Solution:

J = 1
O = 9
I = 6
N = 8
T = 3
(1+9+6+8+3)*(1+9+6+8+3)*(1+9+6+8+3) = 19683.

Solution:

It is possible when you write the numbers in their Roman form.
XI (11) - When you remove me from XI, it becomes X i.e. 10
IX (9) - When you remove me from IX, it becomes X i.e. 10

Solution:

Your friend's statement is actually true and it's not different from what you have answered.

25 - 55 + (85 + 65) = 25 - 55 + 150 = 120 = 5!
5! (factorial) = 5 * 4 * 3 * 2 * 1 = 120

Yes, that was a tricky question, quite capable to confuse anybody.

Solution:

   9567
+ 1085
======
 10652

Solution:

As shown below, we can make equation as 6 = 6 = 6.

Solution:

9 x 8 - 7 + 6 x 5 - 4 = 91.

Solution:

Solution well explained in picture below.

Solution:

{a +b +abs (a-b)}/2
It is shown that {a +b-abs (a-b)}/2 is < {a, b}

Solution:

6/(1 - 3/4) = 24

Solution:

We have provided you with one of the possible solutions. However, there can be three more solutions to this problem.