JEE Exam > JEE Questions > This section contains 2 paragraphs. Based upo...
Start Learning for Free
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Question Nos. 10 and 11
a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2
The common difference is
- a)1
- b)2
- c)3
- d)none
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
This section contains 2 paragraphs. Based upon one of paragraph 2 mult...
Most Upvoted Answer
This section contains 2 paragraphs. Based upon one of paragraph 2 mult...
Explanation:
Given Information:
- The terms a, b, c are in arithmetic progression (A.P.)
- The common difference is unknown
- The sum of the squares of the terms is d = a^2 + b^2 + c^2
Using the A.P. formula:
- For an A.P., the nth term can be represented as: a + (n-1)d
- The sum of the first n terms of an A.P. can be represented as: n/2 [2a + (n-1)d]
Sum of squares formula:
- d = a^2 + b^2 + c^2
Substitute the A.P. terms into the sum of squares formula:
- d = (a + (n-1)d)^2 + (a + 2(n-1)d)^2 + (a + 3(n-1)d)^2
Expand and simplify the equation:
- d = a^2 + 2ad(n-1) + d^2 + a^2 + 4ad(n-1) + 4d^2 + a^2 + 6ad(n-1) + 9d^2
- d = 3a^2 + 12ad(n-1) + 14d^2
Comparing with the given information:
- Since d = a^2 + b^2 + c^2, we can equate the coefficients of a, d, and constant terms
- 3a^2 = a^2, 12ad(n-1) = 0, 14d^2 = b^2 + c^2
From the second equation:
- 12ad(n-1) = 0
- This implies that the common difference, d, is 0
Therefore, the correct answer is option 'A' - 0.
Given Information:
- The terms a, b, c are in arithmetic progression (A.P.)
- The common difference is unknown
- The sum of the squares of the terms is d = a^2 + b^2 + c^2
Using the A.P. formula:
- For an A.P., the nth term can be represented as: a + (n-1)d
- The sum of the first n terms of an A.P. can be represented as: n/2 [2a + (n-1)d]
Sum of squares formula:
- d = a^2 + b^2 + c^2
Substitute the A.P. terms into the sum of squares formula:
- d = (a + (n-1)d)^2 + (a + 2(n-1)d)^2 + (a + 3(n-1)d)^2
Expand and simplify the equation:
- d = a^2 + 2ad(n-1) + d^2 + a^2 + 4ad(n-1) + 4d^2 + a^2 + 6ad(n-1) + 9d^2
- d = 3a^2 + 12ad(n-1) + 14d^2
Comparing with the given information:
- Since d = a^2 + b^2 + c^2, we can equate the coefficients of a, d, and constant terms
- 3a^2 = a^2, 12ad(n-1) = 0, 14d^2 = b^2 + c^2
From the second equation:
- 12ad(n-1) = 0
- This implies that the common difference, d, is 0
Therefore, the correct answer is option 'A' - 0.
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
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer?
Question Description
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. 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 This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer?.
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. 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 This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer?.
Solutions for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. 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 This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctParagraph for Question Nos. 10 and 11a, b, c, d is an A.P. with integer terms and d = a2 + b2 + c2The common difference isa)1b)2c)3d)noneCorrect answer is option 'A'. 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