Maharashtra State BoardHSC Science (Electronics) 11th
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Answer the following: Suppose (1 + kx)n = 1 − 12x + 60x2 − .... find k and n. - Mathematics and Statistics

Sum

Answer the following:

Suppose (1 + kx)n = 1 − 12x + 60x2 − .... find k and n.

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Solution

(1 + kx)n = 1 − 12x + 60x2 − ...

∴ `1 + ("nk")x + ("n"("n" - 1))/2 "k"^2x^2 + ...` = 1 − 12x + 60x2 + ...

Equating the coefficients on both sides, we get

∴ nk = − 12    ...(i)

and `("n"("n" - 1))/2 "k"^2` = 60   ...(ii)

∴ n2k2 – nk2 = 120

∴ 144 – (nk)k = 120    …[From (i)]

∴ 144 – 120 = –12k     …[From (i)]

∴ k = `-24/12` = − 2

Substituting the value of k in equation (i), we get

n = `(-12)/"k"`

= `(-12)/(-2)`

= 6

Concept: General Term in Expansion of (a + b)n
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4 | Q II. (26) | Page 86
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