3, 10, 101,?

The digits are removed one by one from the beginning and the end in order alternately

so as to obtain the subsequent terms of the series.

The pattern is - 21, - 19, - 17, - 15,.....

So, missing term = 48 - 13 = 35.

P @ Q ? P is the wife of Q ...(1)

Q $ T ? Q is the brother of T ...(2)

T # U ? T is the daughter of U

Hence, ? Q is the son of U ...(3)

U * W ? U is the father of W.

From (1) and (3), U is the father-in-law of P.

M is the father of N and N is the son of V.

Hence, V is the mother of N.

From (1), P is the brother of V

Therefore, M is the brother-in-law of P because V is the wife of M.

From (2), the daughter of N, is the granddaughter of V. From this we do not get any relation of M to P.

Brother of mother means maternal uncle. Hence only nephew of Aamir's maternal uncle means Aamir himself. Therefore Sonia is the wife of Aamir.

Clearly, 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54,.....

So, the series is a G.P. in which a = 2, r = 3.

Therefore 8th term = ar^8-1 = ar⁷ = 2 x 3⁷ = (2 x 2187) = 4374.

The pattern is - 45, - 35, - 25, .....

So, missing term = 20 - 15 = 5.

The series consists of squares and cubes of consecutive natural numbers i.e. 1², 1³, 2², 2³, 3², 3³, 4², .....

So, missing term = 4³ = 64.

The pattern is x 2, x 3/2, x 2, x 3/2, x 2,.....

So, missing term = 18 x 3/2 = 27.

The pattern is x 2 + 1, x 2 - 1, x 2 + 1, x 2 - 1,.....

So, missing term = 101 x 2 + 1 = 203.