c) ^ 2 = (a - b) ^ 2 - (c - a) ^ 2
On simplifying, we get
2ac - 2bc = 2ab - 2ac
ac - bc = ab - ac
c(a + c) = b(a + c)
c = b [∵ a ≠ c]
Therefore, (b - c) = 0
Hence, (b - c) , (c - a) ,(a - b) are in A.P.
Therefore, the correct option is (a) A.P.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None?
Question Description
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None?.
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None?.
Solutions for 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? defined & explained in the simplest way possible. Besides giving the explanation of
28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None?, a detailed solution for 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? has been provided alongside types of 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? theory, EduRev gives you an
ample number of questions to practice 28. If (b - c) ^ 2 , (c - a) ^ 2 (a - b) ^ 2 are in A.P. then (b - c) , (c - a) , (a - b) are in (a) A.P. (b)G .P (c) H.P. (d) None? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup