Question
Download Solution PDFLet a, b, c be in A.P. then 1/ab, 1/ca and 1/bc are in
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If a,b, c are in AP, then 2b = a + c or b - a = c - b
Calculation:
Given: a, b, c are in AP
Let 1/ab, 1/ca and 1/bc be in AP
⇒\(\rm \frac{1}{ca}\rm -\frac{1}{ab}=\rm \frac{1}{bc}-\rm \frac{1}{ca} \)
\(\rm \frac{1}{a}( \frac{1}{c}- \frac{1}{b})= \frac{1}{c}( \frac{1}{b}- \frac{1}{a})\\ ⇒ \frac{b-c}{abc}= \frac{a-b}{abc}\)
⇒ b - c = a - b
⇒2b = a + c
⇒ a,b, c are in AP, which is true.
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.