Question

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a²y² + … , and a₁ = a₂ = 10, then (m, n) is

(20, 45)

(35, 20)

(45, 35)

(35, 45)

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Solution

(35, 45)

left parenthesis 1 minus straight y right parenthesis to the power of straight m space left parenthesis 1 plus straight y right parenthesis to the power of straight n space equals space left square bracket 1 minus to the power of straight m straight C subscript 1 straight y space plus to the power of straight m straight C subscript 2 straight y squared space minus........ right square bracket left square bracket 1 plus to the power of straight n straight C subscript 1 straight y space plus to the power of straight n straight C subscript 2 straight y squared plus... right square bracket space equals space 1 space plus space left parenthesis straight n minus straight m right parenthesis space plus open curly brackets fraction numerator straight m left parenthesis straight m minus 1 right parenthesis over denominator 2 end fraction plus fraction numerator straight n left parenthesis straight n minus 1 right parenthesis 2 over denominator 2 end fraction minus mn close curly brackets straight y squared space plus.... therefore space straight a subscript 1 space equals straight n minus straight m space equals space 10 space and space straight a subscript 2 space equals space fraction numerator straight m squared plus straight n squared space minus straight m minus straight n minus 2 mn over denominator 2 end fraction space equals space 10 So comma space straight n minus straight m equals 10 space and space left parenthesis straight m minus straight n right parenthesis squared space minus left parenthesis straight m plus straight n right parenthesis space equals space 20 rightwards double arrow straight m plus straight n space equals space 80 therefore comma space straight m space equals space 35 comma space straight n space equals space 45

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Binomial Theorem

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a²y² + … , and a₁ = a₂ = 10, then (m, n) is

(20, 45)

(35, 20)

(45, 35)

(35, 45)

Some More Questions From Binomial Theorem Chapter

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NCERT Sample Papers

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Binomial Theorem

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a2y2 + … , and a1 = a2 = 10, then (m, n) is (20, 45) (35, 20) (45, 35) (35, 45)

Some More Questions From Binomial Theorem Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a²y² + … , and a₁ = a₂ = 10, then (m, n) is

(20, 45)

(35, 20)

(45, 35)

(35, 45)