If x 4 occurs in the r t h term in the expansion of ( x 4 + 1 x 3 ) 16 , then r = Options: A . &nbsp7 B . &nbsp8 C . &nbsp9 D . &nbsp10

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

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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