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# Linear Arrangements Questions for MAH-CET

Instructions

Study the following information carefully and answer the questions given below:
Eight persons â€” E, F, G, H, W, X, Y and Z â€” are sitting in two parallel rows containing four persons each. E. F, G and H are sitting in row-1 facing north and W. X, Y and Z are sitting in row-2 facing south (but not necessarily in the same order.) Thus, each person sitting in row â€“ 1 faces another person sitting in row â€“ 2, Each of the two rows consists of one Doctor, one Engineer, one Pilot and one Scientist (but not necessarily in the same order).
â€¢ The Doctor of row-1 sits second to the right of H. X faces one of the immediate neighbours of H. Only one person sits between the X and the Scientist.
â€¢ The one who faces the Scientist of row â€“ 2 is an immediate neighbour of E. Only one person sits between E and the Pilot.
â€¢ W sits second to the right of Z. Y does not face G. The Scientist of row-1 faces the Engineer of row â€“ 2.
â€¢ G faces one of the immediate neighbours of the Doctor of row-2. The Doctor of row-2 does not sit at any of the extreme ends of the line. Z is not a Doctor.

Question 1:Â If Y and X interchange their places, so do H and Z, then who amongst the following will face E?

a)Â Y

b)Â H

c)Â F

d)Â W

e)Â Other than those given as options

Solution:

In row-1, E,F,GÂ & H are sitting facing north while W,X,YÂ & Z are sitting in row-2 facing south.

The Doctor of row-1 sits second to the right of H.

Case 1Â : H sits at extreme left end of row 1.

Also,Â X faces one of the immediate neighbours of H, => X sits opposite to the person who is immediate right of H and Scientist in row -2 sits at extreme left end.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 and H is the pilot.

W sits second to the right of Z, => W sits at extreme right end of row-2 and Z to the immediate left of X.Â Only position left in row-2 is extreme left end, which is now filled by Y being the scientist. The arrangement isÂ :

But doctor of row(II) does not sit at end and Z is also not the doctor. Thus, this case is not possible.

Case 2Â : H sits at second from left end of row-1, => Doctor sits at extreme right end in this row.

Also,Â X faces one of the immediate neighbours of H, =>Â X sits at extreme right end of row-2 and the scientist sits second to the left of X.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 sitting at extreme right and H is the pilot.

W sits second to the right of Z, =>Â W sits to the immediate left of X and Z to the extreme left end of row-2.Â Only position left in row-2 is occupied by Y being the scientist.

Since, Y and G does not sit opposite to each other, => G sits at extreme left end of row-1.

The arrangement isÂ :

Currently, Z is facing E, if Z and H interchange their positions, then H will face E.

=> Ans – (B)

Question 2:Â Which of the given statements is true with respect to the given arrangement?

a)Â G is a Scientist.

b)Â Y sits to the immediate right of X.

c)Â F and Z face each other.

d)Â None of the given statements is true

e)Â The Engineer of one row faces the Doctor of another row.

Solution:

In row-1, E,F,GÂ & H are sitting facing north while W,X,YÂ & Z are sitting in row-2 facing south.

The Doctor of row-1 sits second to the right of H.

Case 1Â : H sits at extreme left end of row 1.

Also,Â X faces one of the immediate neighbours of H, => X sits opposite to the person who is immediate right of H and Scientist in row -2 sits at extreme left end.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 and H is the pilot.

W sits second to the right of Z, => W sits at extreme right end of row-2 and Z to the immediate left of X.Â Only position left in row-2 is extreme left end, which is now filled by Y being the scientist. The arrangement isÂ :

But doctor of row(II) does not sit at end and Z is also not the doctor.Â Thus, this case is not possible.

Case 2Â : H sits at second from left end of row-1, => Doctor sits at extreme right end in this row.

Also,Â X faces one of the immediate neighbours of H, =>Â X sits at extreme right end of row-2 and the scientist sits second to the left of X.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 sitting at extreme right and H is the pilot.

W sits second to the right of Z, =>Â W sits to the immediate left of X and Z to the extreme left end of row-2.Â Only position left in row-2 is occupied by Y being the scientist.

Since, Y and G does not sit opposite to each other, => G sits at extreme left end of row-1.

The arrangement isÂ :

Clearly, G is a scientist.

=> Ans – (A)

Question 3:Â Which of the following represent both the immediate neighbours of Y?

a)Â Z and the Scientist of row-2

b)Â X and the Engineer of row-2

c)Â W and the Doctor of row-2

d)Â X and the Pilot of row-2

e)Â W and the Pilot of row-2

Solution:

In row-1, E,F,GÂ & H are sitting facing north while W,X,YÂ & Z are sitting in row-2 facing south.

The Doctor of row-1 sits second to the right of H.

Case 1Â : H sits at extreme left end of row 1.

Also,Â X faces one of the immediate neighbours of H, => X sits opposite to the person who is immediate right of H and Scientist in row -2 sits at extreme left end.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 and H is the pilot.

W sits second to the right of Z, => W sits at extreme right end of row-2 and Z to the immediate left of X.Â Only position left in row-2 is extreme left end, which is now filled by Y being the scientist. The arrangement isÂ :

But doctor of row(II) does not sit at end and Z is also not the doctor.Â Thus, this case is not possible.

Case 2Â : H sits at second from left end of row-1, => Doctor sits at extreme right end in this row.

Also,Â X faces one of the immediate neighbours of H, =>Â X sits at extreme right end of row-2 and the scientist sits second to the left of X.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 sitting at extreme right and H is the pilot.

W sits second to the right of Z, =>Â W sits to the immediate left of X and Z to the extreme left end of row-2.Â Only position left in row-2 is occupied by Y being the scientist.

Since, Y and G does not sit opposite to each other, => G sits at extreme left end of row-1.

The arrangement isÂ :

The immediate neighbors of Y are = W (doctor) and Z (pilot).

=> Ans – (E)

Question 4:Â Who amongst the following sits to the immediate left of Pilot of row-1?

a)Â H

b)Â The Doctor of row-1

c)Â The Engineer of row – 1

d)Â G

e)Â F

Solution:

In row-1, E,F,GÂ & H are sitting facing north while W,X,YÂ & Z are sitting in row-2 facing south.

The Doctor of row-1 sits second to the right of H.

Case 1Â : H sits at extreme left end of row 1.

Also,Â X faces one of the immediate neighbours of H, => X sits opposite to the person who is immediate right of H and Scientist in row -2 sits at extreme left end.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 and H is the pilot.

W sits second to the right of Z, => W sits at extreme right end of row-2 and Z to the immediate left of X.Â Only position left in row-2 is extreme left end, which is now filled by Y being the scientist. The arrangement isÂ :

But doctor of row(II) does not sit at end and Z is also not the doctor.Â Thus, this case is not possible.

Case 2Â : H sits at second from left end of row-1, => Doctor sits at extreme right end in this row.

Also,Â X faces one of the immediate neighbours of H, =>Â X sits at extreme right end of row-2 and the scientist sits second to the left of X.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 sitting at extreme right and H is the pilot.

W sits second to the right of Z, =>Â W sits to the immediate left of X and Z to the extreme left end of row-2.Â Only position left in row-2 is occupied by Y being the scientist.

Since, Y and G does not sit opposite to each other, => G sits at extreme left end of row-1.

The arrangement isÂ :

In row-1, the person who is sitting to the immediate left of H (pilot) = G (scientist)

=> Ans – (D)

Question 5:Â Which of the following represents the people sitting at extreme ends of both the lines?

a)Â F, H and X, Y

b)Â F, H and Z, W

c)Â G, E and Z, X

d)Â E, H and X, Z

e)Â G, E and W, Y

Solution:

In row-1, E,F,GÂ & H are sitting facing north while W,X,YÂ & Z are sitting in row-2 facing south.

The Doctor of row-1 sits second to the right of H.

Case 1Â : H sits at extreme left end of row 1.

Also,Â X faces one of the immediate neighbours of H, => X sits opposite to the person who is immediate right of H and Scientist in row -2 sits at extreme left end.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 and H is the pilot.

W sits second to the right of Z, => W sits at extreme right end of row-2 and Z to the immediate left of X.Â Only position left in row-2 is extreme left end, which is now filled by Y being the scientist. The arrangement isÂ :

But doctor of row(II) does not sit at end and Z is also not the doctor.Â Thus, this case is not possible.

Case 2Â : H sits at second from left end of row-1, => Doctor sits at extreme right end in this row.

Also,Â X faces one of the immediate neighbours of H, =>Â X sits at extreme right end of row-2 and the scientist sits second to the left of X.

Now,Â The one who faces the Scientist of row – 2 is an immediate neighbour of E, => E is doctor in row-1 sitting at extreme right and H is the pilot.

W sits second to the right of Z, =>Â W sits to the immediate left of X and Z to the extreme left end of row-2.Â Only position left in row-2 is occupied by Y being the scientist.

Since, Y and G does not sit opposite to each other, => G sits at extreme left end of row-1.

The arrangement isÂ :

In row-1, the person at ends = G,E and in row-2 = X,Z

=> Ans – (C)

Instructions

Study the following information carefully and answer the questions giver. below.
Eight persons E, F, G, H, W X, Y and Z are sitting in two parallel rows containing four persons each in such a way that there is an equal distance between adjacent persons. E, F, G and H are sitting in row-1 facing north and W, X, Y and Z are sitting in row-2 facing south. (but not necessarily in the same order.) Thus, each person sitting in row-1 faces another persons sitting in row-2 Each of the two rows consists of the one Professor, one Leader, one Technician and one Doctor (but not necessarily in the same order).
â€¢ The Doctor of row-1 sits second to the right of H. E is an immediate neighbour of H. E faces the Leader of row-2.
â€¢ X sits to the immediate right of the Leader. X faces one of the immediate neighbours of the Professor of row-1. The Professor of row-1 does not sit at any of the extreme ends of the line.
â€¢ W sits second to the left of Y. Z does not face G. F faces the Professor of row-2. In both the rows, onlye one person sits between the Professor and the Technician. W is not a Doctor.

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Question 6:Â Which of the following represent the people sitting at extreme ends of both the lines ?

a)Â F, H and Z, W

b)Â G, H and X, Y

c)Â E, H and Y, Z

d)Â G, F and Z, Y

e)Â G, F and W, Y

Solution:

H sits second from the left end of row 1 and the doctor sits second to the right of H, i.e. extreme right end of row-1.

E faces the leader of row-2 and the leader is not at an end since X sits to its right, => E sits to the immediate right of H and opposite to the leader of row-2.

X facesÂ one of the immediate neighbours of the Professor of row-1 and The Professor of row-1 does not sit at any of the extreme ends of the line

=> E is the professor.

Y sits at extreme right end of row-2 and W sits second to the left of it.

Since,Â Z does not face G, => Z faces F and G sits at extreme left end of row-1. Z is the professor.

In both the rows, only one person sits between the Professor and the Technician, => X and G are technician.

Person sitting at ends are = G,F and Y,Z

=> Ans – (D)

Question 7:Â If E and X interchange their places and so do G and Z, then who amongst the following will face W ?

a)Â X

b)Â Other than those given as options

c)Â A

d)Â Z

e)Â H

Solution:

H sits second from the left end of row 1 and the doctor sits second to the right of H, i.e. extreme right end of row-1.

E faces the leader of row-2 and the leader is not at an end since X sits to its right, => E sits to the immediate right of H and opposite to the leader of row-2.

X facesÂ one of the immediate neighbours of the Professor of row-1 and The Professor of row-1 does not sit at any of the extreme ends of the line

=> E is the professor.

Y sits at extreme right end of row-2 and W sits second to the left of it.

Since,Â Z does not face G, => Z faces F and G sits at extreme left end of row-1. Z is the professor.

In both the rows, only one person sits between the Professor and the Technician, => X and G are technician.

Currently, W is sitting opposite to E, if EÂ and X interchange their position, then X will sit opposite to W.

=> Ans – (A)

Question 8:Â Which of the given statements is true with respect to the given arrangement?

a)Â None of the given statements is true

b)Â Y sits to the immediate right of Z.

c)Â The Technician of one row faces the Doctor of another row.

d)Â Y and H face each other

e)Â H is a Technician

Solution:

H sits second from the left end of row 1 and the doctor sits second to the right of H, i.e. extreme right end of row-1.

E faces the leader of row-2 and the leader is not at an end since X sits to its right, => E sits to the immediate right of H and opposite to the leader of row-2.

X facesÂ one of the immediate neighbours of the Professor of row-1 and The Professor of row-1 does not sit at any of the extreme ends of the line

=> E is the professor.

Y sits at extreme right end of row-2 and W sits second to the left of it.

Since,Â Z does not face G, => Z faces F and G sits at extreme left end of row-1. Z is the professor.

In both the rows, only one person sits between the Professor and the Technician, => X and G are technician.

Clearly, technician of row-1 faces the doctor of row-2.

=> Ans – (C)

Question 9:Â Who amongst the following sits to the immediate left of the Leader of row-1?

a)Â The Professor of row-1

b)Â F

c)Â H

d)Â G

e)Â No one

Solution:

H sits second from the left end of row 1 and the doctor sits second to the right of H, i.e. extreme right end of row-1.

E faces the leader of row-2 and the leader is not at an end since X sits to its right, => E sits to the immediate right of H and opposite to the leader of row-2.

X facesÂ one of the immediate neighbours of the Professor of row-1 and The Professor of row-1 does not sit at any of the extreme ends of the line

=> E is the professor.

Y sits at extreme right end of row-2 and W sits second to the left of it.

Since,Â Z does not face G, => Z faces F and G sits at extreme left end of row-1. Z is the professor.

In both the rows, only one person sits between the Professor and the Technician, => X and G are technician.

G sits to the immediate left of the leader of row-1.

=> Ans – (D)

Question 10:Â Which of the following represent both the immediate neighbours of W ?

a)Â X and the Leader of row-2

b)Â Y and the Technician of row-2

c)Â Y and the Doctor of row-2

d)Â X and the Professor of row-2

e)Â Z and the Doctor of row-2

Solution:

H sits second from the left end of row 1 and the doctor sits second to the right of H, i.e. extreme right end of row-1.

E faces the leader of row-2 and the leader is not at an end since X sits to its right, => E sits to the immediate right of H and opposite to the leader of row-2.

X facesÂ one of the immediate neighbours of the Professor of row-1 and The Professor of row-1 does not sit at any of the extreme ends of the line

=> E is the professor.

Y sits at extreme right end of row-2 and W sits second to the left of it.

Since,Â Z does not face G, => Z faces F and G sits at extreme left end of row-1. Z is the professor.

In both the rows, only one person sits between the Professor and the Technician, => X and G are technician.

Immediate neighbors of W are X (technician) and Z (professor).

=> Ans – (D)

Instructions

Study 1 the following information carefulâ€™ ly and answer the questions given below :
Nine persons â€“ G, H, I, J, K, R, S, T and U â€” are seated in a straight line facing North, with equal distance between each other but not necessarily in the same order.
Only two persons sit to the left of I. Only one person sits between I and U. H sits fourth to the right of R. R is not an immediate neighbour of U. Less than three persons sit between R and U. Number of persons sitting between I and U is half as that between H and J. Only three persons sit between K and T. K is not an immediate neighbour of J. Only two persons sit between T and G.

Question 11:Â Which of the following pairs represent the persons sitting at the extreme ends of the line?

a)Â H, U

b)Â U, G

c)Â K, G

d)Â U, S

e)Â I, G

Solution:

Only two persons sit to the left of I, => I sits at the third position from left end.

Only one person sits between I and U, => U sits at the extreme left end of the line.

Since, less than 3 people sit between R and U, and R is not an immediate neighbor of U, => R sits third to the right of U and also, H sits fourth to the right of R.

Number of persons sitting between I and U is half as that between H and J, => 2 persons are sitting between H and J.

Since, K is not an immediate neighbor of J, => K sits second to the right of U and T sits to the immediate right of J.

Only two persons sit between T and G, => G sits at the extreme right end of the line and the remaining place is occupied by S.

The arrangementÂ :

U and G are sitting at the extreme ends of the line.

=> Ans – (B)

Question 12:Â Who sits second to the left of J?

a)Â T

b)Â No one as J sits at one of the extreme ends of the line.

c)Â I

d)Â G

e)Â S

Solution:

Only two persons sit to the left of I, => I sits at the third position from left end.

Only one person sits between I and U, => U sits at the extreme left end of the line.

Since, less than 3 people sit between R and U, and R is not an immediate neighbor of U, => R sits third to the right of U and also, H sits fourth to the right of R.

Number of persons sitting between I and U is half as that between H and J, => 2 persons are sitting between H and J.

Since, K is not an immediate neighbor of J, => K sits second to the right of U and T sits to the immediate right of J.

Only two persons sit between T and G, => G sits at the extreme right end of the line and the remaining place is occupied by S.

The arrangementÂ :

I is sitting second to the left of J.

=> Ans – (C)

Question 13:Â Who amongst the following sit exactly between T and G?

a)Â I, J

b)Â H, J

c)Â R, U

d)Â H, S

e)Â J, R

Solution:

Only two persons sit to the left of I, => I sits at the third position from left end.

Only one person sits between I and U, => U sits at the extreme left end of the line.

Since, less than 3 people sit between R and U, and R is not an immediate neighbor of U, => R sits third to the right of U and also, H sits fourth to the right of R.

Number of persons sitting between I and U is half as that between H and J, => 2 persons are sitting between H and J.

Since, K is not an immediate neighbor of J, => K sits second to the right of U and T sits to the immediate right of J.

Only two persons sit between T and G, => G sits at the extreme right end of the line and the remaining place is occupied by S.

The arrangementÂ :

Clearly, S and H are sitting between T and G.

=> Ans – (D)

Question 14:Â Which of the following statements is true with respect to S as per the given arrangement?

a)Â S is an immediate neighbour of U.

b)Â None of the given options is true.

c)Â S sits at one of the extreme ends of the line.

d)Â More than two persons sit between S and R.

e)Â S sits second to the left of G.

Solution:

Only two persons sit to the left of I, => I sits at the third position from left end.

Only one person sits between I and U, => U sits at the extreme left end of the line.

Since, less than 3 people sit between R and U, and R is not an immediate neighbor of U, => R sits third to the right of U and also, H sits fourth to the right of R.

Number of persons sitting between I and U is half as that between H and J, => 2 persons are sitting between H and J.

Since, K is not an immediate neighbor of J, => K sits second to the right of U and T sits to the immediate right of J.

Only two persons sit between T and G, => G sits at the extreme right end of the line and the remaining place is occupied by S.

The arrangementÂ :

The only statement that is true is S is sitting second to the left of G.

=> Ans – (E)

Question 15:Â In which of the given pairs of persons, is odd number of persons sitting between them?

a)Â H, T

b)Â I, H

c)Â U, R

d)Â J, K

e)Â G, K

Solution:

Only two persons sit to the left of I, => I sits at the third position from left end.

Only one person sits between I and U, => U sits at the extreme left end of the line.

Since, less than 3 people sit between R and U, and R is not an immediate neighbor of U, => R sits third to the right of U and also, H sits fourth to the right of R.

Number of persons sitting between I and U is half as that between H and J, => 2 persons are sitting between H and J.

Since, K is not an immediate neighbor of J, => K sits second to the right of U and T sits to the immediate right of J.

Only two persons sit between T and G, => G sits at the extreme right end of the line and the remaining place is occupied by S.

The arrangementÂ :

Number of persons sitting betweenÂ :

H and T = 1 Â (odd)

I and H = 4

U and R = 2

J and K = 2

G and K = 6

=> Ans – (A)