Number of permutations of 1, 2, 3, 4, 5, 6, 7, 8, and 9 taken all at a time are such that the digit 1 appearing somewhere to the left of 2 3 appearing to the left of 4 and 5 somewhere to the left of 6, is `kxx7!` Then the value of `k` is _________.

Number of permutations of 1,2,3,4,5,6,7,8 , and 9 taken all at a time are such that digit 1 appearing somewhere to the left of 2 and digit 3 appearing to the left of 4 and digit 5 somewhere to the left of 6 , is (e.g. 815723946 would be one such permutation)

Mode of .2, 7, 5, 3, 7, 1, 6, 9, 7, 3, 6, 3 is

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9} . Find A′.

The H.M of 7 values 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 and 1/8 is

The points ( 5 , 2 , 4) , ( 6 , - 1 , 2) and ( 8 , - 7 , k) are collinear if k=

Union,of {1, 3,5, 7,..} and {2, 4, 6, 8,..} is

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 } . Find A ∩ B and hence show that A ∩ B = B .

The points (5, 2, 4), (6, -1, 2) and (8,-7, k) are collinear if k =

The number of four-digit numbers that can be formed by using the digits 1,2,3,4,5,6,7,8 and 9 such that the least digit used is 4 , when repetition of digits is allowed is

A={1,2,3,4,5,6,7,8,9,10}, B={2,3,5,7}. Find A cap B