Logic:

(X), (X³ - 1)

Checking all the options:

(1) 7, 342 → (7), (73 - 1)

(2) 5, 124 → (5), (53 - 1)

(3) 3, 26 → (3), (33 - 1)

(4) 2, 15 → (2), (X⁴ - 1)

Here, '2, 15' is different from the others.

Hence, the correct answer is "Option (4)".

Family Chart:

Decoding the Symbols:

Given: A + B % C = D # F

It means: A is the Daughter of B, B is the Brother of C, C is the Son of D, D is the Wife of F.

Here, F is the 'Father’s father' of A.

Hence, the correct answer is "Option 3".

Preparing the family according to the symbols:

According to the statement:

Raj grandfather has a son Ajay. Ajay has one daughter and one son. Raj is pointing towards his sister.

Hence, the correct answer is "Sister".

The logic followed here is : 

1. First letter - Shifted to the third position.
2. Second letter - Shifted to first position.
3. Third letter - Shifted to second position.
4. Fourth and fifth letter - No change
5. Sixth and seventh letter - Interchange position with each other.
6. Eighth and ninth letter - Interchange position with each other.

So,

• ‘HYPOCRISY’ is written as ‘YPHOCIRYS’

​Similarly,

• ‘INTEGRITY’ is written as:

Logic : Letters are written in the reverse order within the word.

​So,

• ‘APPRECIATE’ is written as ‘ETAICERPPA’

Given:

YUA, SOC, MIE, GEG, ?

Logic:

Here, 'AAI' is the correct answer as per logic.

Hence, the correct answer is "AAI".

Given series : I _ F I _ N D _ F _ I N N _ I F F _ N _ D

After filling in the blanks with letters given in the option we get, 

1. D D F F I D N

I D F I D N D F F F I N N I I F F D N N D → Doesn't follow any pattern

2. F F I I D N N

I F F I F N D I F I I N N D I F F N N N D → Doesn't follow any pattern.

3. I D D F I D N

I I F I D N D D F F I N N I I F F D N N D → Doesn't follow any pattern.

4. F N I F D I N

I F F I N N D /  I F F I N N D  / I F F I N N D → A particular pattern is repeating itself.

Hence, "Option 4" is the correct answer.

As given 10th September 1994 = Friday

∵ 10th September to 20th October 1994 = 40 days ÷ 7 = 5 odd day

So the day on 20th October 1994 = Friday + 5 odd days = Wednesday

Now the day on 20th October 1995 = Thursday (As the number of odd days in complete year = 365/7 = 1)

Hence the correct answer is "Thursday".

According to the English alphabets and their positional values:

The pattern followed in the given codes is:

The alphabets are decreased to 1 positional value.

First & third and fourth & sixth alphabets are interchanged.