If the coefficients of x

Question:

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

(a) $-\frac{7}{9}$

(b) $-\frac{9}{7}$

(c) $\frac{7}{9}$

 

(d) $\frac{9}{7}$

Solution:

(d) $\frac{9}{7}$

Coefficients of x2 Coefficients of x3

${ }^{9} C_{2} \times 3^{9-2} a^{2}={ }^{9} C_{3} \times 3^{9-3} a^{3}$

$\Rightarrow a=\frac{{ }^{9} C_{2}}{{ }^{9} C_{3}} \times 3$

$=\frac{9 ! \times 3 ! \times 6 ! \times 3}{2 ! \times 7 ! \times 9 !}$

$=\frac{9}{7}$

 

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now