Time 3Hr Artificial Intelligence MA61008 Spring 2018

Instruction: The question paper is printed on both sides. There are 14 questions. Every question carries7 marks. Do not use calculator. No query will be entertained. Show rough work. Write answer in a box.

1. a ... h are blocks. P, Q, Rand S are double sizeblocks. The base ofR can be modified as {S,df}.How the bases of others can be modified?

h P Q R ST T ce T T

2. A person is supposed to choose one among A, B or C. After that a coin is tossed.Depending upon the choice and the outcome of the coin the person gets profit. Let Harichooses B and coin shows tail then what are the responsibilities of Hari and coin?[Example: Let Anil chooses C and coin shows head R(Anil)=47 R(coin)= -52.Reason: Maximum possible average profit is 573. In case of C average profit is 526.Responsibility (Anil)=573-526=47. The coin has increased the profit from 526 to 578.

H TA 714 432B 582 116C 578 474

3. Let S={a,b,c,d,g,h,p,q.Lu,v,w}. There are 3 reasons for S to be good.Reason.: aES bES CES dES gES hES Reasons: UES YES WES bES Reason): PES qES rES CESHow many reasons are present for an empty set to be bad?Example: Let there be 3 reasons for set K={ e,g,h,j,p,q,r,s,t,u,v,w} to be good.Reasoru: UES YES WES Reasor»: PES qES rES SES tES Reason): UES PES gES hESThere are 23 reasons for an empty set to be bad. One of them is v ~ S P ~ S another w ~ S q ~ S g ~ SAll 23 are: u{pqrst} vp v{qrst}{gh} wp w{qrst}{gh} total 5+(1+4*2)*2=23

4. ABCDEF is a hollow polygon object. The object has hole at G=(817, 1000). Coordinates of points:A:( 1000,0) B:(2000,0) C:(2000,2000) 0:(0,2000) E:(O,1 000) F:( 1000,1000)Example: Let a robot starts from R(50,50). The path followed is RT(Oo) TG(900) GH(Oo) HC(900)CB( 180°) BA(2700) AF(3600) FG(2700) GF(90o) FA( 180°) AB(900) BCCOo) outQuestion: What will be the path followed when one more hole is put at W(2000,1723)':>

5. A king writes 'p or 'q' at the back ofJajaj, Lalit and Sani. The king says there is at least one 'q'. Let Jalajhas "p' and Lalit and Sani has 'q'. The king asks Jalaj his letter. Then he asks Lalit then Sani. What aretheir replies?Example: A king writes 'p' or 'q' at the back of Anil, Hari and Oipu. The king says there is at least one"q '. Let Anil and Hari have 'p' and Dipu has 'q. The king asks Hari his letter. Hari says do not know.Now king asks Dipu. He says 'q'. The king asks Hari again. Hari says "if Dipus reply is based on myreply then 'q' else 'p' ".

6. We 'want to solve Knapsack problem using branch and bound technique.Among GHIJ we do not consider the inclusion of GJ and exclusion of HI.[t is because G+J<H+l. Since wt(G+J»wt(H+I) and Ut(G+J)<Ut(H+I).Similarly state what is not considered among ABC? What is not considered amonz DEF? Give reason.C>

Item A B C 0 E F G I-I I JWeight 14 5 10 13 5 8 14 15 16 18Utility 40 10 28 15 9 7 40 42 43 44

7. There are 8 cards A..H. Anil is given 3 cards, Hari 2 and Ravi '). Anil says he has one card among ABC,one among OEF and one among FGH. What is the probability in the mind of Anil that Hari knows at leastone of his cards? Example: Ravi knows is 4/5 or 3/5. Method is following'

Anil Ravi 3 from Ravi not know Probability that Ravi knowsADG BCEFH BEH,CEH 8/10ADF BCEGH (B/C)E(G/H) 6110ABF CDEGH C(D/E)(G/H) 6110

P.T.O.

8. India 400 and 600. England 300 and 587 for 7. India has three bowlers Anil, Dipu and Hari.Anil takes 0.1 wicket (on average) per over and concedes 5 runs per over (on average).Dipu takes 0.05 wickets per over and concedes 'x ' runs per over.Hari takes 0.15 wickets/over and concedes 10 runs per over.The Indian caption prefers to give a spell of 10 overs to Dipu. What is 'x'? Answer format 8.17<x<9.22.Example: India 400,600 Australia 300, 301/6 India needs 4 wickets and England 400 runs for victory.Hari will be given bowling. Reason: (400-10x)/(4-0.5)«400-100)/(4-1.5»(400-50)/(4-1)

9. When temperature is 26 and pressure is 88 what is humidity? Fuzzy rules are followingIf temperature is 25 ± 10 humidity is 329 ± 100.If pressure is 86 ± 10 humidity is 456 ± 100.Let the validity of these rules 0.20 and 0.77 respectively.Example: When validity of these rules is 0.34 and 0.63 then humidity is 402.Reason: When T=26 then 25 ± 10 is 10% false. When P=88 then 86 ± 10 is 20% false.Let H=389 then 329± 100 is 60% false and 456± 100 is 67% false.Here contradiction max[(60-1 0)*0.34, (67-20)*0.63]=max[ 17,29.61 ]=29.61.Let H=402 then 329 ± 100 is 73% false and 456 ± 100 is 54% false.Here contradiction max[(73-1 0)*0.34, (54-20)*0.63]=max[21.42,2IA2]= 21.42. It is minimum.

10. There are two medicines A and B which are made using sulphur and in their processing fuel is used.Initially a person (arbitrarily) decides to make 386 unit of A and 834 units of B. Now 1068 units ofsulphur remains. Now using l-level thinking he makes (834+ 1OO)(B) and (386-65)(A). Let profit on everyunit of medicine A be 2.8. How much is the profit on every unit of medicine B?

11. Cake size is 1000. Unit length of cake has got unit utility. There is a laddu at left end. Its utility for 'P' and'Q' is 108 and 20 respectively. P cuts the cake in two parts. Q takes one of the paris. Q also cuts theremaining part. P takes one of them. Write equation as given in following example. How much utility 'P'and 'Q' get? Example: The utility of laddu for P and Q be 60 and 20 respectively. P cuts the cake in twoparts. Q takes one of them. P cuts the remaining pari in two paris. Q takes one of them. The equation is

if (x+20+(1000-x)/2»(1000-x+x/2+10) then (1000-x)/2 else x/2+60-10 Solution: x=490-c: P:295 Q:765

12. Find g([9, 13,48,46,56,81,11,23]) according to following logic.g(A)=9 when size(A)=O=head(A)+ 700 when g(tail(A))=odd=g(tail(A))+lOOO when g(tail(A))=even

13. Ram has a bag with 5 red and 7 green balls. Ram tells Hari that the bag has 6 red and 6 green balls. Ramtells Hari to remove 2 balls and see the color of the removed balls. Then Hari has an option to give Rs 52to Ram and remove a ball. If the color of the last removed ball is red then Ram will give Rs. 100 to Hari.Find gains of Ram and Hari.Example: Let the amounts be 37 and 100 respectively.The gain ofHari is (-20*7+70*3+42*13)1132=6161132=154/33. Hint: When Hari has true knowledge thengain is (3*70+13*42)1132=(210+546)1132=7561132=189/33=63111.Balls removed Probability Hari thinks Remaining Hari thinks Gain Remaining Actual Gain Hariboth red 201132 4R6G -37+ 1OO*OAyes 3R 7G -37+ 100*0.3=-7IRIG 701132 5R 5G -37+ 100*0.5yes 4R6G -37+ 100*0.4=3both green 421132 6R4G -37+ 100*0.6yes 5R5G -37+ 100*0.5=13

14. It is known that disease is either Flu or Flu-Plague both or Malaria. Tests and their costs are given. Whichtests should be conducted? What is total cost involved? Notation: Test E cannot detect plague.

Test A B C D E F G H I JFlu No No No Yes Yes Yes Yes Yes No YesPlague No Yes Yes No No Yes Yes Yes No YesMalaria Yes No Yes No Yes No Yes Yes Yes Nocost 305 623 402 152 103 204 107 128 923 815