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The 10th term of the expansion of (x-1)11 (in decreasing powers of x) is
- a)-x
- b)-11 x
- c)-x2
- d)-11C₂x2
Correct answer is option 'D'. Can you explain this answer?
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The 10th term of the expansion of (x-1)11 (in decreasing powers of x) ...
Binomial Theorem
The binomial theorem is a powerful algebraic formula used to expand an expression that contains two terms. The formula is as follows:
(a + b)n = an + nan-1b + n(n-1)/2! a(n-2)b2 + … + bn
where n is a positive integer and the coefficients for each term are given by the binomial coefficients, which can be calculated using the following formula:
(n choose k) = n! / (k! (n-k)!)
where n! represents the factorial of n and k ranges from 0 to n.
Expanding (x-1)11
To find the 10th term of the expansion of (x-1)11, we need to figure out the coefficient for the term with x2. Using the binomial theorem, we can write:
(x-1)11 = x11 - 11x10 + 55x9 - 165x8 + 330x7 - 462x6 + 462x5 - 330x4 + 165x3 - 55x2 + 11x - 1
We can see that the coefficient for the term with x2 is -55, so the 10th term is:
-55x2
However, the question asks for the answer in terms of the binomial coefficient, so we need to use the formula to find the coefficient:
(11 choose 2) = 11! / (2! 9!) = 55
Therefore, the 10th term of the expansion is:
-55Cx2, which is equivalent to -55x2
Answer: d) -11Cx2
The binomial theorem is a powerful algebraic formula used to expand an expression that contains two terms. The formula is as follows:
(a + b)n = an + nan-1b + n(n-1)/2! a(n-2)b2 + … + bn
where n is a positive integer and the coefficients for each term are given by the binomial coefficients, which can be calculated using the following formula:
(n choose k) = n! / (k! (n-k)!)
where n! represents the factorial of n and k ranges from 0 to n.
Expanding (x-1)11
To find the 10th term of the expansion of (x-1)11, we need to figure out the coefficient for the term with x2. Using the binomial theorem, we can write:
(x-1)11 = x11 - 11x10 + 55x9 - 165x8 + 330x7 - 462x6 + 462x5 - 330x4 + 165x3 - 55x2 + 11x - 1
We can see that the coefficient for the term with x2 is -55, so the 10th term is:
-55x2
However, the question asks for the answer in terms of the binomial coefficient, so we need to use the formula to find the coefficient:
(11 choose 2) = 11! / (2! 9!) = 55
Therefore, the 10th term of the expansion is:
-55Cx2, which is equivalent to -55x2
Answer: d) -11Cx2
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The 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. 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 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. 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 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. Can you explain this answer?.
The 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. 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 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. 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 10th term of the expansion of (x-1)11 (in decreasing powers of x) isa)-xb)-11 xc)-x2d)-11C₂x2Correct answer is option 'D'. Can you explain this answer?.
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