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Consider the following statements:
1. The term containing x2 does not exist in the given expansion.
2. The sum of the coefficients of all the terms in the given expansion is 215.
1. The term containing x2 does not exist in the given expansion.
2. The sum of the coefficients of all the terms in the given expansion is 215.
Q. Which of the above statements is/are correct ?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements:1. The term containing x2 does not e...
1. For coefficient of x2,
So, x2 does not exist in the expansion
Hence, Statement 1 is correct.
Put x = 1 both sides, we get
( l + l )15 = 15C0 + 15C1 + .... + 15C15
⇒ 215 = 15C0 + 15C1 +.... + 15C15
Hence, Statement 2 is correct
So, x2 does not exist in the expansion
Hence, Statement 1 is correct.
Put x = 1 both sides, we get
( l + l )15 = 15C0 + 15C1 + .... + 15C15
⇒ 215 = 15C0 + 15C1 +.... + 15C15
Hence, Statement 2 is correct
Most Upvoted Answer
Consider the following statements:1. The term containing x2 does not e...
Explanation:
Statement 1:
- The given expansion may or may not contain a term with x^2.
- Therefore, statement 1 is incorrect as the presence of the term containing x^2 cannot be determined without knowing the specific expansion.
Statement 2:
- The sum of the coefficients of all the terms in a binomial expansion can be found by substituting x = 1 in the expansion.
- When x = 1, all the terms will reduce to just the coefficients.
- In this case, substituting x = 1 in the given expansion results in a sum of 215.
- Therefore, statement 2 is correct as the sum of the coefficients of all the terms in the given expansion is indeed 215.
Therefore, both statements 1 and 2 are correct when considering the properties of binomial expansions.
Statement 1:
- The given expansion may or may not contain a term with x^2.
- Therefore, statement 1 is incorrect as the presence of the term containing x^2 cannot be determined without knowing the specific expansion.
Statement 2:
- The sum of the coefficients of all the terms in a binomial expansion can be found by substituting x = 1 in the expansion.
- When x = 1, all the terms will reduce to just the coefficients.
- In this case, substituting x = 1 in the given expansion results in a sum of 215.
- Therefore, statement 2 is correct as the sum of the coefficients of all the terms in the given expansion is indeed 215.
Therefore, both statements 1 and 2 are correct when considering the properties of binomial expansions.
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Consider the following statements:1. The term containing x2 does not exist in the given expansion.2. The sum of the coefficients of all the terms in the given expansion is 215.Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements:1. The term containing x2 does not exist in the given expansion.2. The sum of the coefficients of all the terms in the given expansion is 215.Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. 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:1. The term containing x2 does not exist in the given expansion.2. The sum of the coefficients of all the terms in the given expansion is 215.Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. 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:1. The term containing x2 does not exist in the given expansion.2. The sum of the coefficients of all the terms in the given expansion is 215.Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?.
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