Q1:

Find the numbers of prime factors of 4004

Q2:

Two numbers in base B are 504 and 625. If the sum of these numbers in the decimal system is 562. Find the base (B).

Q3:

For two positive numbers a and b, ${(a+b)}^{a+b}$ is divisible by 729. Find the minimum value of (a$\times$b)

Q4:

In an apartment block there are 10 residents. The number of cars owned by the residents is 15. Four of the residents do not own any car, exactly 3 own one car each and one person owns 4 cars. What may be the maximum number of cars owned by any resident?

Q5:

The number ${(12ABC7)}^X$ ends in 1. What is the remainder if D121 if divided by x if A, B, C, D and x are all single digit positive integers?

Q6:

If 1+2=5,2+4=20, 4+9=97 then find 7+8?

Q7:

A and B are two single digit numbers. If A+B is divided by 7 remainder is 4 and when A-B is divided by 7 remainder is 3. Find the remainder obtained when (AB) is divided by 7.

Q8:

Find the remainder when $34\times 68\times 199\times 45\times 53$ is divided by 33

Q9:

P689K862K is divisible by 16. Find the maximum value of P x K

Q10:

How many divisors of N=420 will be of the form 4n+1, where n is a whole number?

Q11:

How many zeros will be there at the end of $1003\times 1001\times 999\times \mathrm{.......}\times \mathrm{123?}$

Q12:

How many numbers of zeros are there at the end of 32! In base 4?

Q13:

How many divisors of ${10}^{\mathrm{5 }}$will have atleast one zero in its end?

 

Q14:

In a book 648 digits are used to count number of pages. Find the number of pages the book has?

Q15:

Instead of multiplying from 3/2, a boy divided the number by 2/3. The new number he obtained is.