The given number series is 3, 11, 80, 291, 803

$$\begin{gathered} 3 \\ 3 + 2 3 = 3 + 8 = 11 \\ 11 + 4 3 = 11 + 64 = 75 ( not 80 ) \\ 75 + 6 3 = 75 + 216 = 291 \\ 291 + 8 3 = 291 + 512 = 803 \end{gathered}$$

Given the number series is 4, 6, 12, 30, 81, 315.

Here it follows a pattern that

4

4 x 1.5 = 6

6 x 2 = 12

12 x 2.5 = 30

30 x 3 = 90 not equals to 81

90 x 3.5 = 315

Hence the odd one in the series is 81.

Given number sequence is 28, 16, 28, 76, 274

Here the sequence follows a pattern that

28

28 x 0.5 + 2 = 14 + 2 = 16

16 x 1.5 + 4 = 24 + 4 = 28

28 x 2.5 + 6 = 70 + 6 = 76

76 x 3.5 + 8 = 266 + 8 = 274

274 x 4.5 + 10 = 1233 + 10 = 1243

Hence, the next number in the given number sequence is 1243.

The given series is 1/2, 1, 3/2, 6, 5/2, 3

1/2

1/2 + 1/2 = 1

1 + 1/2 = 3/2

3/2 + 1/2 = 2 (Not 6)

2 + 1/2 = 5/2

5/2 + 1/2 = 3

Hence, the odd man in the given number series is 6.

Here the given series 28, 12, 4, 2, -2 follows a pattern that

$$\begin{gathered} 28 \\ 28 - 2 4 = 28 - 16 = 12 \\ 12 - 2 3 = 12 - 8 = 4 \\ 4 - 2 2 = 4 - 4 = 0 ( NOT 2 ) \\ 0 - 2 1 = 0 - 2 = - 2 \end{gathered}$$

Hence, the odd man in the given series is 2.

Here the given series 222, 271, 308, 332, 348, 357 follows a pattern that

222

222 + 49  271

271 + 36 = 307 (NOT 308)

307 + 25 = 332

332 + 16 = 348

348 + 9 = 357

Hence, the odd man in the fiven number series is 308.

The given number series is 14, 27, 105, 525, 4993

14

14 x 2 - 1 = 27

27 x 4 - 3 = 105

105 x 6 - 5 = 625 (not 525)

625 x 8 - 7 = 4993

Hence, the odd man or number in the given number series is 525.