Solution:

EAT

Explanation:
EAT becomes ATE simply my moving letter 'E' at the end

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules

Solution:

There are 3 fruits (1 grapes, 1 apples, and 1 oranges).

Solution:

2003.

Explanation:
Its a series of prime numbes.

Solution:

16

Explanation:
9 [1x1] squares
5 [2x2] squares
1 [4x4] square
1 [4x4] square

9 + 5 + 1 + 1 = 16 squares.

Solution:

Hockey Stick $49.50 & ball $0.50

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

The equation can be solved by substituting
B = 7
A = 8
S = 8
E = 3
L = 5

Therefore the equation now looks as:
7483 +
7455
-------
14938
-------

Solution:

You must put labels on the tablets as A and B before using. In that case, if you pour tablets together, you will get 3A, 2A 1B, 1A 2B or 3B. If they are from the same bottles you can take one from another bottle and save the remaining two for another day. If you get two from same and one from other, you can draw one from another bottle and you will have two pairs of which you can eat one and save the other.