Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# If the Coefficients of X2 and X3 in the Expansion of (3 + Ax)9 Are the Same, Then the Value of a Is(A) − 7 9(B) − 9 7(C) 7 9(D) 9 7 - Mathematics

MCQ

If the coefficients of x2 and x3 in the expansion of (3 + ax)9 are the same, then the value of a is

#### Options

• $- \frac{7}{9}$

• $- \frac{9}{7}$

• $\frac{7}{9}$

• $\frac{9}{7}$

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#### Solution

$\frac{9}{7}$

Coefficients of x2 Coefficients of x3

$^{9}{}{C}_2 \times 3^{9 - 2} a^2 = ^{9}{}{C}_3 \times 3^{9 - 3} a^3$
$\Rightarrow a = \frac{^{9}{}{C}_2}{^{9}{}{C}_3} \times 3$
$= \frac{9! \times 3! \times 6! \times 3}{2! \times 7! \times 9!}$
$= \frac{9}{7}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 33 | Page 48
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