Binomial Theorem

 $The\ total\ no\ of\ terms\ in\ the\ \exp ansion\ of\ \left(x+a\right)^{51}-\left(x-a\right)^{51}\ is$  

• 102

• 25

• 26

• none of these

 $Given\ the\ integers\ r>1,n>2\ and\ cofficients\ of\ \left(3r\right)th\ and\ \left(r+2\right)th\ terms\ in\ the\ binomial\ \exp ansion\ of\ \left(1+x\right)^{2n}\ are\ equal\ then\ choose\ the\ correct\ option$  

• n=2r

• n=3r

• n=2r+1

• none of these

 $Fourth\ of\ the\ \exp ansion\ \left(\frac{x}{2}+y\right)^7\ is$  

•  $\frac{25x^3y^4}{16}$  

•  $\frac{35x^4y^3}{16}$  

•  $\frac{70x^4y^3}{16}$  

•  $\frac{35x^4y^3}{32}$  

 $Coefficient\ of\ x^{-3}\ in\ the\ \exp ansion\ of\ \left(x+\frac{1}{x^2}\right)^{9\ }is$  

• 126

• 125

• 126x

•  $125x^2$  

 $Positive\ value\ of\ m\ for\ which\ the\ coefficient\ of\ x^2\ in\ the\ \exp ansion\ of\ \left(1+x\right)^m\ is\ 6$  

•  $m=6$  

•  $m=5$  

•  $m=3$  

•  $m=4$  

 $The\ coefficient\ of\ x^n\ in\ the\ \exp ansion\ of\ \left(1+x\right)^{2n}\ and\ \left(1+x\right)^{\left(2n-1\right)}\ are\ in\ the\ ratio$  

•  $1:2$  

•  $1:3$  

•  $3:1$  

•  $2:1$  

 $The\ value\ of\ k,\ for\ which\ coefficient\ of\ x^2\ and\ x^3\ will\ be\ equal\ in\ the\ \exp ansion\ of\ \left(3+kx\ \right)^9is$  

•  $\frac{3}{7}$  

•  $\frac{7}{9}$  

•  $\frac{9}{7}$  

•  $\frac{7}{3}$  

 $The\ term\ independent\ of\ x\ in\ the\ \exp ansion\ of\ \left(x^3+\frac{3}{x^2}\right)^{15}\ is$  

•  $15_{C_9}\left(3\right)^9$  

•  $15_{C_6}\left(3\right)^6$  

•  $15_{C_9}\left(3\right)^4$  

•  $15_{C_9}\left(3\right)^7$  

 $The\ no\ of\ terms\ in\ the\ \exp ansion\ of\ \left(1+2x+x^2\right)^{20}is$  

•  $40$  

•  $20$  

•  $21$  

•  $41$