Question

The number of $6$ digit numbers that can be formed using the digits $0,1,2,5,7$ and $9$ which are divisible by $11$ and no digit is repeated, is :

• A. 36
• B. 60
• C. 48
• D. 72

Answer 1

Answer: (B)

Find the total number of ways
Given digits are $0,1,2,5,7$ and 9
The number is said to be divisible 11 if the difference between the sum of digits at the o. 0 or divisible by 11
Let the six digit number be $=$ xyzuvw
The difference of $(y+u+w)-(x+z+v)=0$ or divisible by 11
Using the above digits
Case - I $\{x,z,v\}=\{9,2,1\},\{b,d,f\}=\{7,5,0\}$
Numbers can be formed $=3!\times 3!=36$
Case - II $\{a,c,e\}=\{7,5,0\},\{b,d,f\}=\{9,2,1\}$
Numbers can be formed $=2\times 2!\times 3!=24$
$\therefore$ The total numbers can be formed $=24+36=60$