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If in the expansion of [(x4)+(1/x3)]15 in rth term x4 occurs, then r=
- a)7
- b)8
- c)9
- d)10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If in the expansion of [(x4)+(1/x3)]15 in rth term x4 occurs, then r=a...
Solution:
We can expand the given expression using the binomial theorem as follows:
[(x4) (1/x3)]15 = (x4/x3)15 = x(4-3)15 = x1⁵ = x
Now, we need to find the term in the expansion of (x4/x3)15 in which x4 occurs.
Let's consider the general term in the expansion of (x4/x3)15:
Tr+1 = (15Cr) (x4)r (1/x3)15-r
For x4 to occur in Tr+1, we must have r=4, because then (x4)r = (x4)4 = x16, which cancels with (1/x3)15-4 = (1/x3)11 to give x.
Therefore, r = 4+1 = 5.
Hence, the term in the expansion of (x4/x3)15 in which x4 occurs is the 5th term.
But we need to find the corresponding term in the expansion of [(x4) (1/x3)]15, which has the same coefficient as the 5th term in the expansion of (x4/x3)15.
Since (x4/x3)15 = x1⁵, we know that the coefficient of x4 in the expansion of (x4/x3)15 is 0.
Therefore, the 5th term in the expansion of (x4/x3)15 corresponds to the 9th term in the expansion of [(x4) (1/x3)]15.
Hence, the answer is (C) 9.
We can expand the given expression using the binomial theorem as follows:
[(x4) (1/x3)]15 = (x4/x3)15 = x(4-3)15 = x1⁵ = x
Now, we need to find the term in the expansion of (x4/x3)15 in which x4 occurs.
Let's consider the general term in the expansion of (x4/x3)15:
Tr+1 = (15Cr) (x4)r (1/x3)15-r
For x4 to occur in Tr+1, we must have r=4, because then (x4)r = (x4)4 = x16, which cancels with (1/x3)15-4 = (1/x3)11 to give x.
Therefore, r = 4+1 = 5.
Hence, the term in the expansion of (x4/x3)15 in which x4 occurs is the 5th term.
But we need to find the corresponding term in the expansion of [(x4) (1/x3)]15, which has the same coefficient as the 5th term in the expansion of (x4/x3)15.
Since (x4/x3)15 = x1⁵, we know that the coefficient of x4 in the expansion of (x4/x3)15 is 0.
Therefore, the 5th term in the expansion of (x4/x3)15 corresponds to the 9th term in the expansion of [(x4) (1/x3)]15.
Hence, the answer is (C) 9.
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If in the expansion of [(x4)+(1/x3)]15 in rth term x4 occurs, then r=a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If in the expansion of [(x4)+(1/x3)]15 in rth term x4 occurs, then r=a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in the expansion of [(x4)+(1/x3)]15 in rth term x4 occurs, then r=a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?.
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