Title T2 2022.pdf ✅

Duration: 1 Hour Course : T. Y. B. Tech. (Semester V) Date : 04/11/2022 Indian Institute of Information Technology, Pune Instructions: Linear and Nonlinear Optimization (1) All questions are compulsory. Term 2 Examination (2) Figures to the right indicate maximum marks. (3) Write your MIS Number on Question Paper. (4) Writing anything on question paper (except MIS No.) is not allowed. (5) Mobile phones, smart wvatches and programmable calculators are strictly prohibited. (6) Exchange/Sharing of stationary, calculator etc. not allowed. Q1. Give the mathematical formulation of an assignment problem. How does it diffèr from a transportation problem? Q 3. Consider the following LP problem; Q 2. For the following payof matrix with respect to player A ; Find the optimal strategies for both the players. Also find the value of game. Player A A3 A1 A2 T1,I2, T3 >0 4z1 + 4z2 + 4T3<72 Player B B 1 -2 1 A4 -4 As 1 Maz(Z) = 571 + 1032 + 8T Subject to; 31 + 502 + 2r3 < 60; B Ba -1 2 -3 -5 3 -2 Student MIS No.: 3 -4 3 B4 -1 4 4 -5 Bs -2 Academic Year: 2022 -2023 Max. Marks: 20 5 -4 5 LP with the optimal solution z] =0,T2 = 8,T3 = 10 and Mar(Z) = 160 of the given problem is shown in the following table [o2) [04) [04]
B Ch beXES) X1 x2 10 X3 Max(Z)= 160 10 2/3 26/3 Aj-:11/3 Demand 1/3 D; S,5 Source S,4 Ss 8 10 X2 7 4 Destination 1 D, D; | Da 108 (a) Find the range of the coefñcient Co of variable c, and the value of the objective function such that the current optimal solution remains unchanged. 6 (b) Discuss the effect on the ontimal basic feasible solution by adding a new constraint T| + 3¢2 + 4z3 < 50 to the given set of constraints. 7 Q. A manufacturer wants to shin 22 lo2ds of his product as shown below. The matrix gives the Klometrestrom sources of supply to the destinations. The shipping cost is Rs 10 per load per km. 6 5 X3 1 6 6 4 1/3 5 -1/3 4 Ds Supply (a) Find the initial basic feasible solution using VAM method. 2/3 S2 (d) Are there multiple optimum solutions? If yes, identify them. -1/6 8 S/12 S/3 5/3 (b) Solve using MODI method to minimize the total transfortation cost? (c) Check whether the solution is degenerate or not, if yes, then resolve the degeneracy. (10] (e) Write the dual of the given transportation problem and use it for checking the optimum solution.
Examination: Mid Term 2 Max Marks: 20 Student MIS No.: t|01SO SN. 1 Indian Institute of Information Technology, Pune 2 Instructions: (1) All questions are conpulsory. (2) Figures to the right indicate maximum marks. (8) Mobile phones and programmable calculators are strictly prohibited. (4) Do not write/mark on the question paper 3. 4 Subject: Cryptograpl1y and Network Security Academic Year: 2022-23 Find 3P in Elliptic curve: Extend the Diffie-Hellman key exchange scheme to enable three parties to 2+3 share a single secret among them. Can we implement Diffie-Hellman key exchange protocol for two party using Elliptic curve cryptosystem? Justify your answer with proper steps of operation. Questions Define a cryptographic one-way hash function and write down the properties 2+4 of cryptographic hash functions. Briefly describe the working principle of SHA-] with proper block diagram. Y'=x+3x +45 (mod 8831) where the base point P =(4,11). Choose p -13 and q = 11. Compute n and o(n). Let e =7 is a public key. Compute a value for private key d If the message is M =3 then findout ciphertext Cusing RSA algorithm and verify its correctness by performing decryption of received ciphertext. (i) On two consecutive ciphertext blocks? Ke Rartext Inaialzim Vecto (M OR Consider the following block cipher mode. What is the effect of a 3 bit 2+2 transmission error in the cipher text if the three erroneous bits occur? Justify the answer for both cases. (ii) On two ciphertext blocks that are separated by at least one error-free ciphertext block? bleck cipher encrypton úphertert Key’ Time: 1 Hour Semester: B.tech 5h SEM Plaintext |block cipher Cphertext - PMaintext block cjpher ecryptin Ciohertext Key Marks Plaintext block cipher encrypbsn dphetext 5
Examination: Term 2 Subject: Information Retrieval Max Marks: 20 Student MIS No.: Indian Institute of Information Technology, Pune 1 What is the difference between stemming and lemmatization? Explain the porter stemmer algorithm. (i) Bear Semester: V 2. Explain the weighted edit distance approach. Find the minimum edit distanoe in transforming the term NUMPY to NUMBXPR using Levenshtein distance algorithm. (Use dynamic programming concept and consider the weight of insertion and deletion are 1 and substitution is 2) Show all intermediate stens properly. (ii) Bearer Academic Year: 2022-23 Times: 1 Hour (ii) Tymczak 3. Explain cosine similarity technique in vector space model. Why do we use cosine similarity instead of Euclidean distance? Justify your answer with an example. [5] (iv) Pfister [S] 4. Write the algorithmic steps for soundex algorithm. Calculate the soundex encode for: [6] [4]