Solution:

As shown in the picture below, you should tilt the barrel so the liquid will touch the upper end of the barrel. So if the bottom part of the barrel is visible then it's not half full.

Solution:

4%

Explanation:
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.

Solution:

They were the same person "Grover Cleveland".

Solution:

The pregnant lady.

The detective Byomkesh Bakshi noticed that the pregnant women look 6-7 months pregnant in January, May, and even in July. So that pregnant lady is the thief we are looking for and must be faking her pregnancy.

Solution:

450

Explanation:
60 / 2(10+5) = ?
60 / 2(15) = ?
60 / 2 x 15 = ?
Using the BODMAS rule, we need to apply division first.
30 x 15 = ?
450 ..... The Answer

Solution:

Batsman-8

1st over:
1st Ball, Batsman-1 got out
2nd Ball, Batsman-3 got out
3rd Ball, Batsman-4 got out
4th Ball, Batsman-5 got out
5th Ball, Batsman-6 got out
6th Ball, Batsman-7 got out

Before the start of a new over, the batsmen will swap strikes.
i.e Batsman-2 at nonstriker will become striker and batsman-8 will go at the nonstriker end.

2nd over:
1st Ball, Batsman-2 got out
2nd Ball, Batsman-9 got out
3rd Ball, Batsman-10 got out
4th Ball, Batsman-11 got out.

Solution:

So, for 100 tigers to catch 100 sheep, it would still take the same amount of time because each tiger is catching one sheep in 3 minutes. Therefore, it would take 3 minutes for 100 tigers to catch 100 sheep.

Solution:

7, 4, 6, 5, 8

Solution:

The next one is 8
77 : 7*7 = 49
49 : 4*9 = 36
36 : 3*6 = 18
18 : 1*8 = 8

Solution:

At that moment, the time, and day could be written as '12:34 5/6/78'