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Let us draw the diagram according to the information given in the question,

PU = QR + ST 

= 30 km + 20 km

= 50 km

Hence, 50 km is the distance between starting and ending point.

Let us draw the diagram according to the information given in the question,

Here, the first point is to the northwest of the second point and thus form a group whereas in RP this pattern is not followed.

1. SU → S is in north west of U.

2) RP → R is in north east of P.

3. QT → Q is in north west of T.

4. RT → R is in north west of T.

5. QU → Q is in north west of U

Hence, RP does not belong to that group.

Let us draw the diagram according to the information given in the question,

By using the Pythagorean Theorem,

QS = \(\sqrt{(QR)^2 + (RS)^2} \)

QS = \(\sqrt{(30)^2 + (40)^2} \)

QS = \(\sqrt{2500} \)

QS = 50 km

Hence, 50 km is the Shortest distance between Q and S.

Given statements: F = G < H < J ≤ K > L; O ≥ F; K ≥ C

On combining: O ≥ F = G < H < J ≤ K > L; K ≥ C

Conclusions:

I. H > C → False (as H < J ≤ K ≥ C → clear relation between H and C cannot be determined)

II. L > G → False (as L < K ≥ J > H > G → clear relation between L and G cannot be determined)

Hence, the correct answer is ‘None is True’.

Given Statements: A > B > C, D ≤ E < C, D ≥ F

On combining:  A > B > C > E ≥ D ≥ F

Conclusions:

I. B > D → True (as B > C > E ≥ D →B > D)

II. F ≤ E → True (as E ≥ D ≥ F → E ≥ F)

Hence, both I and II are true.

Given Statements: X < C, W > D, G ≥ W, C = D

On combining: X < C = D < W ≤ G

Conclusions:

I. C ≤ G → False (as C = D < W ≤ G → C < G)

II. W > X → True (as X < C = D < W → X < W)

Hence, only II is true.

Given statements: P > Q < R; P = X < Y < Z

On combining: P = X > Q < R; P = X < Y < Z

Conclusions:

I. X > Q → True (as P = X > Q)

II. P < Z → True (as P = X < Y < Z → P < Z)

Hence, both conclusions I and II are true.

Given:

A certain number of persons are sitting in a row facing north. 

Now,

1) E sits sixth from one of the end.

2) Seven persons sit between E and A, who sits fourth from an end.

The possibilities are -

3) A sits third to the left of B.

4) Five persons sit between F and B.

The possibilities are -

5) F sits second to the left of G, who sits third from an end. This is not possible in Case I so it gets elimiated.

6) One person sits between G and H. There are not for than four person between A and H.

7) C sits to the right of E but not to the immediate right.

8) D sits third to the right of C. This is not possible in Case II (b) so it gets eliminated.

The final arrangement is -

13 persons are sitting between G and D.

Hence, the correct answer is 13.

Given:

A certain number of persons are sitting in a row facing north. 

Now,

1) E sits sixth from one of the end.

2) Seven persons sit between E and A, who sits fourth from an end.

The possibilities are -

3) A sits third to the left of B.

4) Five persons sit between F and B.

The possibilities are -

5) F sits second to the left of G, who sits third from an end. This is not possible in Case I so it gets elimiated.

6) One person sits between G and H. There are not for than four person between A and H.

7) C sits to the right of E but not to the immediate right.

8) D sits third to the right of C. This is not possible in Case II (b) so it gets eliminated.

The final arrangement is -

F is third to the left of A.

Hence, the correct answer is Third to the left.

Given:

A certain number of persons are sitting in a row facing north. 

Now,

1) E sits sixth from one of the end.

2) Seven persons sit between E and A, who sits fourth from an end.

The possibilities are -

3) A sits third to the left of B.

4) Five persons sit between F and B.

The possibilities are -

5) F sits second to the left of G, who sits third from an end. This is not possible in Case I so it gets elimiated.

6) One person sits between G and H. There are not for than four person between A and H.

7) C sits to the right of E but not to the immediate right.

8) D sits third to the right of C. This is not possible in Case II (b) so it gets eliminated.

The final arrangement is -

As many persons sitting to the right of C as to the left of A.

Hence, the correct answer is A.