1) If (67⁶⁷ + 67) is divided by 68, the remainder is :

2) If m and n are natural numbers such that 2^m – 2ⁿ = 960, what is the value of m ?

5) The least number of five digit is exactly divisible by 88 is :

6) The smallest 4-digit number exactly divisible by 7 is :

7) The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, then the dividend is :

8) In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48, then the dividend is :

11) If n is any positive integer, 3⁴ⁿ – 4³ⁿ is always divisible by :

13) A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :

14) A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when numbers is divided by 6 ?

15) 7386038 is divisible by :

16) The number of terms between 11 and 200 which are divisible by 7 but not by 3 are :

17) The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :

18) The difference between the square of two consecutive odd integers is always divisible by :

19) The difference between two numbers is 1365. When the large number is divided by the smaller one, the quotient is 6 and the remainder is 15. What is the smaller number ?

20) The number of digits in the smallest number, which when multiplied by 7 yields all nines, is :

21) A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :

23) The smallest 6-digit number exactly divisible by 111 is :

28) The sum of the digits of a natural number (10ⁿ – 1) is 4707, where n is a natural number. The value of n is :

29) 111, 111, 111, 111 is divisible by :

30) The difference between the squares of any two consecutive integers is equal to :

31) How many 3-digit numbers are there in between 100 and 300, having first and the last digit as 2 ?

32) How many numbers will be there between 300 and 500, where 4 comes only one time ?

33) The product of any three consecutive natural numbers is always divisible by :

34) The numbers 2272 and 875 are divided by a three-digit numbers N, giving the same remainder. The sum of the digits of N is :

35) Which one of the following numbers is divisible by 15 ?

36) The value of 5² + 6² + …. + 10² + 20² is :

37) Which is not a prime number ?

38) Let a number of three digits have for its middle digit the sum of the other two digits. Then it is a multiple of :

39) 136 × 12 × 8 = ?

40) A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer both 9’s are wrong but the other digits are correct, then the correct answer will be :

41) If a number 774958A96B is divisible by 8 and 9, the respective values of A and B will be :

44) If n is a whole number greater than 1, then n² (n² – 1) is always divisible by :

45) The sum of digits of a two-digit number is 12 and the difference between the two-digits of the two-digit number is 6. What is the-digit number ?

46) The unit’s digit in the product 274 × 318 × 577 × 313 is :

48) Find the least 6-digit number which is exactly divisible by 349 ?

49) The remainder when 7⁸⁴ is divided by 342 is :