previous question papers

• 222 ^222 divided by 7 wt is remainder
  Asked In TCS
  222=31*7+5
  31*1+5 when divided by 7 gives 5 as remainder
  
  =>5^222
  now 5^2^111
  =>25^111
  (7*3+4)^111 when devided by 7 gives 4 as remainder
  
  =>4^2^55*4^1=16^55*4^1
  =>(7*2+2)^55 when devided by 7 gives 2 as remainder
  =>2^55*4=2^54*2*4=2^54*8=8^18*8
  
  hence 8^18*8=(7+1)^18*8 when divided by 7 gives 1^18*8
  =>8
  
  and when 8 is divided by 7 gives 1 as remainder.
  
  Hence answer will be 1.
  1700 lottery tickets are sold for $25 each, and one grand prize of $4100 is awarded. If you purchase one ticket, find your expectation per ticket.
  expectation= prob of wining * rewards
  here,
  expectation =1/1700 * 4100 = 2.41
  but ticket cost $25 each
  now expectation here = 2.41 - 25 = -22.59(ans)
  1! + 2! + ��. + 50!=?
  Asked In TCS
  1! = 1 (units digit 1)
  2! = 2 (units digit 2)
  3! = 6 (units digit 6)
  4! = 24 (units digit 4)
  5!, 6!.... the units digit will be 0 because all the terms will include 5x2=10
  
  units digit of 1!+2!+... will be 1+2+6+4+0+0+0.... = 3
  
  
  
  how many different digit number are there which have digit 1,2,3,4,5,6,7,8, such that digit 1 appears exactly once
  
  its answer is 4c1 *7^3 how? why 4c1 is use here .?
  Digit 1 can appear in any of the 4 positions of a 4 digit number => 4C1
  
  Further,as repetition is allowed,the othe three digits can have any of the remaining 7 numbers
  
  So total no of different 4 digit numbers possible = 4C1 * 7 * 7 *7 = 4C1 * 7^3
  3. (209*144)^2 + (209*209)+(209*144)+(144*144) = ? a)905863729 b)905368729 c)905729368 d)65
  Answer will be a)905863729 by digit sum method
  A pizza shop made pizzas with many flavours. There are 9 different flavors, in that 2 flavors are taken to make pizza. In how many ways they can arrange?
  9c2=36
  . A car manufacturer produces only red and blue TCS Models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come throughthe test area at any one time?
  p(5 consecutive cars of same color)=p(5 red)+p(5 blue)
  =1/2^5+1/2^5
  =1/16
  Metal strip of width �x� cm. 2 metal strips are placed one over the other, then the combine length of 2 strips is �y�. If �z� strips are placed in that manner. What is the final width of that arrangement?
  as we observe in question that when 2 metal strips are placed one over the other then combine length is 2 but width doesnt change so any many no. of strip u place over the metal length only changes but not the width so ans is X
  . Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? a)1/2 b)1/6 c)1/12 d)6/10
  Coin has 2 Faces probability of it showing correct option is 1/2
  how many divisors are there for 1758
  Asked In TCS
  1758 = 2*3*293
  293 is a prime no.
  so the no. of divisors is given by
  (1+1)*(1+1)*(1+1) = 8
  
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