SATHEE: Binomial Theorem 1 Question 27

Binomial Theorem 1 Question 27

29.

If $(1 + a x)^{n} = 1 + 8 x + 24 x^{2} + \dots$ , then $a = \dots$ and $n = \dots$ .

$(1983, 2 M)$

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Answer:

Correct Answer: 29. ( $a = 2$ and $n = 4$ )

Solution:

Given,

$\begin{aligned} (1 + a x)^{n} = 1 + 8 x + 24 x^{2} + \dots \\ \Rightarrow 1 + a n x + \frac{n (n - 1)}{2!} a^{2} x^{2} + \dots = 1 + 8 x + 24 x^{2} + \dots \\ ∴ a n = 8 and a^{2} \frac{n (n - 1)}{2} = 24 \\ \Rightarrow 8 (8 - a) = 48 \\ \Rightarrow 8 - a = 6 \Rightarrow a = 2 \\ Hence, a = 2 and n = 4 \end{aligned}$

Binomial Theorem 1 Question 27

29.

Answer:

Engineering Preparation

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Binomial Theorem 1 Question 27

29.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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