If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then value of n is:
- 2.
- 7.
- 11.
- 14.
[Hint: 2nC2 = nC1 + nC3 ⇒ n2 - 9n + 14 = 0 ⇒ n = 2 or 7.]
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If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then value of n is:
[Hint: 2nC2 = nC1 + nC3 ⇒ n2 - 9n + 14 = 0 ⇒ n = 2 or 7.]
The coefficient of xn in the expansion of (1 + x)2n and (1 + x)2n - 1 are in the ratio.
Hint: $^{2\text{n}}\text{C}_\text{n} : \ ^{2\text{n} - 1}\text{C}_\text{n}$
Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then:
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1 : 4 are:
$[\text{Hint}:\frac{^{24}\text{C}_\text{r}}{^{24}\text{C}_{\text{r}+1}}=\frac{1}{4}\ \frac{\text{r}+1}{24-\text{r}}\ \frac{1}{4}\Rightarrow4\text{r}+4=24-4\Rightarrow\text{r}=4]$
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The total number of terms in the expansion of (x + a)100 + (x - a)100 after simplification is:
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