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The coefficient of x4 in the expansion of (1 + x + x2 + x3)n is:
- a)nC4 + nC2
- b)nC4 + nC2+ nC4.nC2
- c)nC4 + nC2+ nC1.nC2
- d)nC4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + ...
x4 can be achieved in the following ways:
x4 . 1(n-4) . (x2)0 . (x3)0
Hence, coefficient will be nC4 .
x2 . 1(n-3) . (x2)1 . (x3)0
Hence, coefficient will be 3nC3.
x1 . 1(n-2) . (x2)0 . (x3)1
Hence, coefficient will be 2nC2.
x0 . 1(n-2) .(x2)2 .(x3)0
Hence, coefficient will be nC2 .
Hence, the required coefficient will be
nC4 + 3nC3 + 3nC2
= nC4 + 3(nC3 + nC2).
= nC4 + 3(n+1C3).
= nC4 + nC2 + nC1 . nC2
x4 . 1(n-4) . (x2)0 . (x3)0
Hence, coefficient will be nC4 .
x2 . 1(n-3) . (x2)1 . (x3)0
Hence, coefficient will be 3nC3.
x1 . 1(n-2) . (x2)0 . (x3)1
Hence, coefficient will be 2nC2.
x0 . 1(n-2) .(x2)2 .(x3)0
Hence, coefficient will be nC2 .
Hence, the required coefficient will be
nC4 + 3nC3 + 3nC2
= nC4 + 3(nC3 + nC2).
= nC4 + 3(n+1C3).
= nC4 + nC2 + nC1 . nC2
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Community Answer
The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + ...
Explanation:
Expansion of (1 + x + x2 + x3)n:
- When we expand the given expression using the binomial theorem, we will get terms of the form xk where k ranges from 0 to 3n.
- The coefficient of xk in the expansion is given by nCm where m is the number of x terms in the product that gives xk.
Finding the coefficient of x4:
- To find the coefficient of x4 in the expansion, we need to look for terms in the expansion where the powers of x add up to 4.
- This can happen in the following ways:
- From x1 * x3 = x4 with coefficients nC1 * nC3
- From x2 * x2 = x4 with coefficient nC2 * nC2
Calculating the total coefficient:
- The total coefficient of x4 will be the sum of the coefficients from the above two cases.
- Therefore, the total coefficient of x4 in the expansion is nC1 * nC3 + nC2 * nC2 which simplifies to nC4 + nC2.
Therefore, the correct answer is option 'C' (nC4 + nC2).
Expansion of (1 + x + x2 + x3)n:
- When we expand the given expression using the binomial theorem, we will get terms of the form xk where k ranges from 0 to 3n.
- The coefficient of xk in the expansion is given by nCm where m is the number of x terms in the product that gives xk.
Finding the coefficient of x4:
- To find the coefficient of x4 in the expansion, we need to look for terms in the expansion where the powers of x add up to 4.
- This can happen in the following ways:
- From x1 * x3 = x4 with coefficients nC1 * nC3
- From x2 * x2 = x4 with coefficient nC2 * nC2
Calculating the total coefficient:
- The total coefficient of x4 will be the sum of the coefficients from the above two cases.
- Therefore, the total coefficient of x4 in the expansion is nC1 * nC3 + nC2 * nC2 which simplifies to nC4 + nC2.
Therefore, the correct answer is option 'C' (nC4 + nC2).
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The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. 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 coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. 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 coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer?.
The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. 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 coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. 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 coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer?.
Solutions for The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The coefficient of x4in the expansion of (1 + x + x2+ x3)n is:a)nC4 + nC2b)nC4 + nC2+ nC4.nC2c)nC4+nC2+ nC1.nC2d)nC4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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