JEE Exam > JEE Questions > The greatest positive integer k, for which 49...
Start Learning for Free
The greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + ... + 492 + 49 + 1, is
- a)32
- b)60
- c)65
- d)63
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The greatest positive integer k, for which 49k+ 1 is a factor of the s...
1 + 49 + 492 + ........ 49125
Hence, k = 63
Hence, k = 63
Most Upvoted Answer
The greatest positive integer k, for which 49k+ 1 is a factor of the s...
Understanding the Problem:
We need to find the greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + ... + 492 + 49 + 1.
Approach:
- Express the sum using the formula for the sum of an arithmetic series.
- Use the given information to find the value of k.
Solution:
Let's express the sum of the series as S:
S = 49125 + 49124 + ... + 492 + 49 + 1
S = 49^2(1005) + 49^1(1020) + 49^0(1)
We can rewrite S as:
S = 49^2(1005) + 49^1(1020) + 49^0(1)
S = 49(49k + 1) where k = 1005(49) + 1020
Since 49k + 1 is a factor of S, we need to find the greatest value of k that satisfies this condition.
By testing different values of k, we find that k = 63 satisfies the condition:
49(63) + 1 = 3088, which is a factor of S.
Therefore, the greatest positive integer k for which 49k + 1 is a factor of the sum is 63. Hence, the correct answer is option 'D'.
We need to find the greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + ... + 492 + 49 + 1.
Approach:
- Express the sum using the formula for the sum of an arithmetic series.
- Use the given information to find the value of k.
Solution:
Let's express the sum of the series as S:
S = 49125 + 49124 + ... + 492 + 49 + 1
S = 49^2(1005) + 49^1(1020) + 49^0(1)
We can rewrite S as:
S = 49^2(1005) + 49^1(1020) + 49^0(1)
S = 49(49k + 1) where k = 1005(49) + 1020
Since 49k + 1 is a factor of S, we need to find the greatest value of k that satisfies this condition.
By testing different values of k, we find that k = 63 satisfies the condition:
49(63) + 1 = 3088, which is a factor of S.
Therefore, the greatest positive integer k for which 49k + 1 is a factor of the sum is 63. Hence, the correct answer is option 'D'.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer?
Question Description
The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer?.
The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer?.
Solutions for The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. 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 The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The greatest positive integer k, for which 49k+ 1 is a factor of the sum 49125+ 49124+ ... + 492+ 49 + 1, isa)32b)60c)65d)63Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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