A) 8
B) 49
C) 50
D) 51
E) 52
Correct Answer: B
Solution :
\[(n+2)!=2550\times n!\] \[\Rightarrow \] \[(n+2)(n+1).n!=2550.n!\] \[\Rightarrow \] \[(n+2)(n+1)=2550\] \[\Rightarrow \] \[{{n}^{2}}+3n-2548=0\] \[\Rightarrow \] \[{{n}^{2}}+52n-49n-2548=0\] \[\Rightarrow \] \[n(n+52)-49(n+52)=0\] \[\Rightarrow \] \[(n+52)(n-49)=0\] \[\Rightarrow \] \[n=-52,49\] \[\Rightarrow \] \[n=49\] \[(here\,\,n\ne -52)\]You need to login to perform this action.
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