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A natural number N has ‘k’ distinct prime factors. If the total number of factors of N is 72, then what is the product of all the possible values of k?

10000! = (100!)^K Ă— P, where P and K are integers. What can be the maximum value of K?

18^2000+12^2000-5^2000-1 is divisible by

a)323
b)221
c)299.
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Find the number of three-digit numbers that can be expressed as the sum of four consecutive,five consecutive and seven consecutive positive integers.

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A school having 270 students provides facilities for playing four games Cricket, Football, Tennis and Badminton. There are a few students in the school who do not play any of the four games. It is known that for every student in the school who plays at least N games, there are two students who play at least (N 1) games, for N = 2, 3 and 4. If the number of students who play all the four games is equal to the number of students who play none, then how many students in the school play exactly two of the four games?

a30
b60
c90
d120
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A and B are stationed at two points Q and R respectively on a flowing river.The direction of flow of river is from Q to R.When A and B swim towards each other,they meet at P,which is at a distance of 20m from the point R.When A swims towards B and B swims away from A,they meet at S,which is at a distance of 40m from the point R.B's speed in still water is five times the speed at which the river flows.

1)Find the ratio of speeds of A and B in still water
a)6:1
b)7:1
c)8:1
d)5:1

2)On a particular day A and B start swimming towards each other simultaneosly from the points where they are stationed.When A was 'y'm away from the point P,B turns back and they meet at the point R.Find the value of y.
a)52m
b)56m
c)58m
d)60m
e)none of these
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