જો left( {begin{array}{*{20}{c}}
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Question

$\left( {\begin{array}{*{20}{c}}
  {n\, - \,1} \ 
  r 
\end{array}} ight)\, = \,\left( {\,{k^2}\, - \,3\,} ight)\,\left( {

Vedclass · Accepted Answer

$( - 2, - \sqrt 3 ]\,\, \cup \,\,[\sqrt 3 ,2)$

Vedclass · Answer

$\left( {\begin{array}{*{20}{c}}
  {n\, - \,1} \ 
  r 
\end{array}} ight)\, = \,\left( {\,{k^2}\, - \,3\,} ight)\,\left( {\begin{array}{*{20}{c}}
  n \ 
  {r\, + \,1} 
\end{array}} ight)$

$\frac{{\left( {\begin{array}{*{20}{c}}
  {n\, - \,1} \ 
  r 
\end{array}} ight)}}{{\left( {\begin{array}{*{20}{c}}
  n \ 
  {r\, + \,1} 
\end{array}} ight)}}\, = \,{k^2}\, - \,3\,$

$\frac{{(n\, - \,1)!}}{{(n\, - \,1\, - \,r)\,!\,r\,!}}\, 	imes \,\frac{{(n\, - \,r\, - \,1)\,!\,(r\, + \,1)!}}{{n!}}\, = \,{k^2}\, - \,3\,\,$

હવે $0 \leq  r \leq  n - 1  $   $ 1 \leq r + 1 \leq  n  $

$\frac{1}{n}\, \leqslant \,\frac{{r\, + \,1}}{n}\, \leqslant \,1\,\,\,$

$\,0\, < \,\frac{{r\, + \,1}}{n}\, \leqslant \,1$

$3 < {k^2} \leqslant 4\,$

$k \in [ - 2, - \sqrt 3 ) \cup (\sqrt 3 ,2]$

જો $\left( {\begin{array}{{20}{c}}
{n\, - \,1} \\
r
\end{array}} \right)\,\, = \,\,\left( {\,{k^2}\, - \,3\,} \right)\,\,\left( {\begin{array}{{20}{c}}
n \\
{r\, + \,1}
\end{array}} \right)\,$ તો $k\, \in \,\,..........$

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એક જૂથમાં $4$ કુમારીઓ અને $7$ કુમારી છે. જેમાં ઓછામાં ઓછી $3$ કુમારી આવેલ હોય એવી $5$ સભ્યોની કેટલી ટુકડીઓ બનાવી શકાય.

જો $\left( {\begin{array}{{20}{c}}
{189} \\
{35}
\end{array}} \right) + \left( {\begin{array}{{20}{c}}
{189} \\
x
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{190} \\
x
\end{array}} \right)\,\,$ હોય તો ,$x\, = \,\,.........$

જો $\left( {\begin{array}{*{20}{c}} {n\, - \,1} \\ r \end{array}} \right)\,\, = \,\,\left( {\,{k^2}\, - \,3\,} \right)\,\,\left( {\begin{array}{*{20}{c}} n \\ {r\, + \,1} \end{array}} \right)\,$ તો $k\, \in \,\,..........$

Similar Questions

એક જૂથમાં $4$ કુમારીઓ અને $7$ કુમારી છે. જેમાં ઓછામાં ઓછી $3$ કુમારી આવેલ હોય એવી $5$ સભ્યોની કેટલી ટુકડીઓ બનાવી શકાય.

જો $\left( {\begin{array}{*{20}{c}} {189} \\ {35} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {189} \\ x \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {190} \\ x \end{array}} \right)\,\,$ હોય તો ,$x\, = \,\,.........$

જો $\left( {\begin{array}{{20}{c}}
{n\, - \,1} \\
r
\end{array}} \right)\,\, = \,\,\left( {\,{k^2}\, - \,3\,} \right)\,\,\left( {\begin{array}{{20}{c}}
n \\
{r\, + \,1}
\end{array}} \right)\,$ તો $k\, \in \,\,..........$

જો $\left( {\begin{array}{{20}{c}}
{189} \\
{35}
\end{array}} \right) + \left( {\begin{array}{{20}{c}}
{189} \\
x
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{190} \\
x
\end{array}} \right)\,\,$ હોય તો ,$x\, = \,\,.........$