series

✅ The correct answer is option A.
Numbers are alternatively multiplied by 3 and divided by 2.
So, the next number = 54 ÷ 2 = 27.

✅ The correct answer is option B.
There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.

✅ The correct answer is option C.
Numbers are 12, 22, 32, 42, 52, 62, 72.
So, the next number is 82 = 64.

✅ The correct answer is option C.
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.
So, the next number is 8 x 9 = 72.

✅ The correct answer is option A.
Terms at odd places are 5, 6, 7, 8 etc. and each term at even place is 16.
So, 9 is wrong.

✅ The correct answer is option C.
Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 100.

✅ The correct answer is option B.
Numbers are (23 – 1), (33 – 1), (43 – 1), (53 – 1), (63 – 1), (73 – 1) etc.
So, the next number is (83 – 1) = (512 – 1) = 511.

✅ The correct answer is option A.
Subtract 20, 25, 30, 35, 40, 45 from successive numbers.
So, 0 is wrong.

✅ The correct answer is option D.
2nd term = (1st term) x 3 – 4 = 10 x 3 – 4 = 26.
3rd term = (2nd term) x 3 – 4 = 26 x 3 – 4 = 74.
4th term = (3th term) x 3 – 4 = 74 x 3 – 4 = 218.
5th term = (4th term) x 3 – 4 = 218 x 3 – 4 = 650.
5th term must be 650 instead of 654.

✅ The correct answer is option D.
The numbers are 7 x 8, 8 x 9, 9 x 10, 10 x 11, 11 x 12, 12 x 13.
So, 150 is wrong.