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Mathematics Test 86

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Mathematics Test 86
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Weekly Quiz Competition
  • Question 1
    4 / -1

    How many numbers can be possible by using digits 3, 4, 5, 6, 7, 8 which are greater than 750000, if repetition is not allowed :-

  • Question 2
    4 / -1

    The number of ways of selecting a committee of 4 women and 5 men from 10 women and 9 men, if Mrs. A refuses to serve on the committee if Mr. B is a member of the committee, is :-

    Solution

    10C49C5 – 9C38C4 = 26460 – 5880

    = 20580

     

  • Question 3
    4 / -1

    Number of ways in which 5 alike red balls and 6 alike green balls can be arranged so that no two red balls are together, is-

  • Question 4
    4 / -1

    The 60 permutations of ALLEN are arranged in dictionary order, as if each were on ordinary five letter word. The last letter of word which occurs at 23rd position is :-

  • Question 5
    4 / -1

    A man invites a party to (m + n) friends to dinner and places m at one particular round table and n at another. The number of ways of arranging the guest are :-

  • Question 6
    4 / -1

    The maximum number of intersection points of five line and four circles is :-

  • Question 7
    4 / -1

    Number of positive integral solution of the equation xyz = 90 is equal to :-

  • Question 8
    4 / -1

    The coefficient of t50 in

    (1 + t2)25 (1 + t25) (1 + t40) (1 + t45) (1 + t47) is

    Solution

    As we are interested in coefficient of t50, we shall ignore all the term with exponent more than 50. Thus we can write as

    (1 + 25C1t2 + ..... + 25C25t50) × (1+t25+t40+t45+t47)

    As all the terms in the first have even exponent we can ignore t25, t45 and t47 too thus coefficient of t50 is

    = 25C25 + 25C5 = 1 + 25C5

     

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