119567 The coefficient of \(x^4\) in the expansion of \(\left(1+x+x^2+x^3\right)^{11}\), is

119568 The coefficient of \(x^5\) in the expansion of \((1+x)^{21}+(1+x)^{22}+\ldots . .+(1+x)^{30}\) is

119569 If \(y=3 x+6 x^2+10 x^3+\ldots . . . \infty\), then is \(\frac{1}{3} y-\frac{1.4}{3^2 2} y^2+\frac{1.4 .7}{3^2 3} y^3 \ldots . . \infty\) is equal to

119570 The sum of the series
\(\sum_{\mathrm{r}=0}^{\mathrm{n}}(-1)^{\mathrm{r}} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{\mathbf{2}^{\mathrm{r}}}+\frac{\mathbf{3}^{\mathrm{r}}}{\mathbf{2}^{2 \mathrm{r}}}+\frac{\mathbf{7}^{\mathrm{r}}}{\mathbf{2}^{3 \mathrm{r}}}+\frac{\mathbf{1 5}^{\mathrm{r}}}{\mathbf{2}^{4 \mathrm{r}}}+\ldots . \mathrm{m} \text { terms }\right)\)
is

119567 The coefficient of \(x^4\) in the expansion of \(\left(1+x+x^2+x^3\right)^{11}\), is

119568 The coefficient of \(x^5\) in the expansion of \((1+x)^{21}+(1+x)^{22}+\ldots . .+(1+x)^{30}\) is

119569 If \(y=3 x+6 x^2+10 x^3+\ldots . . . \infty\), then is \(\frac{1}{3} y-\frac{1.4}{3^2 2} y^2+\frac{1.4 .7}{3^2 3} y^3 \ldots . . \infty\) is equal to

119570 The sum of the series
\(\sum_{\mathrm{r}=0}^{\mathrm{n}}(-1)^{\mathrm{r}} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{\mathbf{2}^{\mathrm{r}}}+\frac{\mathbf{3}^{\mathrm{r}}}{\mathbf{2}^{2 \mathrm{r}}}+\frac{\mathbf{7}^{\mathrm{r}}}{\mathbf{2}^{3 \mathrm{r}}}+\frac{\mathbf{1 5}^{\mathrm{r}}}{\mathbf{2}^{4 \mathrm{r}}}+\ldots . \mathrm{m} \text { terms }\right)\)
is

119567 The coefficient of \(x^4\) in the expansion of \(\left(1+x+x^2+x^3\right)^{11}\), is

119568 The coefficient of \(x^5\) in the expansion of \((1+x)^{21}+(1+x)^{22}+\ldots . .+(1+x)^{30}\) is

119569 If \(y=3 x+6 x^2+10 x^3+\ldots . . . \infty\), then is \(\frac{1}{3} y-\frac{1.4}{3^2 2} y^2+\frac{1.4 .7}{3^2 3} y^3 \ldots . . \infty\) is equal to

119570 The sum of the series
\(\sum_{\mathrm{r}=0}^{\mathrm{n}}(-1)^{\mathrm{r}} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{\mathbf{2}^{\mathrm{r}}}+\frac{\mathbf{3}^{\mathrm{r}}}{\mathbf{2}^{2 \mathrm{r}}}+\frac{\mathbf{7}^{\mathrm{r}}}{\mathbf{2}^{3 \mathrm{r}}}+\frac{\mathbf{1 5}^{\mathrm{r}}}{\mathbf{2}^{4 \mathrm{r}}}+\ldots . \mathrm{m} \text { terms }\right)\)
is

119567 The coefficient of \(x^4\) in the expansion of \(\left(1+x+x^2+x^3\right)^{11}\), is

119568 The coefficient of \(x^5\) in the expansion of \((1+x)^{21}+(1+x)^{22}+\ldots . .+(1+x)^{30}\) is

119569 If \(y=3 x+6 x^2+10 x^3+\ldots . . . \infty\), then is \(\frac{1}{3} y-\frac{1.4}{3^2 2} y^2+\frac{1.4 .7}{3^2 3} y^3 \ldots . . \infty\) is equal to

119570 The sum of the series
\(\sum_{\mathrm{r}=0}^{\mathrm{n}}(-1)^{\mathrm{r}} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{\mathbf{2}^{\mathrm{r}}}+\frac{\mathbf{3}^{\mathrm{r}}}{\mathbf{2}^{2 \mathrm{r}}}+\frac{\mathbf{7}^{\mathrm{r}}}{\mathbf{2}^{3 \mathrm{r}}}+\frac{\mathbf{1 5}^{\mathrm{r}}}{\mathbf{2}^{4 \mathrm{r}}}+\ldots . \mathrm{m} \text { terms }\right)\)
is