How many parallelograms are formed by a set of 4 parallel lines intersecting on other set of 7 parallel
lines ?
ans126
7. If A works total in 10 days and B works total in 15 Days. If A+B of cost is Rs. 5000 then what is the
share of B ?
ans 2000
8. Remainder of 2^47/47 ?
ans 2
9. How many arrangements will start and end with a vowel for TOGETHER ?
ans 1080
10. IF X^Y denotes X raised to the power Y, Find the last two digits of (1941 ^ 3843 ) + (1961 ^4181 ) .
ans 82
11. When the number is written in base b, we have 12*25 =333. The value of b is ?
ans 7
12. Find the 25th word if the word RANKED is arranged in dictionary order....TCS Placement Paper
ans AEDKNR
13. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining
work in 3 days. How long does it need for B if he alone completes the work?
ans 37 1/2
14. 302th of 1st year is saturday. What is the 15th day of 5th Year ?
ans Wednesday
15. 1*1!+2*2!+3*3!................2012*2012!= ????
ans 2013!-1
16. There is a tank, and two pipes A and B. A can fill tank in 25mins and B can empty the tank in 20
minutes . If both the pipes are opened at same time. How much time required the tank can fill ??

17. At the end of 1994 Rohit was half as old as his grandmother. The sum of the years in which they born
is 3844. How old Rohit was at the end of 1999?
ans 53 Years
18. A person starts writing all the 4 digits number , how many times he has written the digit 2 ?
ans 3700
19. If the lcm of 2 natural numbers A and B is 1260, what is the minimum possible value of A+B ?
ans71
20. Let n be a natural number, then n(n*n-1) is always divisible by ?

21. There is a circle with 2 triangles inscribed in it in opposite directions making a star. The triangle is
equlateral of side 12. You have to tell the area of the remaining portion of the circle ?
22. For which of the following number 2^74 + 2^2058 + 2^2 a perfect square ?
a) 2012
b) 2100
c) 2010
d) 2010TCS Placement Paper
23. The last digit of the expression 4+92+43+94+45+96+.......+499+9100 is ?
24. 2^74 + 2^2058 + 2^2n. what is d value of n make it perfect square ??
25. If 50% of the 2:3 solution of milk and water is replaced with water. What is the concentration of the
solution is required ?
26. 4kg of metal contains 1/5 copper and rest is zinc. Another 5 Kg of metal contains 1/6 of copper and
rest is zinc. The ratio of copper and zinc into the mixture of these two metals ?
27. In what proprotion water to be mixed with spirit to gain 12.5% by selling it at cost price ?
28. A number has exactly 3 prime factors, 125 factors of this number are perfect cubes, total how many
factors does this number have ?
29. How many 8 digits numbers can be formed with repetition by using 1,2,3,4,5 which are divisible by 4
?
30. In a race, Mohan beats Sohan by 40m and Sohan beats Rohan by 80m. Mohan beats Rohan by 104m.
Find the length of the race in m ?

• 7) A=10 days
  B= 15 days
  A:B = 10:15 =2:3
  So 2x+3x=5000=> x= 1000
  A’s share = 2000
  B’s share = 3000
  --------------------------------
  8) 2 as a^p – a is dividable by p when p is prime
  ------------------------------------------------------------------------
  9) TOGETHER
  Starting with ‘O’ = 6!/2! =360
  Starting with ‘E’ the last letter is either ‘O’ or’E’ = 2*(6!/2!) = 720
  360+720=1080
  ---------------------------------
  10) Take last 2 digit of 1941 and take last 2 digits of 1961
  41^1=41 r=1 61^1=61 r=1
  41^2=81(take last 2 digits of ans)r=2 61^2=21 r=2
  41^3=21 r=3 61^3=81 r=3
  41^4=61 r=4 61^4=41 r=4
  41^5=01 r=0 61^5=01 r=0
  41^6=41 61^6=61
  hence power cycle is repeating and it is 5 hence for 1961 it is 5
  r-remainder for 1961 power cycle-5
  for 1941 power cycle-5, 4181 mod 5=rem 1=61
  3843 mod 5=rem 3=21
  therefore 21+61=82
  ----------------------------------
  11) let base be x
  convert all the num to base x
  (1*x+2*x^0)*(2*x+5*x^0)=(3*x^0+3*x^1+3*x^2)
  solving X=7
  ---------------------------------
  12) Words starting with A……..is 120
  we have to find the 25th word in dictionary order.
  so obviously words start with A.
  the there are 24 words starting with AD…
  there are again 24 words starting with AE…..
  so 25th word will be started with AE..
  now we have to find the 25th word
  that will be AEDKNR
  -------------------------------
  13) Work done by A in 20 days = 80/100 = 8/10 = 4/5
  Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)
  Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
  Work done by A and B in 1 day = 1/15 —(2)
  Work done by B in 1 day = 1/15 – 1/25 = 2/75
  So B can complete the work in 75/2 days = 37 (1/2) days
  ---------------------------------------------------------------------------------------
  14) ans Wednesday
  -------------------------------
  15)n*n!+(n+1)*(n+1)!+------+(n+m)*(n+m)! = (n+m+1)!-1=2012+1=2013!-1
  --------------------------------------------------------------------------------------------------------
  16) the tank can never be filled because the emptying pipe (B) takes lesser time than filling pipe (A)
  => 1/25 - 1/20 = -1/100
  -------------------------------------------------
  17) grandmother =x ;; rohit =x/2
  1994-x +1944- x/2 = 3844
  3988-3844=x+x/2
  144=3x/2
  X=96
  Rohit = x/2 = 96/2=48
  Rohit @1994 =48
  @1999 =48+5=53
  -------------------------------
  18) Work done by A in 20 days = 80/100 = 8/10 = 4/5
  Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)
  Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
  Work done by A and B in 1 day = 1/15 —(2)
  Work done by B in 1 day = 1/15 – 1/25 = 2/75
  So B can complete the work in 75/2 days = 37 (1/2) days
  ----------------------------------------------------------------------------------
  19) Factors of 1260 are 2*2*3*3*7*5
  Now minimum possible two numbers A and B formed from these factors are
  7*5=35=A
  2*2*3*3=36=B
  so minimum value of A+B is 71
  -------------------------------------------
  20) n(n*n-1)=n^3-n=(n-1)(n)(n+1)
  any 3 consecutive natural numbers product is divisible by 6
  -------------------------------------------------------------------------------------------
  21) sqrt(3)/4)*(a*a)=1/2 * 12(base) * altitude
  so altitude is=6sqrt(3)
  now the small triangle below that altitude having the altitude is
  (sqrt(3)/4)*(a*a) where a=4 because all 12 triangle is equilateral = 1/2 * 4(base) * altitude
  sp altitude=2sqrt(3)
  so diameter of circle=6sqrt(3) + 2sqrt(3) = 8sqrt(3)
  so radius is = 4sqrt(3)
  remaining area= 22/7 * r * r - 12* (sqrt(3)/4) * a * a where a=4
  so ans is=67.718
  -------------------------------------
  22) a^2 + 2ab + b^2 = (a+b)^2
  Here, 2^74 + 2^2058 + 2^2 = (2^37)^2 + 2*2^37*2^2020 + (2^1)^2
  If the number is a perfect square, then 2^1 should equal 2^2020.
  Hence, 1=2020
  -----------------------------------------------------------------------------------------------
  23) 43+45+………499 are in a.p.
  n/2(2a+(n-1)d)
  last digit of this sum is 9.
  Similarly 92+94+………..9100.
  Last digit of this sum is 0.
  So 9+4+0 = 13.
  3 is last digit.
  -----------------------------------------
  24) a^2 + 2ab + b^2 = (a+b)^2
  Here, 2^74 + 2^2058 + 2^2n = (2^37)^2 + 2*2^37*2^2020 + (2^n)^2
  If the number is a perfect square, then 2^n should equal 2^2020.
  Hence, n=2020
  ----------------------------
  25) milk:water=2:3 =40:60
  take out 50 %(50 ltr means milk=20 ltr water=30 ltr) remaining
  milk:water=20:30
  add 50 ltr of water
  ratio
  milk:water=20:(30+50) =20:80
  1:4
  so initially milk= 40%
  after milk=20%
  so reduction in concentration= 20%
  ---------------------------------------------------
  26) 4kg of a metal contains 1/5 ‘parts of ‘ copper and rest is zinc. another 5kg of metal contains 1/6 ‘parts of ‘of copper and rest is zinc.
  Then amt of copper in 4 kg mixture = 4/5 kg.
  Then amt of zinc in 4 kg mixture = 16/5 kg
  Then amt of copper in 5 kg mixture = 5/6 kg
  Then amt of zinc in 5 kg mixture = 25/6 kg
  Ratio of copper to zinc in final mixture = (4/5 +5/6) : (16/5+25/6)
  = 49/30 : 221/30 = 49:221
  -----------------------------------------------------
  27)if the total quantity=100
  Actual quantity of spirit to be sold to get 12.5% gain=100*100/112.5=800/9
  So the water =100-(800/9)=100/9
  Proportion of water:spirit =100/9 : 800/9= 1:8
  -----------------------------------------------------------------
  28) Number of factors = either (2a)^n or (2a-1)^n
  Based on following conditions
  If 2(a-1) > 3(b-1) , then (2a-1)^n
  If 2(a-1) < 3(b-1) , then (2a)^n
  If 2(a-1) = 3(b-1) , then both are possible.
  Here 2(a-1) > 3(b-1)
  => no of factors = (2a-1)^n = 9^3= 729
  ---------------------------------------------------------
  29) last 2 digits can be 12, 24, 32, 44, 52 .
  so 5^(8-1) = 5^7
  =78125
  ----------------------------
  30) 40*80 /(40+80-104) = 3200/16 =200m
  --------------------------------------------------------------
• 10 years agoHelpfull: Yes(12) No(1)
• parallelogram qn => 4C2*7C2 = 6*21=126
• 10 years agoHelpfull: Yes(4) No(1)
• 30. 40*80 /(40+80-104) = 3200/16 =200m
• 10 years agoHelpfull: Yes(2) No(0)
• 10 sol : Remember 1 raised to any power will give 1 as unit digit.
  To find the digit in the 10th place, we have to multiply, 10th digit in the base and unit digit in the power.
  So the Last two digits of the given expression = 21 + 61 = 82
• 9 years agoHelpfull: Yes(1) No(0)
• 30.answer is 200
• 10 years agoHelpfull: Yes(0) No(0)
• 23.answer will be 0.
• 10 years agoHelpfull: Yes(0) No(2)
• distance=s*t.
  so, 18*(t+40*60)=28*t.
  solving we get 72 mins =1 hr 12 mins. so 7.12 pm
• 9 years agoHelpfull: Yes(0) No(0)