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Find the coefficients
(i) x7 in 
(ii) x _7 in 
(ii) x _7 in (iii) Find the relation between a and b, so that these coefficients are equal.
Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. Can you explain this answer?
Verified Answer
Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between...
Correct Answer :- ab = 1
Explanation : rth term in the expansion of (a + b)ⁿ is given by nCr(a)r(b)n-r
To find the coefficient of x⁷ in (ax² + 1/bx)¹¹
rth term is given by 11Cr(ax²)r (1/bx)11-r
= 11Cr ar (1/b)11-r x(r-22+2r)
=11Cr ar (1/b)11-r x3r-22
To find the coefficient of x⁷, 3r - 11 should be 7
=> 3r - 11 = 7
=> 3r = 18
=> r = 6
Thus the coefficient of x⁷ is 11C6 a⁶b⁻⁵
To find the coefficient of x⁻⁷ in (ax - 1/bx²)¹¹
rth term is given by 11Cr = (ax)r(-1/bx²)11-r
= 11Cr ar (-1/b)11-r x(r-22+2r)
=11Cr ar (1/b)11-r x3r-22
To find the coefficient of x⁻⁷, 3r - 22 should be -7
=> 3r - 22 = -7
=> 3r = 15
=> r = 5
Thus the coefficient of x⁷ is 11C(a)⁵(-1/b)⁶ = 11C6 a⁵b⁻⁶
Given that these coefficients are equal
=>11C6 a⁶b⁻⁵ = 11C6 a⁵b⁻⁶
⇒ a = 1/b
⇒ ab = 1
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Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. 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 Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. Can you explain this answer?.
Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. 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 Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the coefficients(i) x7in(ii) x_7in(iii) Find the relation between a and b, so that these coefficients are equal.Correct answer is '(i) 11C5 (ii) 11C6 (iii) ab = 1'. Can you explain this answer?.
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