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 . &nbsp18 B . &nbsp16 C . &nbsp12 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 o

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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