Formation of greatest and smallest numbers

(C) Smallest 7-digit number
$=1000000$
also $1+999999$
$=1000000$
So, answer is either A or B.

$\Rightarrow$  The given numbers are $9,,6,,0,,5,,8,,1$

Smallest  6  digit number that can be formed by the digits 9,6,0,5,8,1 is  1,05,689.  

Three digit numbers that can be formed from 0, 1 and 2 are $102$ and $201$.
So, (c) is not a three digit number.

The numbers formed by $2, 0$ and $3$ are $203, 302, 023, 320, 230$ and $032$.

$128$ can be written using the general form $abc = 100 \times  a + 10 \times  b + c$
By changing the alphabetic orders of $a, b, c$, we get $3$ more numbers from $3$ digit number.
Here, $281, 821$ and $182$ are formed from the $3$ digit number $128$.

L.C.M. of $8$, $16$, $40$ and $80 = 80$.
$\dfrac { 7 }{ 8 } =\dfrac { 70 }{ 80 }$; $\dfrac { 13 }{ 16 } =\dfrac { 65 }{ 80 }$; $\dfrac { 31 }{ 40 } =\dfrac { 62 }{ 80 } $

$\dfrac { 3 }{ 4 } =0.75,\quad \dfrac { 5 }{ 6 } =0.833,\quad \dfrac { 1 }{ 2 } =0.5,\quad \dfrac { 2 }{ 3 } =0.66,\quad \dfrac { 4 }{ 5 } =0.8,\quad \dfrac { 9 }{ 10 } =0.9$.

$3,9,7,8,6$

Consider the given digits.

$2,3,6,7$

the number formed using given digits are

Smallest three digit number which can be formed is if we arrange them in ascending order, i.e. $479$

According to given information
The $5$-digit number is even
$\therefore$ $5$th number will be $0$ or $2$ which are the only even numbers
So, the greatest $5$-digit even number that can be formed is $97520$

$ Let\quad the\quad number\quad be\quad written\quad as\quad follows\ Place\quad value\quad \longrightarrow Hundreds\quad \quad \quad Tens\quad \quad \quad Units\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad c\ Reversing\quad \longrightarrow \quad \quad \quad \quad \quad c\quad \quad \quad \quad \quad \quad \quad \quad b\quad \quad \quad \quad \quad \quad a\ \ Units\quad place:-\quad Given\quad a>c\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\quad \ \quad \quad c+10-a=4\ \Rightarrow a=c+6----(1)\ Tens\quad place:-\quad upper\quad row\quad b\quad has\quad become\quad b-1\ \therefore \quad We\quad borrow\quad 10\quad and\quad the\quad result\quad is\ \quad \quad (b-1+10)-b=9.\ Hundreds\quad place:-\quad a\quad has\quad become\quad a-1\ \therefore \quad (a-1)-c\quad is\quad the\quad result.\ Substituting\quad the\quad value\quad of\quad a\quad from\quad (1),\quad the\quad result\ will\quad be\quad c+6-1-c=5\ \therefore \quad The\quad other\quad two\quad numbers\quad are\quad 5,\quad 9\quad \quad (Ans)\ \quad \quad (i.e.\quad The\quad result\quad is\quad 594) $

Let the number be 10x + y (for 2 digits) or 100x + 10y + z (for 3 digits). Solving 10x + y = 6(x + y) gives 4x = 5y, so x=5, y=4 (number 54). Checking 3 digits: 100x + 10y + z = 6(x + y + z) leads to 94x + 4y = 5z, which has no solutions for digits x, y, z.

$400-9=391$

Smallest 7-digit number
$= 1000000$

The numbers formed by $4$,$6$ and $2$ are $462$ ,$264$ and $642$.

    It is clear from options.It is just expressed in mathematical form.