Answer:
(a) We have, 5445 \[\begin{matrix} 5 & 4 & 4 & 5 \\ \downarrow & \downarrow & \downarrow & \downarrow \\ E & O & E & O \\ \end{matrix}\] where, O = Odd and E = Even Sum of digits at odd places from right = 5 + 4 = 9 Sum of digits at even places from right = 4 + 5 = 9 Now, difference = 9 ? 9 = 0, so 5445 is divisible by 11. (b) We have, 10824 \[\begin{matrix} 1 & 0 & 8 & 2 & 4 \\ | & | & | & | & | \\ O & E & O & E & O \\ \end{matrix}\] Sum of digits at odd places from right = 4 + 8 + 1 = 13 Sum of digits at even places from right = 2 + 0 = 2 Now, difference = 13 ? 2 = 11, so 10824 is divisible by 11. (c) We have, 7138965 \[\begin{matrix} 7 & 1 & 3 & 8 & 9 & 6 & 5 \\ | & | & | & | & | & | & | \\ O & E & O & E & O & E & O \\ \end{matrix}\] Sum of digits at odd places from right = 5 + 9 + 3 + 7 = 24 Sum of digits at even places from right = 6 + 8 + 1 = 15 Now, difference = 24 ? 15 = 9 \[\because \] 9 is not a multiple of 11, so 7138965 is not divisible by 11. (d) We have, 70169308 \[\begin{matrix} 7 & 0 & 1 & 6 & 9 & 3 & 0 & 8 \\ | & | & | & | & | & | & | & | \\ E & O & E & O & E & O & E & O \\ \end{matrix}\] Sum of digits at odd places from right = 8 + 3 + 6 + 0 = 17 Sum of digits at even places from right = 0 + 9 + 1 + 7 = 17 Now, difference = 17 ? 17 = 0 \[\therefore \] 70169308 is divisible by 11. (e) We have, 10000001 \[\begin{matrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ | & | & | & | & | & | & | & | \\ E & O & E & O & E & O & E & O \\ \end{matrix}\] Sum of digits at odd places from right = 1 + 0 + 0 + 0 = 1 Sum of digits at even places from right = 0 + 0 + 0 + 1 = 1 Now, difference = 1 ? 1 = 0, so 10000001 is divisible by 11. (f) We have, 901153 \[\begin{matrix} 9 & 0 & 1 & 1 & 5 & 3 \\ | & | & | & | & | & | \\ E & O & E & O & E & O \\ \end{matrix}\] Sum of digits at odd places from right = 3 + 1 + 0 = 4 Sum of digits at even places from right = 5 + 1 + 9 = 15 Now, difference = 15 ? 4 = 11, so 901153 is divisible by 11.
You need to login to perform this action.
You will be redirected in
3 sec