If the ratio of the coefficient of third and fourth term in the expansion of ( x − 1 2 x ) n is 1:2, then the value of n will be Options: A . &nbsp 18 B . &nbsp 16 C . &nbsp 12 D . &nbsp -10

Answer: Option D : D T 3 = n C 2 ( x ) n − 2 ( − 1 2 x ) 2 and T 4 = n C 3 ( x ) n − 3 ( − 1 2 x ) 3 But according to the condition, − n ( n − 1 ) × 3 × 2 × 1 × 8 n ( n − 1 ) ( n − 2 ) × 2 × 1 × 4 = 1 2 ⇒ n = -10

If the ratio of the coefficient of third and fourth term in the expansion

Question

If the ratio of the coefficient of third and fourth term in the expansion of $(x - \frac{1}{2 x})^{n}$ is 1:2, then the value of n will be

Options:

A . 18

B . 16

C . 12

D . -10

Answer: Option D
:
D

$T_{3}$ = $^{n} C_{2}$ $(x)^{n - 2}$ $(- \frac{1}{2 x})^{2}$ and $T_{4}$ = $^{n} C_{3}$ $(x)^{n - 3}$ $(- \frac{1}{2 x})^{3}$

But according to the condition,

$\frac{- n (n - 1) \times 3 \times 2 \times 1 \times 8}{n (n - 1) (n - 2) \times 2 \times 1 \times 4}$ = $\frac{1}{2}$ ⇒ n = -10

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