$(\alpha + p)^{m - 1} + (\alpha + p)^{m - 2} (\alpha + q) + (\alpha + p)^{m - 3} (\alpha + q)^2 + ...... (\alpha + q)^{m - 1}$ 

વિસ્તરણમાં $\alpha ^t$ નો સહગુણક મેળવો.

જ્યાં $\alpha \ne - q$ અને $p \ne q$  

  • A

    $\frac{{^m{C_t}\,\,\left( {{p^t}\, - \,{q^t}} \right)}}{{p\, - \,q}}$

  • B

    $\frac{{^m{C_t}\,\,\left( {{p^{m\, - \,t}}\, - \,{q^{m\, - \,t}}} \right)}}{{p\, - \,q}}$

  • C

    $\frac{{^m{C_t}\,\,\left( {{p^t}\, + \,{q^t}} \right)}}{{p\, - \,q}}$

  • D

    $\frac{{^m{C_t}\,\,\left( {{p^{m\, - \,t}}\, + \,{q^{m\, - \,t}}} \right)}}{{p\, - \,q}}$

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શ્રેણી $\frac{{{C_0}}}{2} - \frac{{{C_1}}}{3} + \frac{{{C_2}}}{4} - \frac{{{C_3}}}{5} + $..... ના $(n + 1)$ પદનો સરવાળો કરો.

ધારો કે  $\alpha=\sum_{k=0}^n\left(\frac{\left({ }^n C_k\right)^2}{k+1}\right)$ અને  $\beta=\sum_{k=0}^{n-1}\left(\frac{{ }^n C_k{ }^n C_{k+1}}{k+2}\right)$. છે. જો  $5 \alpha=6 \beta$, હોય તો  $n$=...........................

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$\sum\limits_{k = 0}^{10} {^{20}{C_k} = } $

$^n{C_1}\sum\limits_{r = 0}^1 {^1{C_r}} { + ^n}{C_2}\left( {\sum\limits_{r = 0}^2 {^2{C_r}} } \right){ + ^n}{C_3}\left( {\sum\limits_{r = 0}^3 {^3{C_r}} } \right) + ......{ + ^n}{C_n}\left( {\sum\limits_{r = 0}^n {^n{C_r}} } \right)$ ની કિમત મેળવો 

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