If \( \left(1+2 x+3 x^{2}\right)^{10}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{20} x^{20} \), then
\(....
If \( \left(1+2 x+3 x^{2}\right)^{10}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{20} x^{20} \), then
\( \mathrm{P} \)
\( a_{1} \) equals
W
(1) 10
(2) 20
(3) 210
(4) 420
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2024-01-23 | If \( n \) is positive integer and if \( \left(1+4 x+4 x^{2}\right)^{n}=\sum_{r=0}^{2 n} a_{r} x.... |
| 2024-01-23 | Let \( F(n)=\sum_{r=0}^{n-1}\left(\frac{{ }^{n} C_{r}}{{ }^{n} C_{r}+{ }^{n} C_{r+1}}\right) \),.... |
| 2024-01-23 | If \( \sum_{r=0}^{10}\left(\frac{r}{{ }^{10} C_{r}}\right)=20 \), find the value of \( \sum_{r=0.... |
| 2024-01-23 | If \( { }^{m} C_{1}={ }^{n} C_{2} \), then correct statement is.... |
| 2024-01-23 | For a positive integer \( n \), if the expansion of
\( \left(\frac{5}{x^{2}}+x^{4}\right)^{n} \).... |
| 2024-01-23 | If \( (8+3 \sqrt{7})^{n}=P+F \), where \( P \) is an integer and \( F \) is
a proper fraction th.... |
| 2024-01-23 | The coefficient of \( a^{8} b^{6} c^{4} \) in the expansion of \( (a+b+c)^{18} \) is-.... |
| 2024-01-23 | Values of \( x \) for which the sixth term of the expansion of
\( E=\left(3^{\log _{3} \sqrt{9^{.... |
| 2024-01-23 | The middle term in the expansion of \( \left(x+\frac{1}{2 x}\right)^{2 n} \) is.... |
| 2024-01-23 | If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\ldots . .+C_{n} x^{n} \), then \( C_{0} C_{2} \)
\( +.... |
| 2024-01-23 | If \( \left(1+2 x+3 x^{2}\right)^{10}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{20} x^{20} \), then
\(.... |
| 2024-01-23 | \( 1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3 .5}{4.8 .12}+\ldots \ldots= \).... |
| 2024-01-23 | The sum of the numerical coefficients in the
expansion of \( \left(1+\frac{x}{3}+\frac{2 y}{3}\r.... |
| 2024-01-23 | If \( x+y=1 \), then \( \sum_{r=0}^{n} r^{2 n} C_{r} x^{r} y^{n-r} \) equals.... |
| 2024-01-23 | If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\ldots . .+C_{n} x^{n} \), then the
value of \( \mathr.... |
| 2024-01-23 | If \( T_{0}, T_{1}, T_{2}, \ldots \ldots T_{n} \) represent the terms in the expansion of \( (x+.... |
| 2024-01-23 | The number of terms whose values depend on \( x \) in the
expansion of \( \left(x^{2}-2+\frac{1}.... |
| 2024-01-23 | The term independent of \( x \) in the expansion of
\( \left(\frac{1}{2} x^{1 / 3}+x^{-1 / 5}\ri.... |
| 2024-01-23 | The coefficient of \( \frac{1}{x} \) in the expansion of
\( (1+x)^{n}\left(1+\frac{1}{x}\right)^.... |
| 2024-01-23 | The coefficient of \( x^{53} \) in the following expansion
\( \sum_{m=0}^{100}{ }^{100} C_{m}(x-.... |
| 2024-01-23 | The number of pairs \( (x, y) \), where \( x, y \in N \) such that
\begin{tabular}{|l|l|l|l|}
\h.... |
0