Today's 5 questions

1.     Find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13

2.     5789^(1!+2!+3!-------+1000!)has the unit digit of ?

3.     Let N be the product of five different odd prime numbers. If N is the five-digit number abcab, 4 < a < 8, how many values of N are possible?
a. 1 
b. 2 
c. 3 
d. 4 
e. more than 4

4.     My grandfather said he was 84 years old but he was not counting the Sundays. How old my grandfather really was? 
a. 96 
b. 97 
c. 98 
d. 64

5.     There is a natural number that becomes equal to the square of a natural no when 100 is added to it and square of another no when 169 is added to it. Find the number.