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If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term, then
- a)r = 10
- b)r = 11
- c)r = 12
- d)r = 13
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term,...
In the expansion of ((x^4) - (1/x^3))^15, the general term can be written as:
T_r = C(15, r) * (x^4)^(15-r) * (-1/x^3)^r
where C(15, r) is the binomial coefficient which stands for the number of ways to choose r elements from a set of 15 elements.
Now, let's simplify T_r:
T_r = C(15, r) * x^(60-4r) * (-1)^r * x^(-3r)
T_r = C(15, r) * (-1)^r * x^(60-7r)
We are given that x^(-17) occurs in the rth term, so we have:
60 - 7r = -17
7r = 77
r = 11
T_r = C(15, r) * (x^4)^(15-r) * (-1/x^3)^r
where C(15, r) is the binomial coefficient which stands for the number of ways to choose r elements from a set of 15 elements.
Now, let's simplify T_r:
T_r = C(15, r) * x^(60-4r) * (-1)^r * x^(-3r)
T_r = C(15, r) * (-1)^r * x^(60-7r)
We are given that x^(-17) occurs in the rth term, so we have:
60 - 7r = -17
7r = 77
r = 11
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Community Answer
If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term,...
Given expression: ((x^4) - (1/x^3))^15
We need to find the value of r such that x^(-17) occurs in the rth term of the expansion.
Using the binomial theorem, the rth term of the expansion is given by:
T(r) = (15Cr) * ((x^4)^(15-r)) * ((-1/x^3)^r)
We need to find the value of r for which the exponent of x in T(r) is -17.
Exponent of x in T(r) = 4(15-r) - 3r
Solving for this equation, we get:
60 - 4r - 3r = -17
7r = 77
r = 11
Therefore, the correct answer is option (b), r = 11.
We need to find the value of r such that x^(-17) occurs in the rth term of the expansion.
Using the binomial theorem, the rth term of the expansion is given by:
T(r) = (15Cr) * ((x^4)^(15-r)) * ((-1/x^3)^r)
We need to find the value of r for which the exponent of x in T(r) is -17.
Exponent of x in T(r) = 4(15-r) - 3r
Solving for this equation, we get:
60 - 4r - 3r = -17
7r = 77
r = 11
Therefore, the correct answer is option (b), r = 11.
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If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term, thena)r = 10b)r = 11c)r = 12d)r = 13Correct 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 If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term, thena)r = 10b)r = 11c)r = 12d)r = 13Correct 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 If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term, thena)r = 10b)r = 11c)r = 12d)r = 13Correct answer is option 'C'. Can you explain this answer?.
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