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Consider the following statements in respect of the expression Sn = n(n + 1)/2
where n is an integer
I. There are exactly two values of n for which Sn = 861
II. Sn = S-(n + 1) and hence for any integer m, we have two values of n for which Sn = m
where n is an integer
I. There are exactly two values of n for which Sn = 861
II. Sn = S-(n + 1) and hence for any integer m, we have two values of n for which Sn = m
Q. Which of the above are not perfect squares?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following statements in respect of the expression Sn= n(n...
STATEMENT I:
n(n + 1)/2 = 861
n(n + 1) = 1722
n2 + n - 1722 = 0
n2 + 42n - 41n - 1722 = 0
n(n + 42) - 41(n + 42) = 0
(n - 41) (n + 42) = 0
∴ n = 41 or -42
n(n + 1)/2 = 861
n(n + 1) = 1722
n2 + n - 1722 = 0
n2 + 42n - 41n - 1722 = 0
n(n + 42) - 41(n + 42) = 0
(n - 41) (n + 42) = 0
∴ n = 41 or -42
There are two integer values of n for which Sn = 861
∴ Statement I is true
∴ Statement I is true
STATEMENT II:
Sn = S-(n + 1) and hence for any integer m, we have two values of n for which Sn = m
Sn = S-(n + 1) and hence for any integer m, we have two values of n for which Sn = m
It is false, because not for all integral values of m, there exists an integral value of n
For example, If m = 5
n(n + 1)/2 = 5
n2 + n - 10 = 0
Finding roots using quadratic equation
n = (1 ± √41)/2, not an integer
n(n + 1)/2 = 5
n2 + n - 10 = 0
Finding roots using quadratic equation
n = (1 ± √41)/2, not an integer
Most Upvoted Answer
Consider the following statements in respect of the expression Sn= n(n...
Analysis:
- The given expression is Sn= n(n + 1)/2, where n is an integer.
- We need to analyze the two statements provided and determine which are not perfect squares.
Statement I:
- There are exactly two values of n for which Sn= 861.
- To find the values of n, we need to solve the equation n(n + 1)/2 = 861.
- By solving this equation, we can find the two integer values of n.
- Since 861 is not a perfect square, the values of n obtained may or may not be perfect squares.
Statement II:
- Sn= S-(n + 1), where S is the sum of the first n natural numbers.
- For any integer m, there are two values of n for which Sn= m.
- This statement implies that there are two possible values of n that satisfy the given equation for any integer m.
- The values of n obtained from this equation may or may not be perfect squares.
Conclusion:
- Statement I states that there are exactly two values of n for which Sn= 861, which may or may not be perfect squares.
- Statement II suggests that for any integer m, there are two values of n for which Sn= m, which may or may not be perfect squares.
- Therefore, only Statement I is not guaranteed to result in perfect squares, making option 'A' the correct choice.
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Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?
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Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?.
Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements in respect of the expression Sn= n(n + 1)/2where n is an integerI. There are exactly two values of n for which Sn= 861II. Sn= S-(n + 1)and hence for any integer m, we have two values of n for which Sn= mQ. Which of the above are not perfect squares?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
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