E=4*4! + 5*5! + 6*6! ........19*19!
Remainder when E is divided by 64
a)0 b)58 c)others

• ans: rem = 40
  
  E = 4*4! + 5*5! + 6*6! ........19*19!
  E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
  E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  E = (20!-4!)
  
  E/64 = (20!-4!)/64
  => rem = 0-24/64 = -24/64
  => rem = -24+64 = 40
• 9 years agoHelpfull: Yes(81) No(3)
• ans: rem = 40
  (4*4!+5*5!+6*6!+7*7!)/64 other terms contain 64 as a multiple in it, therefore they give 0 as a rem.
  (96+600+4320+35280)/64=40296/64=40 as rem.
  
• 9 years agoHelpfull: Yes(11) No(1)
• sry,ans = 40.. (96+600+4320+35280)/64 = 40 as rem
• 9 years agoHelpfull: Yes(2) No(1)
• (5*5!+6*6!+7*7!)/64 as other term will contain 64 as a multiple in it.
  (120*5+6*720*7*5040)/64
  (24+32+16)/64
  72/64
  hence 6 will be the remainder....
  
• 9 years agoHelpfull: Yes(1) No(4)
• (4*4!+5*5!+6*6!+7*7!)/64 other term will contain 64 as a multiple in it.
  (120+600+4320+35280)/64 = 0 as rem
• 9 years agoHelpfull: Yes(1) No(4)
• 
  E = 4*4! + 5*5! + 6*6! ........19*19!
  E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
  E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  E = (20!-4!)
  
  E/64 = (20!-4!)/64
  => rem = 0-24/64 = -24/64
  => rem = -24+64 = 40
• 9 years agoHelpfull: Yes(1) No(3)
• C other
  E can be written as(1!+2*2!+3*3!+4*4!......19*19!)-1+2*2!+3*3!
  20!-1-23
  20!*(-24)%64=-24=40
  Answer 40
• 9 years agoHelpfull: Yes(0) No(6)
• Sry mistake 20!-24%64=-24...so remainder=40
• 9 years agoHelpfull: Yes(0) No(3)
• E = 4*4! + 5*5! + 6*6! ........19*19!
  E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
  E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  E=5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20
  Sn=n*(n+1)/2
  E=20*21/2-(4+3+2+1)
  E=200/64
  REM=8
• 9 years agoHelpfull: Yes(0) No(9)
• 4!*(4+5*5+6*6*5+...)/64 i.e now took only 4!/64 which is 1/8
  hence (4+5*5+....)/8 i.e remainder not greater than 8
• 6 years agoHelpfull: Yes(0) No(0)
• Could anyone explain me how this is possible ?
  E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
  E = (20!-4!)
  since 5!-4!=5 similarly for all ..so shouldn't it be 5+6+7+8+..+20=200 ?
  200%64=40?
• 5 years agoHelpfull: Yes(0) No(0)
• Remainder is 40
• 3 years agoHelpfull: Yes(0) No(0)
• remainder is 40
• 3 years agoHelpfull: Yes(0) No(0)