Solution:

We agree that the series is quite difficult to crack and much tricky as well.

1 can be written as one (consist of 3 letters)
2 can be written as two (consist of 3 letters)
3 can be written as five (consist of 5 letters)
4 can be written as four (consist of 4 letters)
5 can be written as five (consist of 5 letters)
6 can be written as six (consist of 3 letters)

Thus the next term in the series is 3.

Solution:

W02

F21: Friday the 21st.
S23: Sunday the 23rd.
T25: Tuesday the 25th.
T27: Thursday the 27th.
S29: Saturday the 29th.
M31: Monday the 31st.

Avoiding every other day, the next term must be 'Wednesday the 2nd' i.e. 'W02'

Solution:

Did you consider the fact that we could be talking months here?
January - 31 days
February - 28 days
March - 31 days
April - 30 days
May - 31 days

Thus the next number in the sequence will be 31.

Solution:

This sequence is a bit tricky while you may be running in myriad directions, the actual trick to solve this sequence might as well prove to be a bit annoying to you.

So what do we have common in the physical appearance of all the letters of the sequence? Did you think that all of them are made with straight lines?

Consider the in between letters - B, C, D and G. All of them require curvy lines to write but A, E, F and H can be written with straight lines.

Thus the next letter in the sequence will be 'I'.

Solution:

This is quite a tricky puzzle and quite hard to deduce at first impression.

What you have to do is write the number in English
For the first case, 1 and 2 produce 9
1 = One
2= Two
There are three characters in both one and two
3x3 = 9

Similarly for the second case, 3 and 4 produce 20
3 = Three
4 = Four
Three has 5 characters and four has 4 characters
5x4 = 20

Now for the question, seventeen has 9 characters and twelve has 6 characters, thus the missing number is the product of 9 and 6 which is 54.

Solution:

This series can be quite tricky at first glance so look closely. It is almost the same number only, the lowest digit of the previous one is missing from the next.

Thus the next after 975 will be 97 as 5 is the lowest digit.

Solution:

Duck

Look closely at the series. Consider the second letter of every animal's name. You will see that they are vowels and that too in alphabetical order.
fAwn
bEar
lIon
mOle

Thus, the next animal must have U as the second letter and hence dUck is the right answer.

Solution:

4 + 44 + 444 + ....

= 4 [1 + 11 + 111 + ....]

= (4/9) [9 + 99 + 999 + ....]

= (4/9) [(10 - 1) + (10^2 - 1) + (10^3 - 1) + ... + (10^n - 1) ]

= (4/9) [(10 + 10^2 + 10^3 + ... + 10^n) - ( 1 + 1 + 1 + ... n times ) ]

= (4/9) {10 [(10^n - 1 ) / ( 10 - 1 ) ] - n(1) }

= (4/9) [(10/9) (10^n - 1) - n ]
= (4/81) [10^(n+1)-9n-10]

Thus option C is correct.

Solution:

This is a bit difficult series to crack and often puts the interviewee under pressure.

0 is the base one and something you need not focus on as it will be zero no matter what you do.
0.577 is the root of (1/3)
1 is the root of 1
1.732 is the root of 3

If you see the pattern, you will find that at every step the root digit is getting multiplied by 3.

Thus the next digit must be the root of 3*3 = 9
Root of 9 = 3 which is the next number in the sequence.

Solution:

The next two numbers will be 42 and 47.
If you look closely, you will see that the following numbers are either a multiple of 7 or the next digit with a 7 in it.