Find the difference between the roman numeration MMLXV and MCM. Hence convert the difference into binary. 2. Convert the Egyptian numeral ∩∩∩ ||||| into roman numerals. 3. Carry out the operation indi

MMLXV = M + M + L + X + V = $1000 + 1000 + 50 + 10 + 5 = 2065$

MCM = M + CM = $1000 + (1000 - 100) = 1000 + 900 = 1900$

Difference = $2065 - 1900 = 165$

Reading the remainders from bottom to top:
The difference in binary is $\boxed{\text{10100101}_2}$.

2. Convert the Egyptian numeral $\cap\cap\cap |||||$ into roman numerals.

The Egyptian numeral $\cap\cap\cap |||||$ represents:
$\cap$ (heel-bone) = 10
$|$ (single stroke) = 1
So, $\cap\cap\cap ||||| = (3 \times 10) + (5 \times 1) = 30 + 5 = 35$.

$35 = 30 + 5 = \text{XXX} + \text{V} = \text{XXXV}$.
The Roman numeral is $\boxed{\text{XXXV}}$.

3. Carry out the operation indicated in each of the following:

i. $334_5 + 224_5$

  334_5
+ 224_5
-------

Starting from the rightmost digit:
$4_5 + 4_5 = 8_{10} = 1 \times 5 + 3 = 13_5$. Write down 3, carry over 1.
$3_5 + 2_5 + 1_5 (\text{carry}) = 6_{10} = 1 \times 5 + 1 = 11_5$. Write down 1, carry over