How many six-digit numbers are there in which no digit is repeate… - Vidyadip

MCQ

How many six-digit numbers are there in which no digit is repeated, even digits appear at even places, odd digits appear in odd places and the number is divisible by $4$ ?

A
$3600$
B
$2700$
C
$2160$
✓
$1440$

✓

Answer

Correct option: D.

$1440$

d
(d)

$6-$digit number are there in which no digits is repeated and even digits appear on even places and odd digits appear in odd place. Such $6$ digit number which is divisible by $4$. If last two digits are divisible by $4$

i.e. $12,16,32,36,52,56,72,76,92,96$

$\therefore$ Last digits appears only $2$ and $6$

$3$ way $3$ ways $4$ ways $4$ way $5$ way $2 / 6$

$Total numbers =3 \times 3 \times 3,5,7,9$

$=1440$

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