JEE PYQ: Permutation And Combination Question 36
Question 36 - 2019 (10 Apr Shift 1)
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:
(1) 72
(2) 60
(3) 48
(4) 36
Show Answer
Answer: (2)
Solution
Divisibility by 11: (sum of odd-placed digits) $-$ (sum of even-placed digits) $= 0$ or $\pm 11$. Total digit sum $= 24$. Need $S_{\text{odd}} - S_{\text{even}} = 0$ or $\pm 11$. Possible: $(1, 2, 9)(0, 5, 7)$, $(0, 5, 7)(1, 2, 9)$. Arrangements: $= 3! \times 3! \times 2 \times 2 - $ accounting for 0 not in first position. Each valid partition gives $3! \times 3! - 2 \times 2! \times 3! = …$. Total $= 60$.
BETA
