SATHEE: Binomial Theorem 1 Question 35

Binomial Theorem 1 Question 35

37.

The coefficient of $x^{9}$ in the expansion of $(1 + x) (1 + x^{2}) (1 + x^{3}) \dots (1 + x^{100})$ is

(2015 Adv.)

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Answer:

Correct Answer: 37. $(8)$

Solution:

Coefficient of $x^{9}$ in the expansion of $(1 + x) (1 + x^{2}) (1 + x^{3}) \dots (1 + x^{100}) =$ Terms having $x^{9}$ $= [1^{99} \cdot x^{9}, 1^{98} \cdot x \cdot x^{8}, 1^{98} \cdot x^{2} \cdot x^{7}, 1^{98} \cdot x^{3} \cdot x^{6}$ ,

$1^{98} \cdot x^{4} \cdot x^{5}, 1^{97} \cdot x \cdot x^{2} \cdot x^{6}, 1^{97} \cdot x \cdot x^{3} \cdot x^{5}, 1^{97} \cdot x^{2} \cdot x^{3} \cdot x^{4}]$

$∴$ Coefficient of $x^{9} = 8$

Binomial Theorem 1 Question 35

37.

Answer:

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Binomial Theorem 1 Question 35

37.

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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