જો $C_r= ^{100}{C_r}$ , હોય તો $1.C^2_0 - 2.C^2_1 + 3.C^2_3 - 4.C^2_0 + 5.C^2_4 - .... + 101.C^2_{100}$ ની કિમત મેળવો 

  • A

    ${100.^{100}}{C_{50}}\,\,\,$

  • B

    ${51.^{100}}{C_{50}}\,\,\,$

  • C

    ${100.^{200}}{C_{100}}\,\,\,$

  • D

    ${51.^{200}}{C_{100}}\,\,\,$

Similar Questions

જો ${\sum\limits_{i = 1}^{20} {\left( {\frac{{{}^{20}{C_{i - 1}}}}{{{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3}\, = \frac{k}{{21}}$ હોય તો $k$ ની કિમત મેળવો. 

  • [JEE MAIN 2019]

વિધાન $1$: $\mathop \sum \limits_{r = 0}^n \left( {r + 1} \right)\left( {\begin{array}{*{20}{c}}n\\r\end{array}} \right) = \left( {n + 2} \right){2^{n - 1}}$

વિધાન $2$:$\;\mathop \sum \limits_{r = 0}^n \left( {r + 1} \right)\left( {\begin{array}{*{20}{c}}n\\r\end{array}} \right){x^r}\; = {\left( {1 + x} \right)^n} + nx{\left( {1 + x} \right)^{n - 1}}$

  • [AIEEE 2008]

ધારોકે $\sum \limits_{r=0}^{2023} r^{2023} C_r=2023 \times \alpha \times 2^{2022}$, તો $\alpha$ નું મૂલ્ય $............$ છે.

  • [JEE MAIN 2023]

$\left( {\begin{array}{*{20}{c}}{20}\\0\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\1\end{array}} \right)$$+$$\left( {\begin{array}{*{20}{c}}{20}\\2\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\3\end{array}} \right)$$+…..-……+$$\left( {\begin{array}{*{20}{c}}{20}\\{10}\end{array}} \right)$ નો સરવાળો. 

  • [AIEEE 2007]

$(1-x)^{100}$ ના દ્વિપદી વિસ્તરણમાં પ્રથમ $50$ પદોના સહગુણકોનો સરવાળો $.......$ છે.

  • [JEE MAIN 2023]