Page 1 SESSION - 3 Page 2 SESSION - 3 2013 Question Booklet Code CS-C 1/20 CS : COMPUTER SCIENCE AND INFORMATION TECHNOLOGY Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not CS, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number CS C Page 3 SESSION - 3 2013 Question Booklet Code CS-C 1/20 CS : COMPUTER SCIENCE AND INFORMATION TECHNOLOGY Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not CS, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number CS C 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 2/20 Q.1 to Q.25 carry one mark each. Q.1 Using public key cryptography, X adds a digital signature s to message M, encrypts <M, s>, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations? (A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key (B) Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key (C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key (D) Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key Q.2 Match the problem domains in GROUP I with the solution technologies in GROUP II. GROUP I GROUP II (P) Service oriented computing (1) Interoperability (Q) Heterogeneous communicating systems (2) BPMN (R) Information representation (3) Publish-find-bind (S) Process description (4) XML (A) P-1, Q-2, R-3, S-4 (B) P-3, Q-4, R-2, S-1 (C) P-3, Q-1, R-4, S-2 (D) P-4, Q-3, R-2, S-1 Q.3 A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero? (A) This algorithm is equivalent to the first-come-first-serve algorithm. (B) This algorithm is equivalent to the round-robin algorithm. (C) This algorithm is equivalent to the shortest-job-first algorithm. (D) This algorithm is equivalent to the shortest-remaining-time-first algorithm. Q.4 What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production (i.e., of type A ? ? and A ? a) to parse a string with n tokens? (A) n/2 (B) n-1 (C) 2n-1 (D) 2 n Q.5 Consider the languages F = 1 L and { } a L = 2 . Which one of the following represents 1 2 1 L L L * * U ? (A) {?} (B) F (C) a* (D) {?, a} Q.6 Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes? (A) O(1) (B) O(log n) (C) O(n) (D) O(n log n) Q.7 Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort? (A) O(log n) (B) O(n) (C) O(n log n) (D) O(n 2 ) Page 4 SESSION - 3 2013 Question Booklet Code CS-C 1/20 CS : COMPUTER SCIENCE AND INFORMATION TECHNOLOGY Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not CS, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number CS C 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 2/20 Q.1 to Q.25 carry one mark each. Q.1 Using public key cryptography, X adds a digital signature s to message M, encrypts <M, s>, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations? (A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key (B) Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key (C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key (D) Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key Q.2 Match the problem domains in GROUP I with the solution technologies in GROUP II. GROUP I GROUP II (P) Service oriented computing (1) Interoperability (Q) Heterogeneous communicating systems (2) BPMN (R) Information representation (3) Publish-find-bind (S) Process description (4) XML (A) P-1, Q-2, R-3, S-4 (B) P-3, Q-4, R-2, S-1 (C) P-3, Q-1, R-4, S-2 (D) P-4, Q-3, R-2, S-1 Q.3 A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero? (A) This algorithm is equivalent to the first-come-first-serve algorithm. (B) This algorithm is equivalent to the round-robin algorithm. (C) This algorithm is equivalent to the shortest-job-first algorithm. (D) This algorithm is equivalent to the shortest-remaining-time-first algorithm. Q.4 What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production (i.e., of type A ? ? and A ? a) to parse a string with n tokens? (A) n/2 (B) n-1 (C) 2n-1 (D) 2 n Q.5 Consider the languages F = 1 L and { } a L = 2 . Which one of the following represents 1 2 1 L L L * * U ? (A) {?} (B) F (C) a* (D) {?, a} Q.6 Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes? (A) O(1) (B) O(log n) (C) O(n) (D) O(n log n) Q.7 Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort? (A) O(log n) (B) O(n) (C) O(n log n) (D) O(n 2 ) 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 3/20 Q.8 In the following truth table, V = 1 if and only if the input is valid. Inputs Outputs D 0 D 1 D 2 D 3 X 0 X 1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent? (A) Priority encoder (B) Decoder (C) Multiplexer (D) Demultiplexer Q.9 The smallest integer that can be represented by an 8-bit number in 2’s complement form is (A) -256 (B) -128 (C) -127 (D) 0 Q.10 Which one of the following does NOT equal 2 2 2 1 1 1 z z y y x x ? (A) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 + + + + + + z z z y y y x x x (B) 1 1 1 1 1 1 1 1 1 2 2 2 + + + + + + z z y y x x (C) 2 1 0 0 2 2 2 2 z z z y z y y x y x - - - - (D) 2 2 2 2 2 1 2 2 z z z y z y y x y x + + + + Q.11 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? (A) 8/(2e 3 ) (B) 9/(2e 3 ) (C) 17/(2e 3 ) (D) 26/(2e 3 ) Q.12 A binary operation ? on a set of integers is defined as 2 2 y x y x + = ? . Which one of the following statements is TRUE about ?? (A) Commutative but not associative (B) Both commutative and associative (C) Associative but not commutative (D) Neither commutative nor associative Q.13 Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. (A) P only (B) Q only (C) Both P and Q (D) Neither P nor Q Q.14 Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three? (A) 1/8 (B) 1 (C) 7 (D) 8 Page 5 SESSION - 3 2013 Question Booklet Code CS-C 1/20 CS : COMPUTER SCIENCE AND INFORMATION TECHNOLOGY Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not CS, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number CS C 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 2/20 Q.1 to Q.25 carry one mark each. Q.1 Using public key cryptography, X adds a digital signature s to message M, encrypts <M, s>, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations? (A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key (B) Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key (C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key (D) Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key Q.2 Match the problem domains in GROUP I with the solution technologies in GROUP II. GROUP I GROUP II (P) Service oriented computing (1) Interoperability (Q) Heterogeneous communicating systems (2) BPMN (R) Information representation (3) Publish-find-bind (S) Process description (4) XML (A) P-1, Q-2, R-3, S-4 (B) P-3, Q-4, R-2, S-1 (C) P-3, Q-1, R-4, S-2 (D) P-4, Q-3, R-2, S-1 Q.3 A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero? (A) This algorithm is equivalent to the first-come-first-serve algorithm. (B) This algorithm is equivalent to the round-robin algorithm. (C) This algorithm is equivalent to the shortest-job-first algorithm. (D) This algorithm is equivalent to the shortest-remaining-time-first algorithm. Q.4 What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production (i.e., of type A ? ? and A ? a) to parse a string with n tokens? (A) n/2 (B) n-1 (C) 2n-1 (D) 2 n Q.5 Consider the languages F = 1 L and { } a L = 2 . Which one of the following represents 1 2 1 L L L * * U ? (A) {?} (B) F (C) a* (D) {?, a} Q.6 Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes? (A) O(1) (B) O(log n) (C) O(n) (D) O(n log n) Q.7 Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort? (A) O(log n) (B) O(n) (C) O(n log n) (D) O(n 2 ) 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 3/20 Q.8 In the following truth table, V = 1 if and only if the input is valid. Inputs Outputs D 0 D 1 D 2 D 3 X 0 X 1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent? (A) Priority encoder (B) Decoder (C) Multiplexer (D) Demultiplexer Q.9 The smallest integer that can be represented by an 8-bit number in 2’s complement form is (A) -256 (B) -128 (C) -127 (D) 0 Q.10 Which one of the following does NOT equal 2 2 2 1 1 1 z z y y x x ? (A) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 + + + + + + z z z y y y x x x (B) 1 1 1 1 1 1 1 1 1 2 2 2 + + + + + + z z y y x x (C) 2 1 0 0 2 2 2 2 z z z y z y y x y x - - - - (D) 2 2 2 2 2 1 2 2 z z z y z y y x y x + + + + Q.11 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? (A) 8/(2e 3 ) (B) 9/(2e 3 ) (C) 17/(2e 3 ) (D) 26/(2e 3 ) Q.12 A binary operation ? on a set of integers is defined as 2 2 y x y x + = ? . Which one of the following statements is TRUE about ?? (A) Commutative but not associative (B) Both commutative and associative (C) Associative but not commutative (D) Neither commutative nor associative Q.13 Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. (A) P only (B) Q only (C) Both P and Q (D) Neither P nor Q Q.14 Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three? (A) 1/8 (B) 1 (C) 7 (D) 8 2013 COMPUTER SCIENCE & INFORMATION TECH. - CS CS- C 4/20 Q.15 Function f is known at the following points: x 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 f(x) 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of ( ) ? 3 0 dx x f computed using the trapezoidal rule is (A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045 Q.16 Which one of the following functions is continuous at x = 3? (A) ( ) ? ? ? ? ? ? ? < + > - = = 3 if , 3 3 3 if , 1 3 if , 2 x x x x x x f (B) ( ) ? ? ? ? - = = 3 if 8 3 if , 4 x x x x f (C) ( ) ? ? ? > - = + = 3 if 4 3 if , 3 x x x x x f (D) ( ) 3 if , 27 1 3 ? - = x x x f Q.17 Which one of the following expressions does NOT represent exclusive NOR of x and y? (A) y x xy ' ' + (B) y x ' ? (C) y x ? ' (D) y x ' ? ' Q.18 In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from (A) (j mod v) * k to (j mod v) * k + (k-1) (B) (j mod v) to (j mod v) + (k-1) (C) (j mod k) to (j mod k) + (v-1) (D) (j mod k) * v to (j mod k) * v + (v-1) Q.19 What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices? (A) T(n 2 ) (B) T(n 2 log n) (C) T(n 3 ) (D) T(n 3 log n) Q.20 Which of the following statements are TRUE? 1 The problem of determining whether there exists a cycle in an undirected graph is in P. 2. The problem of determining whether there exists a cycle in an undirected graph is in NP. 3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A. (A) 1, 2 and 3 (B) 1 and 2 only (C) 2 and 3 only (D) 1 and 3 only Q.21 Which of the following statements is/are FALSE? 1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. 2. Turing recognizable languages are closed under union and complementation. 3. Turing decidable languages are closed under intersection and complementation. 4. Turing recognizable languages are closed under union and intersection. (A) 1 and 4 only (B) 1 and 3 only (C) 2 only (D) 3 onlyRead More

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