Polynomials related Questions by Balaji

  • 8August
  • 2014
  • 12
    6.1k
    A 4 digit prime no when divided by 24 leaves a remainder r. how many possible values can r take ?



    a)7



    b)8



    c)9



    d)10





    answer choice b



    solution



    24k+r=prime

    r is not equal to 0

    r can be 1

    if r=2 then 24k+r will multiple of 2

    24k+3=3(8k+1)

    r has to be coprime with 24

    r can be 1,5,7,11,13,17,19,23



    8 values totally nothing pi (24)


     


     
    Give the 4 two digit factors of 7^100 - 5^100 ?


    a. 37,74,16,48



    b. 25,50,33,40



    c. none of the above 



    d. cannot be determined





    answer choice a



    solution



    dividend= (7^2)^50 - (5^2)^50



    dividend=(7^2)^25-(5^2)^25



    dividend=(2401)^25-(625)^25 



    this will divisibly by 2401-625=1776



    1776= 2*2*2*2*3*37



    hence 37,74,16,48


     
    what is the highest power of 24 that can divide 70! ?



    a. 20



    b. 22



    c. 25



    d. 33





    answer choice b



    solution



    highest power of 24 that divides 70!

    24=2^3*3



    highest power 3 in 70!



    70/3

    =23+ quotients

    =23+7+2+1

    =33



    (2^2*3)^22=2^66*3^22 divides 70!



    24^22 divides 70!