The number of positive divisors of 2⁵3⁶7³ is

A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 crew of which 2 can stroke only, 1 can row only while 3 can steer only. In how many ways the crew can be arranged for the boat?

A fruit basket contains 4 oranges, 5 apples, 6 mangoes. The number of ways a person make selection of fruits from among the fruits in the basket is

A double decked bus can accommodate 100 passengers, 40 in the upper deck and 60 in the lower deck. In how many ways can a group of 100 passengers be accommodated if 15 refuse to sit in the lower deck and 20 refuse to sit in the upper deck?

A set contains (2n+1) elements. The number of subsets of the set which contain most n elements is

There are 3 routes from Tenali to Vijaywada and 4 routes from Vijaywada to Hyderabad,in how many different ways a person can travel from Tenali to Hyderabad via Vijaywada?

The number of ways in which an examiner can assign 30 marks to 8 questions giving not less than 2 marks to any question is

There are 12 boys to be seated on 2 benches, 6 on each bench. Two of them desire to sit on one bench and two others on the other. The number of ways in which the boys can be seated on the two benches is

In how many ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book?

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only three digits 2,5 and 7. The smallest value of n for which this is possible is