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Thread: TestFunda Answers - Higher Maths

  1. #1901
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    Post TestFunda Answers - Higher Maths

    The number of teams for 8 rounds is: 
    256->128->64->32->16->8->4->2->1
    Thus initially ter wer 256 teams.

    But wat is askd is the numbr of matches that were played to reach the winner.
    The number of matches for 8 rounds is:
    128->64->32->16->16->8->4->2->1

    128+64+32+16+8+4+2+1=255

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    Post TestFunda Answers - Higher Maths

    100 men and women dance with each other.probability that a man cannot dance with more than two women

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    Post TestFunda Answers - Higher Maths

    If a pipe can fill the tank within 6 hrs but due to leak it took 30 min more now if the tank was full how much time will it take to get emptied through the leak????

  4. #1904
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    Post TestFunda Answers - Higher Maths

    Since the HCF of A and 1250 is 1, ths means that both A and 1250 are co-primes to each other. Now 1250 has 2 & 5 as its factors, so A cannot have these.
    Thus A would be all multiples of 3 between 3 & 500 (165 in all)
    all multiples if 7 between 3 & 500 (71 in all)
    all multiples of 11 between 3 & 500 (45 in all) and so on...

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    Post TestFunda Answers - Higher Maths

    Let P = volume of water filled in 1 hour
    L =  Leakage of water in 1 hour

    then P = 1/6       ------(i)

    and P + L = 1/6.5      -------(ii)

    now subtract eq. (i) from eq. (ii), we get
    L = (1/6.5) - (1/6)
     
    L = -1/18

    Thus the leak alone can remove 1/18 units of water in an hour. Thus it'll take 18 hours to empty the tank.

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    Post TestFunda Answers - Higher Maths

    determine the no. of divisors of 2012^8 tat are less than 2012^4.

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    Post TestFunda Answers - Higher Maths


    how many pair of postive integers (a,b) are there such tat their lcm is 2012.



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    Post TestFunda Answers - Higher Maths

    WHAT is the sum of all natural no. which are less than 2012 and co-prime to it.

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    Post TestFunda Answers - Higher Maths

    The possible sets are :
    2012 and (1,2,4,503,1006) ie 5
    1006 and 4 ie 1
    503 and 4 ie 1
    So total sol = 7

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    Post TestFunda Answers - Higher Maths

    2012 = 2.2.503
    numbers less than 2012 and not coprime with it are :
    2,4,6,.............,2012    and 503,1509
    Required ans :
    SUM (1,2,.....2012) - Sum(2,4,6,,,,,2012) - 2012
    =
    1010024

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    Post TestFunda Answers - Higher Maths


    Divisors of 2012^8 :
    2^16.503^8 ie 17*9=  153 
    Divisors of 2012^4 :
      2^8.503^4  ie 9*5 = 45
    Now number of divisors of  2012^8 which are less than 2012^4 = (153-1)/2 =76   (As it its root ie 2012^4 lies in midway of its divisors)
    AlSo number of divisors of 2012^8 that are less than 2012^4 but are not divisors of 2012^4 = 76-45 = 31 


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    Post TestFunda Answers - Higher Maths

    The possible sets are :
    2012 and (1,2,4,503,1006) ie 5
    1006 and 4 ie 1
    503 and 4 ie 1
    So total sol = 7

  13. #1913
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    Post TestFunda Answers - Higher Maths

    2012 = 2.2.503
    numbers less than 2012 and not coprime with it are :
    2,4,6,.............,2012    and 503,1509
    Required ans :
    SUM (1,2,.....2012) - Sum(2,4,6,,,,,2012) - 2012
    =
    1010024

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    Post TestFunda Answers - Higher Maths

    A father of 6 children takes 2 of his children at a time to a circus as often as he can, without taking the same pair of children together more than once. How many times does the father go to the circus?

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    Post TestFunda Answers - Higher Maths

    . By using 1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation of no. is allowed??

  16. #1916
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    Post TestFunda Answers - Higher Maths

    Okay I am sleepy,so there is a slight chance that I could miss something.The answer should be 4! = 24. Isn't ?

  17. #1917
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    Post TestFunda Answers - Higher Maths

    There is very fast solution for this general problem,say we have to find for N then the answer is \frac{1}{2} \times N \times Eulertotient[N].

    This may looks scary but this should take 10 secs to solve.

    For this problem all I have to multiply is 2102 \times 502 = 1010024. 

  18. #1918
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    Post TestFunda Answers - Higher Maths

    Dirrect method for solving this is \lfloor \frac{\sigma_{0}(N^2)}{2}\rfloor.

    PS: http://codecogs.com/latex/eqneditor.php

  19. #1919
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    Post TestFunda Answers - Higher Maths


  20. #1920
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    Post TestFunda Answers - Higher Maths


    I have made a minute error in the earlier latex equation the correct one is \lceil \frac{\sigma_0(N^2)}{2} \rceil

    For this question the  number of solution is 8,the other answer misses (2012,2012) pair! Thanks.


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