Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.8k views
in Linear Inequations by (23.5k points)
closed by

If r is real number such that |r| < 1 and if a = 5 (1 – r), then

(a) –5 < a < 5 

(b) 0 < a < 10 

(c) 0 < a < 5 

(d) –10 < a < 10

1 Answer

+1 vote
by (24.0k points)
selected by
 
Best answer

(c) 0 < a < 10

|r| < 1 

⇒ – 1 < r < 1 

⇒ 1 > –r > – 1 ⇒ – 1 < – r < 1    ( a > b ⇒ a\(x\) < b\(x\), where \(x\) < 0) 

⇒ 0 < 1 – r < 2 

(Adding 1, c < a < b ⇒ c + \(x\) < a + \(x\) < b + \(x\) ∀ \(x\) ∈ R) 

⇒ 0 × 5 < 5 (1 – r) < 5 × 2 

(c < a < b ⇒ c\(x\) < a\(x\) < b\(x\) ∀ \(x\) ∈ R, \(x\) > 0) 

⇒ 0 < 5 (1 – r) < 10 

0 < a < 10.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...