Prove that `(666 …. "to n digits")^(2) +`(888 …. To n digits ) = (444 … to 2n digits ).

Prove that (666....6)^2+(888....8)=4444.....4.

Find the number of n digit numbers, which contain the digits 2 and 7, but not the digits 0, 1, 8, 9.

Find the number of n digit numbers, which contain the digits 2 and 7, but not the digits 0, 1, 8, 9.

Let ' m ' denotes the number of four digit numbers such that the left most digit is odd, the second digit is even and all four digits are different and ' n ' denotes the number of four digit numbers such that left most digit is even, second digit is odd and all four digit are different. If m=nk, then k equals :

If n is a one-digit positive integer, what is n? (1) The units digit of 4^n is 4. (2) The units digits of n^4 is n.

If a_na_(n-1)a-(n-2),.,a_3,a_2,a-1 be a digit having a_1,a_2,a_3,…..a_n unit, tens hundreds places respectively. Then a_n a_(n-1) a_(n-2)….a_3a_2a_1= a_nxx1+a_2xx10^2+a_3xx10^3+…..+a_n10^(n-1) On the basis of above information answer the following question If alpha= 888.....8 (a nunmber of n digits), beta=666.........6 (a number of n digits) and gamma=444.......4 (a number 2n digits) then gamma-alpha= (A) beta (B) beta^2 (C) - beta (D) -beta^2

N is a two - digits number having sum of the digits as S and porduct of digits as P . How many such two -digit numbers exist such that 2N = 2S + 3P ?

A two digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits . Find the two digits number.

The number of 5-digit number that can be made using the digits 1 and 2 and in which at laest one digits is different, is

Prove by using the principal of mathematical inductions 4+ 44 +444+ ….+ 444…4 ( n digits ) = ( 4)/(81) (10 ^(n+1) - 9n -10)