If x 4 occurs in the r t h term in the expansion of ( x 4 + 1 x 3 ) 16 , then r = Options: A . &nbsp 7 B . &nbsp 8 C . &nbsp 9 D . &nbsp 10

Answer: Option C : C T r = 16 C r − 1 ( x 4 ) 16 − r ( 1 x 3 ) r − 1 = 16 C r − 1 x 67 − 7 r → 67 − 7 r = 4 → r = 9

If x4 occurs in the rth term in the expansion of (x4+1x3)16, then r =

Question

If $x^{4}$ occurs in the $r^{t h}$ term in the expansion of $(x^{4} + \frac{1}{x^{3}})^{16}$ , then r =

Options:

A . 7

B . 8

C . 9

D . 10

Answer: Option C
:
C

$T_{r}$ = $^{16} C_{r - 1}$ $(x^{4})^{16 - r}$ $(\frac{1}{x^{3}})^{r - 1}$ = $^{16} C_{r - 1}$ $x^{67 - 7 r}$

$\to 67 - 7 r = 4 \to r = 9$

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