JEE Exam > JEE Questions > Let Xbe the set consisting of the first 2018 ...
Start Learning for Free
Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11,… , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23,…. Then, the number of elements in the set X ∪ Y is _____.
Correct answer is '3748'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Let Xbe the set consisting of the first 2018 terms of thearithmetic pr...
Explanation:
Given Arithmetic Progressions:
- X: 1, 6, 11, ...
- Y: 9, 16, 23, ...
Finding the Number of Terms in X and Y:
- The nth term of an arithmetic progression is given by:
a + (n-1)d, where a is the first term and d is the common difference.
- For X: a = 1, d = 5
The 2018th term of X = 1 + (2018-1) * 5
= 10085
- For Y: a = 9, d = 7
The 2018th term of Y = 9 + (2018-1) * 7
= 14113
Finding the Number of Elements in X ∪ Y:
- The union of two sets includes all unique elements from both sets.
- Since both X and Y have 2018 terms, we have to find the number of unique terms in X ∪ Y.
- The number of unique terms in X ∪ Y is the sum of the number of terms in X and Y minus the number of terms they have in common.
- To find the number of terms they have in common, we need to find the number of terms in the intersection of X and Y.
- The nth term of X: 1 + (n-1)5 = 1 + 5n
- The nth term of Y: 9 + (n-1)7 = 9 + 7n
- Setting the two equations equal gives: 1 + 5n = 9 + 7n
- Solving for n gives n = 4
- Therefore, the number of terms in the intersection of X and Y is 1.
- So, the number of elements in X ∪ Y = 10085 + 14113 - 1 = 24297
Therefore, the number of elements in the set X ∪ Y is 24297.
Given Arithmetic Progressions:
- X: 1, 6, 11, ...
- Y: 9, 16, 23, ...
Finding the Number of Terms in X and Y:
- The nth term of an arithmetic progression is given by:
a + (n-1)d, where a is the first term and d is the common difference.
- For X: a = 1, d = 5
The 2018th term of X = 1 + (2018-1) * 5
= 10085
- For Y: a = 9, d = 7
The 2018th term of Y = 9 + (2018-1) * 7
= 14113
Finding the Number of Elements in X ∪ Y:
- The union of two sets includes all unique elements from both sets.
- Since both X and Y have 2018 terms, we have to find the number of unique terms in X ∪ Y.
- The number of unique terms in X ∪ Y is the sum of the number of terms in X and Y minus the number of terms they have in common.
- To find the number of terms they have in common, we need to find the number of terms in the intersection of X and Y.
- The nth term of X: 1 + (n-1)5 = 1 + 5n
- The nth term of Y: 9 + (n-1)7 = 9 + 7n
- Setting the two equations equal gives: 1 + 5n = 9 + 7n
- Solving for n gives n = 4
- Therefore, the number of terms in the intersection of X and Y is 1.
- So, the number of elements in X ∪ Y = 10085 + 14113 - 1 = 24297
Therefore, the number of elements in the set X ∪ Y is 24297.
Free Test
FREE
| Start Free Test |
Community Answer
Let Xbe the set consisting of the first 2018 terms of thearithmetic pr...
Correct answer is'3748'
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?
Question Description
Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?.
Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?.
Solutions for Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?, a detailed solution for Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? has been provided alongside types of Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup