Three a's, three b's and three c's are placed randomly in `3xx3` matrix. The probability that no row or column contain two identical letters can be expressed as `(p)/(q)`, where p and q are coprime then `(p+q)` equals to :

India and Australia play a series of 7 one-day matches. Each team has equal probability of winning a match. No match ends in a draw. If the probability that India wins atleast three consecutive matches can be expressed as (p)/(q) where p and q are relatively prime positive integers. Find the unit digit of p.

Three different numbers are selected at random from the set A={1,2,3,……..,10} . Then the probability that the product of two numbers equal to the third number is (p)/(q) , where p and q are relatively prime positive integers then the value of (p+q) is :

Show that 1. 272727=1. 27 can be expressed in the form p/q , where p and q are integers and q!=0.

Show that 0. 3333. . . .=0. bar3 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 1. 272727=1. bar27 can be expressed in the form p/q , where p\ a n d\ q are integers and q!=0.

Show that every square matrix A can be uniquely expressed as P+i Q ,where P and Q are Hermitian matrices.

Show that 1. 272727. . .=1. bar 27 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 0. 2353535. . .=0. 2 bar 35 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 0. 2353535. . .=0. 2 bar 35 can be expressed in the form p/q , where p and q are integers and q!=0 .

Let p(x) be a polynomial of degree 4 such that P(1)=P(3)=P(5)=P'(7)=0. If the real number ane1,3,5 is such that P(a)=0 can be expressed as a=(p)/(q) , where p and q are relatively prime, then (p-8q) is……….