Question

\({\rm{Find\;the\;unit\;place}}.{\rm{\;}}\frac{{ - 1!{\rm{\;}} + {\rm{\;}}2! - 3!{\rm{\;}} + {\rm{\;}}4! - 5!{\rm{\;}} + {\rm{\;}}6! - \ldots \ldots \ldots \ldots \ldots \ldots .99!}}{{60}}\)
1. 16
2. 15
3. 19
4. 17

Answer 1

Correct Answer - Option 3 : 19

Calculation:

\( \Rightarrow \frac{{ - 1!{\rm{\;}} + {\rm{\;}}2! - 3!{\rm{\;}} + {\rm{\;}}4! - 5!{\rm{\;}} + {\rm{\;}}6!{\rm{\;}} + {\rm{\;}} \ldots \ldots \ldots \ldots \ldots \ldots .99!}}{{60}}\) 

\( \Rightarrow - \;\frac{1}{{60}}\; + \;\frac{2}{{60}} - \;\frac{6}{{60}}\; + \;\frac{{24}}{{60}} - \;\frac{{120}}{{60}}\; + \;\frac{{720}}{{60}}\; + \; - - - - - - - - - \) 

⇒ Unit place = - 1 + 2 - 6 + 24 - 0 + 0 + -----------

⇒ Unit place = - 1 + 2 - 6 + 24 = 19

∴ the unit place is 19.