Statement:

M > K > L = O ≥ P, K < B = G ≤ Y ≤ T

On combining: M > K < B = G ≤ Y ≤ T,  G = B > K > L = O

Conclusions:

I. L > Y → FALSE (L > K < B = G ≤ Y, As there are reverse signs present between L and Y thus there is no direct relation between them so conclusion I is not possible).

II. O < G → TRUE (G = B > K > L = O There is a clear and direct relation shown between O and G, thus conclusion II follows).

Hence, the correct answer is "Only conclusion II is true".

Statement: N < M = L ≥ K ≤ J = I; O > P = K 

On combining: N < M = L ≥ K = P < O

Conclusions:

I. M > O → FALSE ( N < M = L ≥ K = P < O, As there are both greater and lesser signs between M and O no clear relation could be determined so the conclusion is false).

II. N > P → FALSE ( N < M = L ≥ K = P < O, No clear relation is there between N and P thus conclusion II is also false).

Hence, the correct answer is "Neither conclusion I nor II follows".

Statement:  Z ≥ H, B < H, K < B

Combined statement:  Z ≥ H > B > K

Conclusion: 

I) K > Z → FALSE (Z ≥ H > B > K, as both greater and lesser signs are there the conclusion cannot be true)

II) K = Z → FALSE (Z ≥ H > B > K, as there are no equals to sign between K and Z the conclusion cannot be true)

Hence, "Neither conclusion I nor II follows."

8 people – P, Q, R, S, T, U, V, and X

8 colors – Blue, Green, Red, White, Black, Purple, Yellow, and Orange

1. W sits second to the left of the one who likes Red.

2. S, who sits opposite W, likes Black.

3. R, who likes Purple, sits opposite V, who sits to the immediate right of the one who likes Red.

4. Q sits to the immediate left of the one who likes White.

5. X likes Orange and sits opposite Q.

Case 1

Case 2

6. The one who likes Blue sits to the immediate left of the one who likes Green.

7. T sits opposite P, who likes Yellow. Hence case 1 get eliminated.

Hence, V likes White.

8 people – P, Q, R, S, T, U, V, and X

8 colors – Blue, Green, Red, White, Black, Purple, Yellow, and Orange

1. W sits second to the left of the one who likes Red.

2. S, who sits opposite W, likes Black.

3. R, who likes Purple, sits opposite V, who sits to the immediate right of the one who likes Red.

4. Q sits to the immediate left of the one who likes White.

5. X likes Orange and sits opposite Q.

Case 1

Case 2

6. The one who likes Blue sits to the immediate left of the one who likes Green.

7. T sits opposite P, who likes Yellow. Hence case 1 get eliminated. 

T likes Green.

Hence, P - who likes Yellow, sits opposite T.

8 people – P, Q, R, S, T, U, V, and X

8 colors – Blue, Green, Red, White, Black, Purple, Yellow, and Orange

1. W sits second to the left of the one who likes Red.

2. S, who sits opposite W, likes Black.

3. R, who likes Purple, sits opposite V, who sits to the immediate right of the one who likes Red.

4. Q sits to the immediate left of the one who likes White.

5. X likes Orange and sits opposite Q.

Case 1

Case 2

6. The one who likes Blue sits to the immediate left of the one who likes Green.

7. T sits opposite P, who likes Yellow. Hence case 1 get eliminated.

X likes Orange. V likes White.

Hence, 4 people sit between X and V, when counted from the right of X.

8 people – P, Q, R, S, T, U, V, and X

8 colors – Blue, Green, Red, White, Black, Purple, Yellow, and Orange

1. W sits second to the left of the one who likes Red.

2. S, who sits opposite W, likes Black.

3. R, who likes Purple, sits opposite V, who sits to the immediate right of the one who likes Red.

4. Q sits to the immediate left of the one who likes White.

5. X likes Orange and sits opposite Q.

Case 1

Case 2

6. The one who likes Blue sits to the immediate left of the one who likes Green.

7. T sits opposite P, who likes Yellow. Hence case 1 get eliminated.

W likes Blue. V sits third to the right of W.

Hence, R - who likes Purple, sits opposite V.

8 people – P, Q, R, S, T, U, V, and X

8 colors – Blue, Green, Red, White, Black, Purple, Yellow, and Orange

1. W sits second to the left of the one who likes Red.

2. S, who sits opposite W, likes Black.

3. R, who likes Purple, sits opposite V, who sits to the immediate right of the one who likes Red.

4. Q sits to the immediate left of the one who likes White.

5. X likes Orange and sits opposite Q.

Case 1

Case 2

6. The one who likes Blue sits to the immediate left of the one who likes Green.

7. T sits opposite P, who likes Yellow. Hence case 1 get eliminated.

X likes Orange. S likes Black. P sits between X and S.

Hence, W - who likes Blue, sits fifth to the left of P.

The least possible diagram from the given information is,

Riya is southwest of point A.

Hence, Southwest is the correct answer.

The least possible diagram from the given information is,

Priya is at Northeast of point A.

Hence, None of these is the correct answer.