Indian Institute of Technology Kanpur (IIT-K) 2006 JT - Question Paper

schedules are possible?
(i) U-Q-R-T-P-V-S
(ii) P-T-R-U-Q-V-S
(iii) T-V-R-Q-U-P-S
(iv) Q-U-R-P-V-T-S
(A) (i)-(iii)-(iv) (B) (ii)-(iii)-(iv) (C) (i)-(ii)-(iv) (D) (i)-(ii)-(iii)
Solution for the ques. 56-59:
info we are having from the question:-
Q, U and R are from finance companies
Now first day is Sunday and seventh would be Saturday
S is a manufacturing company
R scheduled on third day of the week
S can't scheduled on sixth day of the week
T can be scheduled on any day of the week other than Saturday
56. 1(sun) two three four five 6(´S) 7(sat)(´T)
Q/U U/Q R
R Q/U U/Q
a) If S is on seventh position
then possible arrangements are
1(sun) two three four five 6(´S) 7(sat)(´T)
Q/U U/Q R S
P, S and T organize among 3 places from four to six in 3! Ways i.e. six ways
From here 12 ways are possible----(1)
1(sun) two three four five 6(´S) 7(sat)(´T)
R Q/U U/Q S
P, S and T organize among 3 places 1, two and six in 3! Ways i.e. six ways
From here 12 ways are possible----(2)
In all 24 ways when S is at seventh position
b) If S is not on seventh position then
i) 1(sun) two three four five 6(´S) 7(sat)(´T)
Q/U U/Q R
Now look for seventh position, we have presumed that S cannot be at seventh position
Therefore seventh position can be filled in two ways either by P or V
Now sixth position can be filled in two ways either V or P which is left and T
5th position can be filled in two ways and for fourth we are left with one only
so no. of ways possible is 1´2´2´2 = eight ways
In all 16 ways possible from this arrangement considering the arrangement of first and second position
ii) 1(sun) two three four five 6(´S) 7(sat)(´T)
R Q/U U/Q
Now look for seventh position, we have presumed that S cannot be at seventh position
Therefore seventh position can be filled in two ways either by P or V
Now sixth position can be filled in two ways either V or P which is left and T
Now second position filled in two ways and first in 1 way
Therefore no. of arrangements possible are 1´2´2´2 = eight ways
In all 16 ways are possible from this arrangement considering arrangements of U and Q in fourth and 5th
position.
In all therefore 24 + 16 + 16 = 56 ways are possible
Hence the ans choice is (C).

Earning:   Approval pending.