Given:

Nine persons are sitting around a circular table.

Some of them are facing towards the centre while some are facing outside the centre.

Now,

1) S is sitting second to the right of H, who is facing inside.

2) Two persons are sitting between S and A. 

The possibilities are -

3) W is sitting third to the left of A.

4) L is sitting second to the left of W.

5) E is sitting third to the right of L and is an immediate neighbour of N.

6) Both E and N are facing the same direction as of H. It means E and N are facing inside.

7) D is sitting fourth to the right of R, who is not sitting near W. This is possible only in Case II (b).

8) S and A are facing the opposite direction to each other. It means S is facing outside.

9) D is not facing outside.

Thus, the final arrangement is -

Hence, the correct answer is Both statement II and III is true.

Given:

Nine persons are sitting around a circular table.

Some of them are facing towards the centre while some are facing outside the centre.

Now,

1) S is sitting second to the right of H, who is facing inside.

2) Two persons are sitting between S and A. 

The possibilities are -

3) W is sitting third to the left of A.

4) L is sitting second to the left of W.

5) E is sitting third to the right of L and is an immediate neighbour of N.

6) Both E and N are facing the same direction as of H. It means E and N are facing inside.

7) D is sitting fourth to the right of R, who is not sitting near W. This is possible only in Case II (b).

8) S and A are facing the opposite direction to each other. It means S is facing outside.

9) D is not facing outside.

Thus, the final arrangement is -

Difference between the number of people facing outside and the number of people facing inside = 5 - 4 = 1.

Hence, the correct answer is One.

Given:

Nine persons are sitting around a circular table.

Some of them are facing towards the centre while some are facing outside the centre.

Now,

1) S is sitting second to the right of H, who is facing inside.

2) Two persons are sitting between S and A. 

The possibilities are -

3) W is sitting third to the left of A.

4) L is sitting second to the left of W.

5) E is sitting third to the right of L and is an immediate neighbour of N.

6) Both E and N are facing the same direction as of H. It means E and N are facing inside.

7) D is sitting fourth to the right of R, who is not sitting near W. This is possible only in Case II (b).

8) S and A are facing the opposite direction to each other. It means S is facing outside.

9) D is not facing outside.

Thus, the final arrangement is -

L is sitting third to the right of E.

Hence, the correct answer is L.

Given:

Nine persons are sitting around a circular table.

Some of them are facing towards the centre while some are facing outside the centre.

Now,

1) S is sitting second to the right of H, who is facing inside.

2) Two persons are sitting between S and A. 

The possibilities are -

3) W is sitting third to the left of A.

4) L is sitting second to the left of W.

5) E is sitting third to the right of L and is an immediate neighbour of N.

6) Both E and N are facing the same direction as of H. It means E and N are facing inside.

7) D is sitting fourth to the right of R, who is not sitting near W. This is possible only in Case II (b).

8) S and A are facing the opposite direction to each other. It means S is facing outside.

9) D is not facing outside.

Thus, the final arrangement is -

Four persons are sitting between N and A when counted from the left of A

Hence, the correct answer is Four.

Given:

Nine persons are sitting around a circular table.

Some of them are facing towards the centre while some are facing outside the centre.

Now,

1) S is sitting second to the right of H, who is facing inside.

2) Two persons are sitting between S and A. 

The possibilities are -

3) W is sitting third to the left of A.

4) L is sitting second to the left of W.

5) E is sitting third to the right of L and is an immediate neighbour of N.

6) Both E and N are facing the same direction as of H. It means E and N are facing inside.

7) D is sitting fourth to the right of R, who is not sitting near W. This is possible only in Case II (b).

8) S and A are facing the opposite direction to each other. It means S is facing outside.

9) D is not facing outside.

Thus, the final arrangement is -

The persons sitting to the just right of R and to the just left of W are facing Inside and Inside respectively.

Hence, the correct answer is Inside, Inside.

Statement: N > V > M ≤ O; M ≥ Z > B

On combining:  N > V > M ≤ O, O ≥ M ≥ Z 

Conclusions:

I. O ≥ Z → TRUE ( N > V > M ≤ O, O ≥ M ≥ Z  As there is a direct relation between O and Z thus the conclusion is true).

II. N > O → FALSE ( N > V > M ≤ O, O ≥ M ≥ Z  As there are both greater and less than equals to signs between N and O thus the conclusion dose not follows).

Hence, the correct answer is "Only option I is true".

Statements: G > D ≥ V = X, M < F ≥ N > X; M > W ≤ Q = Z < P > L

G > D ≥ V = X < N ≤ F > M > W ≤ Q = Z < P > L

Conclusions:

I. V < M → This doesn't follow as V = X < N ≤ F > M. So, this conclusion is not true.

II. W ≤ L → This doesn't follow as W ≤ Q = Z < P > L. So, this conclusion is not true.

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

Statements: Z ≤ X > C; V ≥ B = X; J > K ≥ B

Z ≤ X = B ≤ V

J > K ≥ B = X > C

Z ≤ X = B ≤ K < J

Conclusions:

I. Z < J → This follows as Z ≤ X = B ≤ K < J. Therefore, this conclusion is true.

II. K ≥ C → This doesn't follow as K ≥ B = X > C. Therefore, this conclusion is not true.

Hence, the correct answer is Only conclusion I is true

There are three departments and Seven employees. Three departments are Finance, Production, and Marketing. Seven Employees are P, Q, R, S, T, U, and V.

1) V works in the Marketing department and S neither works in the Finance department nor the marketing department.

So, S works in the Production Department and V works in the Marketing Department.

2) P, R, and S work in different departments and P works with T in the same department.

We know the position of S but the R and P department is not known to us. So, there will be two cases. In one of the cases, we will assume R belongs to the Finance department and in another belong to the Marketing department.

3) U does not work with S. P and U do not work in the same department. V does not work with U. 

According to the given conditions U cannot work with V, P, and S. We cannot place U in any department in Case 1. So, Case 1 would be eliminated.

4) Only two persons work in the Finance department. Also, according to the given conditions not more than three people work in the same department. So, Q works in the Production department.

The final arrangement is:

Hence, T belongs to the Marketing Department.

There are three departments and Seven employees. Three departments are Finance, Production, and Marketing. Seven Employees are P, Q, R, S, T, U, and V.

1) V works in the Marketing department and S neither works in the Finance department nor the marketing department.

So, S works in the Production Department and V works in the Marketing Department.

2) P, R, and S work in different departments and P works with T in the same department.

We know the position of S but the R and P department is not known to us. So, there will be two cases. In one of the cases, we will assume R belongs to the Finance department and in another belong to the Marketing department.

3) U does not work with S. P and U do not work in the same department. V does not work with U. 

According to the given conditions U cannot work with V, P, and S. We cannot place U in any department in Case 1. So, Case 1 would be eliminated.

4) Only two persons work in the Finance department. Also, according to the given conditions not more than three people work in the same department. So, Q works in the Production department.

The final arrangement is:

The Marketing department has three employees and the other departments have two employees each. Hence, the Production and Finance department has a minimum number of Employees.