The term independent of x in the expansion of ( 9x - (1/3 √x) )18, x 0 , is âaâ times the corresponding binomial coefficient. Then âaâ is

Question

The term independent of x in the expansion of ( 9x - (1/3 √x) )18, x > 0 , is âaâ times the corresponding binomial coefficient. Then âaâ is (A) 3 (B) 1/3 (C) -1/3 (D) None of these

Tardigrade Admin · Accepted Answer

Tr+1 = 18 Cr (9x)18-r ( - (1/3 √x))r = (-1)r 18Cr 918 - (3r/2) x18 (3r/2) is independent of x provided r = 12 and then a = 1.

Q. The term independent of x in the expansion of $(9 x - \frac{1}{3 x})^{18}, x > 0$ , is ‘a’ times the corresponding binomial coefficient. Then ‘a’ is

3

1/3

-1/3

None of these

$T_{r + 1} =^{18} C_{r} (9 x)^{18 - r} (- \frac{1}{3 x})^{r}$
$= (- 1)^{r}^{18} C_{r} 9^{18 - \frac{3 r}{2}} x^{18 \frac{3 r}{2}}$
is independent of x provided r = 12 and then a = 1.

Q. The term independent of x in the expansion of (9x−3x​1​)18,x>0 , is ‘a’ times the corresponding binomial coefficient. Then ‘a’ is

3

1/3

-1/3

None of these

Tr+1​=18Cr​(9x)18−r(−3x​1​)r =(−1)r18Cr​918−23r​x1823r​ is independent of x provided r = 12 and then a = 1.

Q. The term independent of x in the expansion of $(9 x - \frac{1}{3 x})^{18}, x > 0$ , is ‘a’ times the corresponding binomial coefficient. Then ‘a’ is

$T_{r + 1} =^{18} C_{r} (9 x)^{18 - r} (- \frac{1}{3 x})^{r}$
$= (- 1)^{r}^{18} C_{r} 9^{18 - \frac{3 r}{2}} x^{18 \frac{3 r}{2}}$
is independent of x provided r = 12 and then a = 1.