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The logic followed here is :-

COUNTRY : FRXQWUB 

Similarly,

EXAMINE : ?

Hence, the correct answer is "HADPLQH".

Thus, the correct answer is Optrion 2.

The logic followed here is :-  

​Logic: Split into two equal halves and interchange them (block shifting).

Given, KITCAT : CATTIK 

Break KITCAT into two equal blocks: KIT | CAT

Now reverse the order of the two blocks: CAT | KIT

So, CATTIK

Similarly,

Split into two equal halves: PEN | TOP

Reverse their order: TOP | PEN

Result → TOP + NEP = TOPNEP

Correct answer: TOPNEP (Option 2)

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: Letter ↓1, Number ↑1

Now, checking the options, we get:

Option 1) Z1# : Y2@ : X3$

Option 2) W4% : V5^ : U6&

Option 3) T7* : S8( : R9)

Option 4) Q10_ : P9@ : O8$

Here, numbers are decreasing, while in all other options numbers are increasing.

Hence, the one which is odd from the rest is "Option 4."

The logic followed here is:

Given:

dream focus build skill → trq, xnz, hmd, clv

focus logic dream → trq, jkp, xnz

trust logic build dream → xnj, clv, jkp, trq

Similarly,

build skill logic trust is codded as clv, hmd, jkp, xnj

Hence, the one which is odd from the rest is "Option 1."

Given:

x + 2y = 14

x − y = 5

Calculations:

From the second equation:

x = 5 + y

Substitute into the first equation:

5 + y + 2y = 14

5 + 3y = 14

3y = 9

y = 3

Now substitute back:

x = 5 + 3

x = 8

∴ The correct answer is 'Option 3.'

The logic followed here is:

Given:

If 6 $ 2 = 20, 

⇒ 6 x 2 = 12

⇒ 6 + 2 = 8

⇒ 12 + 8 = 20

and 4 $ 3 = 19,

⇒ 4 x 3 = 12

⇒ 4 + 3 = 7

⇒ 12 + 7 = 19

Similarly, 5 $ 2 = ?

⇒ 5 x 2 = 10

⇒ 5 + 2 = 7

⇒ 10 + 7 = 17

Hence, the correct answer is "Option 2."$

The logic followed here is:

Given:

'SAVE' is coded as '★3#5', 

S → ★

A → 3

V → #

E → 5

and  'VASE' as '#3★5',

V → # 

A → 3 

S → ★ 

E → 5 

Similarly, for  'EVAS'

E → 5

V → #

A → 3

S → ★

Here, the code for EVAS is 5#3★

Hence, the correct answer is "Option 4."

Given:

Let the two numbers be 3x and 5x (since ratio is 3 : 5).

Their sum is given as 64.

3x + 5x = 64

8x = 64

x = 8

Calculations:

Now find the numbers:

3x = 3 × 8 = 24

5x = 5 × 8 = 40

So, the two numbers are 24 and 40.

∴ The correct answer is "Option 1."

The logic followed here is:

Logic: the pattern is a @ b = a² + b

Given:

If 5 @ 3 = 28 , 

⇒ 5² + 3 = 25 + 3 = 28

and  4 @ 2 = 18,

⇒ 4² + 2 = 16 + 2 = 18 

Similarly,  6 @ 4 = ?

⇒ 6 @ 4 = 6² + 4

= 36 + 4

= 40

Hence, the correct answer is "Option 1."

Family Chart:

Given: 

"She is the daughter of my mother's only son."

→ My mother’s only son = I (the man himself).

So, The girl is his daughter.

Hence, the correct answer is "Option 1".