Question

please help me to solve this

Answer 1

(1) Refer https://brainly.in/question/15617319

(2) Refer https://brainly.in/question/15724141

(3) The $\displaystyle\sf {(r+1)^{th}}$ term in the expansion of $\displaystyle\sf {(3+2x^2)^4}$ is,

$\displaystyle\longrightarrow\sf {T_{r+1}=\ ^4C_r\cdot3^{4-r}\cdot(2x^2)^r}$

$\displaystyle\longrightarrow\sf {T_{r+1}=\ ^4C_r\cdot2^r\cdot3^{4-r}\cdot x^{2r}}$

For getting coefficient of $\displaystyle\sf {x^4,}$

$\displaystyle\longrightarrow\sf {2r=4}$

$\displaystyle\longrightarrow\sf {r=2}$

Hence the coefficient is,

$\displaystyle\longrightarrow\sf {C(T_3)=\ ^4C_2\cdot2^2\cdot3^2}$

$\displaystyle\longrightarrow\sf {\underline {\underline {C(T_3)=216}}}$

(4) Refer https://brainly.in/question/15722367

(5) The expansion contains 8 terms, so 4th and 5th terms are the middle terms. Thus,

$\displaystyle\longrightarrow\sf {T_4=\ ^7C_3\cdot(x^3)^{7-3}\cdot\left (\dfrac {1}{x}\right)^3}$

$\displaystyle\longrightarrow\sf {\underline {\underline{T_4=35x^9}}}$

And,

$\displaystyle\longrightarrow\sf {T_5=\ ^7C_4\cdot(x^3)^{7-4}\cdot\left (\dfrac {1}{x}\right)^4}$

$\displaystyle\longrightarrow\sf {\underline {\underline{T_5=35x^5}}}$