JEE Previous Year Question
The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1,2,3,4,5,7and 9 is_____.
Topic: JEE PYQ
Answer: 576. Full step-by-step solution below.
Correct answer: 576
Solution
(576)Digits are 1, 2, 3,4,5,7, 9
Multiple of 11 Difference of sum at even & odd place is divisible by 11.
Let number of the form abcdefg
(a + c + e + g)-(b + d + f)=11x
a + b + c + d + e + f=31
either a + c + e + g = 21 or 10
b + d + f= 10or21
Case- 1
a + c + e + g = 21
b + d + f= 10
(b,d, f) {(1,2, 7) (2, 3, 5) (1,4, 5)}
(a, c, e, g) {(1, 4, 7, 9), (3, 4, 5, 9), (2, 3, 7, 9)}
Total number in case-1 = (3! x 3) (4!) = 432
Case-2
a + c + e + g = 10
b + d + f=21
(a,b,e,g) {1,2,3,4)}
(b,d,f) &{(5,7,9)}
Total number in case 2 = 3! x 4! = 144
Total numbers = 144 + 432 = 576
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