CBSE 11TH MATHEMATICS - Online Test

Total possibilities  of 5 digit numbers which can be formed using the given digits are 5!= 120 ways.

But since the number should be greater than 56000 we cannot have the numbers starting with 4 or 54

The combinations in which the number 4 comes at the start  is 4!  = 24 ways.

The combinations in which the number 54 comes at the start  is 2! = 6

Hence the numbers greater than 56,000 = 120 - ( 24+ 6) = 120 - 30 = 90 ways.

Total no of subsets=2n=24=16

Here n is the Cardinal no of the Given Set

We have 2 + x < 6

⇒2 + x −2< 6−2

 ⇒x<4

Now 2−3x<−1⇒2−3x−2<−1−2⇒−3x<−3⇒−3x−3>−3−3⇒x>1

Hence the solution of the given system of equations is given by 1<x<4,xϵZ⇒x=2,3