The correct answer is option 2 i.e. (4, 7, 65).

The logic used here is: (x, y, z) = x² + y² = z

(3, 5, 34)

Here, 3² + 5² = 9 + 25 = 34

Similarly, for (4, 7, 65):

4² + 7² = 16 + 49 = 65

Hence, the correct answer is (4, 7, 65).

The correct answer is option 1 i.e. 13.

Logic:

For ab : x → a² + b² = x

Given 54 : 41

5² + 4² = 25 + 16 = 41

Similarly;

3² + 2² = 9 + 4 = 13

32 : 13

Hence, the correct answer is 13.

The correct answer is option 3 i.e. Rajasthan.

Gol Gumbaz : Karnataka

Gol Gumbaz is in Karnataka.

Similarly,

Vijaya Stambh : ?

Vijaya Stambh is in Rajasthan.

Hence, the correct answer is Rajasthan.

The correct answer is option 1 i.e. YOIKBT.

The logic used here is:

Hence, the correct answer is YOIKBT.

The correct answer is option 3 i.e. M.

Given word: INTELLIGENCE

if consonant is changed to the next letter, and each vowel is changed to the previous letter. 

New word: HOUDMMHHDODD

Thus, M will be seventh from the right end.

Hence, the correct answer is M.

The correct answer is option 2 i.e. Seven.

Given word: KNOWLEDGE

After arranging it in alphabetical order from left to right, we get:

DEEGKLNOW

4th letter from the left end and the 2nd letter from the right end = G and O

Thus, seven letters are between G and O.

Hence, the correct answer is Seven.

The correct answer is option 2 i.e. ZOOM

Only the word ZOOM has two vowels and the rest words have only 1 vowel. Hence, ZOOM is the odd word.

Hence, the correct answer is ZOOM.

The correct answer is option 1 i.e. UPJ.

Given series: LVD, OTF, RRH, ?, XNL

L + 3 = O, O + 3 = R, R + 3 = U, U + 3 = X

V - 2 = T, T - 2 = R, R - 2 = P, P - 2 = N

D + 2 = F, F + 2 = H, H + 2 = J, J + 2 = L

Hence, the correct answer is UPJ.

The correct answer is option 3 i.e. 105.

17, 27, 45, 71, ?, 147

17 + 10 = 27

27 + 18 = 45; (10 + 8) = 18

45 + 26 = 71; (18 + 8) = 26

71 + 34 = 105; (26 + 8) = 34

105 + 42 = 147; (34 + 8) = 42

Hence, the correct answer is "105".

The correct answer is option 4 i.e. OSN.

In each consecutive term: The first letter is forwarded by 2, the second is forwarded by 1, and the third letter is pulled backward by 2.

GOV, IPT, KQR, MRP, ?

G + 2 = I, I + 2 = K, K + 2 = M, M + 2 = O

O + 1 = P, P + 1 = Q, Q + 1 = R, R + 1 = S

V - 2 = T, T - 2 = R, R - 2 = P, P - 2 = N

Hence, OSN is the next term.

Hence, the correct answer is OSN.