Question Bank - Number Theory


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Number of Questions : 15
    Topic : Number Theory
    Answer key available ? : Yes (Last Post)
    Source :


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q1) From a set of first 20 consecutive positive integers, 3 are picked randomly and their sum is found as S. How many different values of S are possible?
    A. 18
    B. 52
    C. 57
    D. 1140


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q2) TGₐ is a two digit number in base-a such that T > 0 and T, G < a. For which value of TG, can TGₐ be a perfect square in some base-a?
    A. 32
    B. 43
    C. both of these
    D. none of these


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q3) Find the remainder when 484848 is divided by 728.
    A. 0
    B. 28
    C. 48
    D. none of these


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q4) How many distinct integers are there in the sequence [1²/100], [2²/100], [3²/100], [4²/100]... [100²/100] where [x] is greatest integer less than or equal to x?
    A. 75
    B. 76
    C. 100
    D. 101


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q5) Sum of ten consecutive integers is N. What is the sum of next ten consecutive integers?
    A. 2N
    B. N + 45
    C. N + 55
    D. N + 100


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q6) How many 21 digit numbers are there whose first 10 digits are 1 each and last 10 digits are 2 each and also the complete 21 digit number is divisible by 7?
    A. 0
    B. 1
    C. 2
    D. 3


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q7) What is the highest possible common factor of two consecutive terms of a sequence whose nth term is given by n² + 10?
    A. 1
    B. 2
    C. 41
    D. 59


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q8) On planet LOGIKA, an alien digit φ is being used between 3 and 4 along with all the usual digit we use on earth. What will be the age of a 94 years old inhabitant of LOGIKA on earth?
    A. 103
    B. 104
    C. 114
    D. 115


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q9) Nimai wrote all natural numbers, none of whose digits is a prime number, in order. First ten numbers which Nimai wrote are as follows: 1, 4, 6, 8, 9, 10, 11, 14, 16, 18. What is the 123rd number, Nimai might be writing?
    A. 646
    B. 666
    C. 816
    D. 840


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q10) What is the highest power of 2 which divides [10²ºººº/(10¹ºº + 2)] completely where [x] is greatest integer less than or equal to x?
    A. 99
    B. 100
    C. 199
    D. 200


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q11) Number of factors of 12100 which are less than 110 but not factors of 110 is
    A. 6
    B. 7
    C. 8
    D. 9


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q12) For how many positive integers, N there are odd number of factors of N² + 3N + 13?
    A. 0
    B. 1
    C. 2
    D. 3


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q13) Find the remainder when 6{(p - 4)!} is divided by p where p is a prime number greater than 2013.
    A. 0
    B. 1
    C. p - 1
    D. none of these


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q14) Number of factors of P is Q. Number of factors of Q is R. Number of factors of R is S and number of factors of S is 3. If P is smallest such number then what is the sum of digits of P?
    A. 3
    B. 6
    C. 9
    D. 12


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 15) In how many ways can 100 be written as sum of two or more consecutive odd integers?
    A. 2
    B. 3
    C. 4
    D. 5


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Answer Key:

    #1. B 52
    #2. D none of these
    #3. A 0
    #4. B 76
    #5. D (N + 100)
    #6. C 2
    #7. C 41
    #8. D 115
    #9. A 646
    #10. C 199
    #11. A 6
    #12. B 1
    #13. B 1
    #14. B 6
    #15. D 5



  • @kamal_lohia 20C3..how come 52 is the ans?



  • @kamal_lohia Option A 0 is the answer



  • @kamal_lohia (N+100)


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