Title T1 2022.pdf ✅

Duration: 1 Hour Course: T. Y. B. Tech. (Semester V) Date : 23/09/2022 Instructions: Indian Institute of Information Technology, Pune Linear and Nonlinear Optimization (1) All questions are compulsory. Term 1 Examination (2) Figures to the right indicate maximum marks. (3) Write your MIS Number on Question Paper. 1. Answer the following questions. (4) Writing anything on question paper (except MIS No.) is not allowed. (5) Mobile phones and programmable calculators are strictly prohibited. (6) Exchange/Sharing of stationary, calculator etc. not allowed. (a) State fundamental theorem of duality in LPP. (b) Consider the set S = S;U S where Si = { (*, y) e R? | 11 where z1,T2 >0. 2. Consider the LPP given below and answer the following questions. Min(Z) = 1 - 21:2 + a3 Z1,2 > 0 and z3 is unrestricted in sign. Academic Year: 2022 -2023 Max. Marks: 20 (a) Solve the above LPP using Big M method. (b) Write down the dual of the above LPP. (c) find the dual optimal solution without solving the dual problem. 3. One unit of product A coutributes Rs. 100 and requires one unit of raw material and one hour of labour. Oue unit of product B contributes Rs. 400 and requires 6 units of raw material and 3 hours of labour. A vailability of raw naterial at present is 12 units and there are 6 hours of labour. (a) Fornulate this problenn as a linear progranming problem. (b) How many units of each product should be produced to maximize profit? (Solve using simplex nethod). [o1) (02] [02] [02] [05] [02] [o1] [01] (04
Duration: 1 Hou Course : T. Y. B. Tech. (Semester V) Date: 23/09/2022 lnstructions: Indian lnstitute of Information Technology, Pune Linear and Nonlinear Optimization (1) Al questions are compulsory. Term 1 Examination (2) Figures to the right indicate maximum marks. (3) Write your MIS Number on Question Paper. 1. Answer the following questions. (4) Writing anything on question paper (except MIS No.) is not allowed. (5) Mobile phones and programmable calculators are strictly prohibited. (6) Exchange/Slharing of statiouary, calculator etc. not allowed. (a) State fundamental theorenm of duality in LPP. (b) Consider the set S = S; U S where S1 = {(, y) e R? | 1 0. 2. Consider the LPP given below and answer the following questions. Min(Z) =1 - 2:x2 + 13 C1, T2 >0 and T3 is unrestricted in sign. Acadermic Year : 2022 - 2023 Max. Marks : 20 (a) Solve the above LPP using Big M method. (b) Write down the dual of the above LPP. (c) find the dual optimal solution without solving the dual problem. (a) Formulate this problem as a linear programming problem. 3. Oue unit of product A coutrilbutes Rs. 100 and requires one unit of raw material and one hour of labour. Oue unit of product B contributes Rs. 400 and requires 6 units of raw material and 3 hours of labour. A vailability of raw naterial at present is 12 units and there are 6 hours of labour. (b) How many units of each product should be produced to maximize profit? (Solve using simplex nethod). [01] [02] [02] (02] [05) [02] [01] [01) [04) R=0,2Examination: Term 1 Subject: Information Retrieval Max Marks: 20 Student MIS No.: 1. Consider the following documents: (6) Indian Institute of Information Technology, Pune (ii) doc1 phone ring person happy person doc dog pet happy run jump doc3 cat purr pet person happy doc, life smile run happy docs life laugh walk run run Semestcr: V Academic Ycar: 2022-23 Timcs: I Hour Construct the inverted index for these five documents. What are the returned results for the query cat AND happy (Assume that no stemming or stop-word removal is required). Relating to the sample documeFts above, outline how the processing of the following Boolean query can be optimized; happy ANrunAND pet 2. The performance of an information retrieval system can be evaluated in terms of its precision, P, and recall, R. Give an English-language definition of these two terms. 3. Given the following positional index Two retrieval systems, X and Y, are being compared. Both are given the same query, applied to a collection of 1500 documents. System X returns 400 documents, of which 40 are relevant to the query. System Y returns 30 documents, of which 15 are relevant to the query. Within the whole collection there are in fact 50 documents relevant to the query. (2] (i) Tabulate the results for each system, and compute the precision and recall for both X and Y. Show your working. [2] (3+3] (ii) Both precision and recall need to be taken into account when evaluating retrieval systems. Why is it not sufficient to pick one and use only that? (2) ANGELS: 2: <36,174,252,651>; 4: <13,22,102,432>; 7: <17>; FOOLS: 2: <«1)17,74,222>; 4: <8,78,108,458>; 7: <313,23,193>; FEAR: 2: <87,704,722,901>; 4: <13,43,113,433>;7: <18328,528>; IN: 2: <3,37,76,444,851>; 4: <10,20;110,470,500>;7: <5.19,25,195>; RUSH: 2: <,66,194,321,702>; 4: <9,69,149,429,569>; 7: <14404>; TO: 2: <47,86,234,999>; 4: <14,24,774,944>;7: <199,319,599,709>; TREAD: 2: <57,94,333>; 4: <15,35,155>; 7: <20,320>; WHERE: 2: <67,124,393, 1001>; 4: <11,41,101,421,431>; 7: <15,35,735>; Which documents match the phrase query "fools rush in" AND "angels fear to tread"? 4. What is the difference between data retrieval and information retrieval? [S) (3]
Examination: Term 1 Subject: CNS Max Marks: 20 Student MIS No.: SN. Instructions: () All questions are compulsory. (2) Figures to the right indicate maximum marks. (3) Mobile phones andprogrammable calculators are strictly prohibited. (4) Do not writelmark on the question paper 1 2 3. 4. Indian Institute of Information Technology, Pune 5. 5. Questions What is the number of elements in Z«*? Find all the elements. Explain the security goals confidentiality, integrity and availability. Semester: B.tech 5h SEM Academic Year: 2022-23 Time: 1 Hour Explain the difference between substitution cipher and transposition 2 cipher. What do you consider more secure explain in brief. Or What is one time pad. Explain the application and drawback of the one time pad. Or What are the attacks performed in modern block cipher explain in brief? Or What are the cryptanalysis attack perform in symmetric cipher model Briefly describe the function of Data Encryption Standard (DES) with proper block diagram. What is 2 DES? Explain Meet in the middle Attack in brief. Write the two conditions of Euclidean algorithm which is used to compute greatest common divisor (gcd(a,b). Is the pair (24,320) relatively prime to each other? Or Find the multiplicative inverse of 23 in Zi00. Marks 2 2 5 5