CAT Exam > CAT Questions > Find the number of distinct pairs of non nega...
Start Learning for Free
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|< /><9?>
Most Upvoted Answer
Find the number of distinct pairs of non negative integers (x,y) satis...
**Solution:**
To solve this problem, we need to consider two cases:
**Case 1:** 3 - 2xy ≥ 0
In this case, we have:
3 - 2xy = 2xy + 1 - 2xy = 1
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy ≤ 2 or xy ≤ 1
The pairs that satisfy this inequality are:
(0,0), (0,1), (1,0), (1,1)
**Case 2:** 3 - 2xy < />
In this case, we have:
3 - 2xy = -(2xy - 1)
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy - 1 ≤ -3 or 2xy ≤ -2 or xy ≤ -1
Since x and y are non-negative integers, the inequality xy ≤ -1 cannot be satisfied. Therefore, there are no solutions in this case.
**Final Answer:**
The number of distinct pairs of non-negative integers (x,y) satisfying |3 - 2xy| is 4.
To solve this problem, we need to consider two cases:
**Case 1:** 3 - 2xy ≥ 0
In this case, we have:
3 - 2xy = 2xy + 1 - 2xy = 1
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy ≤ 2 or xy ≤ 1
The pairs that satisfy this inequality are:
(0,0), (0,1), (1,0), (1,1)
**Case 2:** 3 - 2xy < />
In this case, we have:
3 - 2xy = -(2xy - 1)
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy - 1 ≤ -3 or 2xy ≤ -2 or xy ≤ -1
Since x and y are non-negative integers, the inequality xy ≤ -1 cannot be satisfied. Therefore, there are no solutions in this case.
**Final Answer:**
The number of distinct pairs of non-negative integers (x,y) satisfying |3 - 2xy| is 4.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|
Question Description
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|.
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|.
Solutions for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| defined & explained in the simplest way possible. Besides giving the explanation of
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|, a detailed solution for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| has been provided alongside types of Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| theory, EduRev gives you an
ample number of questions to practice Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup