Question

Number of 6 digit numbers divisible by 11 made by using digits 0, 1, 2, 5, 7, 9 without repetition is equal to

• A. 60
• B. 55
• C. 120
• D. 62

Answer 1

Answer: (A)

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 odd and even places equ 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 $=24+36=60$