**GATE 2020 CS Computer Science and information technology**

##### [Q1 – Q25 ,Carry ONE mark each]

Q1➡ | Data StructureWhat is the worst case time complexity of inserting n ^{2} elements into an AVL-tree with n elements initially? |

i ➥ θ(n^{2} log n) |

ii ➥ θ(n^{3}) |

iii ➥ θ(n^{2}) |

iv ➥ θ(n^{4}) |

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Q2➡ | Data Structure The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Which one of the following is the postorder traversal of the tree? |

i ➥ 10, 11, 12, 15, 16, 18, 19, 20 |

ii ➥ 20, 19, 18, 16, 15, 12, 11, 10 |

iii ➥ 11, 12, 10, 16, 19, 18, 20, 15 |

iv ➥ 19, 16, 18, 20, 11, 12, 10, 15 |

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Q3➡ | Computer Organization Consider the following data path diagram: Consider an instruction: R0 ← R1 + R2. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts r and w indicate read and write operations, respectively. 1. R2 _{r}, TEMP1_{r}, ALU_{add}, TEMP2_{w}2. R1 _{r}, TEMP1_{w}3. PC _{r}, MAR_{w}, MEM_{r}4. TEMP2 _{r}, RO_{w}5. MDR _{r}, IR_{w}Which one of the following is the correct order of execution of the above steps? |

i ➥ 2, 1, 4, 5, 3 |

ii ➥ 1, 2, 4, 3, 5 |

iii ➥ 3, 5, 1, 2, 4 |

iv ➥ 3, 5, 2, 1, 4 |

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Q4➡ | Computer Organization Consider the following statements. I. Daisy chaining is used to assign priorities in attending interrupts. II. When a device raises a vectored interrupt, the CPU does polling to identify the source of the interrupt. III. In polling, the CPU periodically checks the status bits to know if any device needs its attention. IV. During DMA, both the CPU and DMA controller can be bus masters at the same time. Which of the above statements is/are TRUE? |

i ➥ I and III only |

ii ➥ I and IV only |

iii ➥ I and II only |

iv ➥ III only |

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Q5➡ | Engineering Mathematics Consider the functions I. e ^{-x}II. x ^{2}-sin xIII. √(x ^{3}+1)Which of the above functions is/are increasing everywhere in [0,1]? |

i ➥ I and III only |

ii ➥ II and III only |

iii ➥ III only |

iv ➥ II only |

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Q6➡ | Algorithms For parameters a and b, both of which are ω(1), T(n) = T(n ^{1/a})+1, and T(b)=1.Then T(n) is |

i ➥ θ(log_{ab} n) |

ii ➥ θ(log_{b} log_{a} n) |

iii ➥ θ(log_{a} log_{b} n) |

iv ➥ θ(log_{2} log_{2} n) |

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Q7➡ | Operating SystemsConsider the following statements about process state transitions for a system using preemptive scheduling. I. A running process can move to ready state. II. A ready process can move to running state. III. A blocked process can move to running state. IV. A blocked process can move to ready state. Which of the above statements are TRUE? |

i ➥ I, II and III only |

ii ➥ II and III only |

iii ➥ I, II and IV only |

iv ➥ I, II, III and IV |

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Q8➡ | Operating Systems Consider allocation of memory to a new process. Assume that none of the existing holes in the memory will exactly fit the process’s memory requirement. Hence, a new hole of smaller size will be created if allocation is made in any of the existing holes. Which one of the following statements is TRUE? |

i ➥ The hole created by next fit is never larger than the hole created by best fit. |

ii ➥ The hole created by worst fit is always larger than the hole created by first fit. |

iii ➥ The hole created by first fit is always larger than the hole created by next fit. |

iv ➥ The hole created by best fit is never larger than the hole created by first fit. |

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Q9➡ | Theory of Computation Consider the language L = {a ^{n}| n≥0} ∪ {a^{n}b^{n}| n≥0} and the following statements.I. L is deterministic context-free. II. L is context-free but not deterministic context-free. III. L is not LL(k) for any k. Which of the above statements is/are TRUE? |

i ➥ III only |

ii ➥ I only |

iii ➥ I and III only |

iv ➥ II only |

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Q10➡ | Compiler DesignConsider the following statements. I. Symbol table is accessed only during lexical analysis and syntax analysis. II. Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment. III. Errors violating the condition ‘any variable must be declared before its use’ are detected during syntax analysis. Which of the above statements is/are TRUE? |

i ➥ I and III only |

ii ➥ II only |

iii ➥ I only |

iv ➥ None of I, II and III |

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Q11➡ | Theory of Computation Consider the following statements. I. If L1 ∪ L2 is regular, then both L1 and L2 must be regular. II. The class of regular languages is closed under infinite union. Which of the above statements is/are TRUE? |

i ➥ II only |

ii ➥ I only |

iii ➥ Neither I nor II |

iv ➥ Both I and II |

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Q12➡ | Theory of Computation Which one of the following regular expressions represents the set of all binary strings with an odd number of 1’s? |

i ➥ (0*10*10*)*0*1 |

ii ➥ 10*(0*10*10*)* |

iii ➥ (0*10*10*)*10* |

iv ➥ ((0 + 1)*1(0 + 1)*1)*10* |

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Q13➡ | Engineering Mathematics Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________. |

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Q14➡ | Engineering MathematicsLet R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ______. |

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Q15➡ | Data Structure What is the worst case time complexity of inserting n elements into an empty linked list, if the linked list needs to be maintained in sorted order? |

i ➥ θ(n) |

ii ➥ θ(n log n) |

iii ➥ θ(1) |

iv ➥ θ(n^{2}) |

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Q16➡ | Computer Network Consider the following statements about the functionality of an IP based router. I. A router does not modify the IP packets during forwarding. II. It is not necessary for a router to implement any routing protocol. III. A router should reassemble IP fragments if the MTU of the outgoing link is larger than the size of the incoming IP packet. Which of the above statements is/are TRUE? |

i ➥ II only |

ii ➥ I and II only |

iii ➥ II and III only |

iv ➥ I only |

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Q17➡ | Database Management System Which one of the following is used to represent the supporting many-one relationships of a weak entity set in an entity-relationship diagram? |

i ➥ Diamonds with double/bold border |

ii ➥ Ovals with double/bold border |

iii ➥ Ovals that contain underlined identifiers |

iv ➥ Rectangles with double/bold border |

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Q18➡ | Database Management System Consider a relational database containing the following schemas. The primary key of each table is indicated by underlying the constituent fields. SELECT s.sno, s.sname FROM Suppliers s, Catalogue c WHERE s.sno = c.sno AND Cost > (SELECT AVG (cost) FROM Catalogue WHERE pno = ‘P4’ GROUP BY pno); The number of rows returned by the above SQL query is |

i ➥ 2 |

ii ➥ 0 |

iii ➥ 4 |

iv ➥ 5 |

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Q19➡ | Computer Network Assume that you have made a request for a web page through your web browser to a web server. Initially the browser cache is empty. Further, the browser is configured to send HTTP requests in non-persistent mode. The web page contains text and five very small images. The minimum number of TCP connections required to display the web page completely in your browser is _______. |

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Q20➡ | Complier Design Consider the following grammar. S → aSB|d B → b The number of reduction steps taken by a bottom-up parser while accepting the string aaadbbb is ________. |

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Q21➡ | Data StructuresConsider a double hashing scheme in which the primary hash function is h _{1}(k) = k mod 23, and the secondary hash function is h _{2}(k) = 1 + (k mod 19). Assume that the table size is 23. Then the address returned by probe 1 in the probe sequence (assume that the probe sequence begins at probe 0) for key value k=90 is _______. |

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Q22➡ | Data StructuresConsider the following C program. The output of the program is ______. |

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Q23➡ | Computer Organization A direct mapped cache memory of 1 MB has a block size of 256 bytes. The cache has an access time of 3 ns and a hit rate of 94%. During a cache miss, it takes 20 ns to bring the first word of a block from the main memory, while each subsequent word takes 5 ns. The word size is 64 bits. The average memory access time in ns (round off to 1 decimal place) is _____. |

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Q24➡ | Digital Logic Design If there are m input lines and n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m + n is ______. |

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Q25➡ | Digital Logic Design A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The minimum number of select lines needed for the multiplexer is _______. |

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**[Q26 – Q55, Carry TWO marks each ]**

Q26➡ | Algorithms Let G = (V,E) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighted edge (u,v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is |

i ➥ θ(|E||V|) |

ii ➥ θ(|E|+|V|) |

iii ➥ θ(|V|) |

iv ➥ θ(|E| log|V|) |

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Q27➡ | Computer Organization A computer system with a word length of 32 bits has a 16 MB byte-addressable main memory and a 64 KB, 4-way set associative cache memory with a block size of 256 bytes. Consider the following four physical addresses represented in hexadecimal notation. A1 = 0x42C8A4, A2 = 0x546888, A3 = 0x6A289C, A4 = 0x5E4880 Which one of the following is TRUE? |

i ➥ A3 and A4 are mapped to the same cache set. |

ii ➥ A1 and A4 are mapped to different cache sets. |

iii ➥ A2 and A3 are mapped to the same cache set. |

iv ➥ A1 and A3 are mapped to the same cache set. |

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Q28➡ | Digital Logic Design Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively. If R3 = R1/R2, what is the value stored in R3? |

i ➥ 0x83400000 |

ii ➥ 0xC8500000 |

iii ➥ 0xC0800000 |

iv ➥ 0x40800000 |

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Q29➡ | Theory of ComputationConsider the following languages. L _{1} = {wxyx | w,x,y ∈ (0 + 1)^{+}}L _{2 }= {xy | x,y ∈ (a + b)*, |x| = |y|, x ≠ y}Which one of the following is TRUE? |

i ➥ L_{1} is context-free but L_{2} is not context-free. |

ii ➥ L_{1} is regular and L_{2} is context-free. |

iii ➥ Neither L_{1} nor L_{2} is context-free. |

iv ➥ L_{1} is context-free but not regular and L_{2} is context-free. |

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Q30➡ | Digital Logic Design Consider the Boolean function z(a,b,c) Which one of the following minterm lists represents the circuit given above ? |

i ➥ Z = ∑(2,3,5) |

ii ➥ Z = ∑(0,1,3,7) |

iii ➥ Z = ∑(1,4,5,6,7). |

iv ➥ Z = ∑(2,4,5,6,7). |

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Q31➡ | Engineering Mathematics Let A and B be two n×n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements, I. rank(AB) = rank(A) rank(B) II. det(AB) = det(A) det(B) III. rank(A + B) ≤ rank(A) + rank(B) IV. det(A + B) ≤ det(A) + det(B) Which of the above statements are TRUE? |

i ➥ I and IV only |

ii ➥ III and IV only |

iii ➥ II and III only |

iv ➥ I and II only |

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Q32➡ | Theory of Computation Which of the following languages are undecidable? Note that indicates encoding of the Turing machine M. L1 = {<M>| L(M) = Φ} L2 = {<M,w,q>| M on input w reaches state q in exactly 100 steps} L3 = {<M>| L(M) is not recursive} L4 = {<M>| L(M) contains at least 21 members} |

i ➥ L2, L3 and L4 only |

ii ➥ L1, L3 and L4 only |

iii ➥ L2 and L3 only |

iv ➥ L1 and L3 only |

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Q33➡ | Computer Network An organization requires a range of IP addresses to assign one to each of its 1500 computers. The organization has approached an Internet Service Provider (ISP) for this task. The ISP uses CIDR and serves the requests from the available IP address space 202.61.0.0/17. The ISP wants to assign an address space to the organization which will minimize the number of routing entries in the ISP’s router using route aggregation. Which of the following address spaces are potential candidates from which the ISP can allot any one to the organization? A. 202.61.84.0/21 B. 202.61.104.0/21 C. 202.61.64.0/21 D. 202.61.144.0/21 |

i ➥ B and C only |

ii ➥ A and D only |

iii ➥ A and B only |

iv ➥ C and D only |

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Q34➡ | Database Management System Consider a schedule of transactions T1 and T2: Here, RX stands for “Read(X)” and WX stands for “Write(X)”. Which one of the following schedules is conflict equivalent to the above schedule? |

i ➥ |

ii ➥ |

iii ➥ |

iv ➥ |

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Q35➡ | Database Management System Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE? |

i ➥ R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute. |

ii ➥ R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key. |

iii ➥ A cell in R holds a set instead of an atomic value. |

iv ➥ R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key. |

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Q36➡ | Operating System Consider the following five disk access requests of the form (request id, cylinder number) that are present in the disk scheduler queue at a given time. (P, 155), (Q, 85), (R, 110), (S, 30), (T, 115) Assume the head is positioned at cylinder 100. The scheduler follows Shortest Seek Time First scheduling to service the requests. Which one of the following statements is FALSE? |

i ➥ Q is serviced after S, but before T. |

ii ➥ R is serviced before P. |

iii ➥ T is serviced before P. |

iv ➥ The head reverses its direction of movement between servicing of Q and P. |

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Q37➡ | Operating System Each of a set of n processes executes the following code using two semaphores a and b initialized to 1 and 0, respectively. Assume that count is a shared variable initialized to 0 and not used in CODE SECTION P. What does the code achieve? |

i ➥ It ensures that no process executes CODE SECTION Q before every process has finished CODE SECTION P. |

ii ➥ It ensures that at most two processes are in CODE SECTION Q at any time. |

iii ➥ It ensures that at most n-1 processes are in CODE SECTION P at any time. |

iv ➥ It ensures that all processes execute CODE SECTION P mutually exclusively. |

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Q38➡ | Compiler DesignConsider the productions A⟶PQ and A⟶XY. Each of the five non-terminals A, P, Q, X, and Y has two attributes: s is a synthesized attribute, and i is an inherited attribute. Consider the following rules: Rule 1: P.i = A.i + 2, Q.i = P.i + A.i, and A.s = P.s + Q.s Rule 2: X.i = A.i + Y.s and Y.i = X.s + A.i Which one of the following is TRUE? |

i ➥ Only Rule 1 is L-attributed. |

ii ➥ Only Rule 2 is L-attributed. |

iii ➥ Neither Rule 1 nor Rule 2 is L-attributed. |

iv ➥ Both Rule 1 and Rule 2 are L-attributed. |

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Q39➡ | Computer Organization A processor has 64 registers and uses 16-bit instruction format. It has two types of instructions: I-type and R-type. Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value. Each R-type instruction contains an opcode and two register names. If there are 8 distinct I-type opcodes, then the maximum number of distinct R-type opcodes is ___________. |

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Q40➡ | Computer Organization Consider a non-pipelined processor operating at 2.5 GHz. It takes 5 clock cycles to complete an instruction. You are going to make a 5-stage pipeline out of this processor. Overheads associated with pipelining force you to operate the pipelined processor at 2 GHz. In a given program, assume that 30% are memory instructions, 60% are ALU instructions and the rest are branch instructions. 5% of the memory instructions cause stalls of 50 clock cycles each due to cache misses and 50% of the branch instructions cause stalls of 2 cycles each. Assume that there are no stalls associated with the execution of ALU instructions. For this program, the speedup achieved by the pipelined processor over the non-pipelined processor (round off to 2 decimal places) is ________. |

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Q41➡ | Engineering Mathematics The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ____. |

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Q42➡ | Data Structure In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a,b]? Assume that the number of reported elements is k. |

i ➥ θ(k log n) |

ii ➥ θ(log n) |

iii ➥ θ(n log k) |

iv ➥ θ(log n + k) |

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Q43➡ | Data Structure Let G = (V,E) be a directed, weighted graph with weight function w:E → R. For some function f:V → R, for each edge (u,v) ∈ E, define w'(u,v) as w(u,v) + f(u) – f(v). Which one of the options completes the following sentence so that it is TRUE? “The shortest paths in G under w are shortest paths under w’ too, _________”. |

i ➥ if and only if ∀u ∈ V, f(u) is negative |

ii ➥ for every f: V→R |

iii ➥ if and only if ∀u ∈ V, f(u) is positive |

iv ➥ if and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G |

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Q44➡ | Engineering MathematicsWhich one of the following predicate formulae is NOT logically valid? Note that W is a predicate formula without any free occurrence of x. |

i ➥ ∀x(p(x) ∨ W) ≡ ∀x p(x) ∨ W |

ii ➥ ∃x(p(x) ∧ W) ≡ ∃x p(x) ∧ W |

iii ➥ ∃x(p(x) → W) ≡ ∀x p(x) → W |

iv ➥ ∀x(p(x) → W) ≡ ∀x p(x) → W |

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Q45➡ | Operating SystemConsider the following set of processes, assumed to have arrived at time 0. Consider the CPU scheduling algorithms Shortest Job First (SJF) and Round Robin (RR). For RR, assume that the processes are scheduled in the order P1,P2,P3,P4. If the time quantum for RR is 4 ms, then the absolute value of the difference between the average turnaround times (in ms) of SJF and RR (round off to 2 decimal places) is ________. |

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Q46➡ | Algorithms Consider a graph G = (V, E), where V = {v _{1}, v_{2}, …, v_{100}}, E = {(vi, vj) | 1 ≤ i < j ≤ 100}, and weight of the edge (v_{i}, v_{j}) is |i – j|. The weight of the minimum spanning tree of G is _______. |

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Q47➡ | Programming Consider the following C functions: The value returned by pp(3,4) is _______. |

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Q48➡ | Data Structure Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is _______. |

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Q49➡ | ProgrammingConsider the following C functions: The return value of fun2 (5) is ______. |

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Q50➡ | Engineering MathematicsFor n>2, let a ∈ {0,1} ^{n} be a non-zero vector. Suppose that x is chosen uniformly at random from {0,1}^{n}. Then, the probability that is an odd number is ________. |

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Q51➡ | Computer Network Consider a TCP connection between a client and a server with the following specifications: the round trip time is 6 ms, the size of the receiver advertised window is 50 KB, slow start threshold at the client is 32 KB, and the maximum segment size is 2 KB. The connection is established at time t=0. Assume that there are no timeouts and errors during transmission. Then the size of the congestion window (in KB) at time t+60 ms after all acknowledgements are processed is ________. |

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Q52➡ | Database Management SystemConsider a database implemented using B+ tree for file indexing and installed on a disk drive with block size of 4 KB. The size of search key is 12 bytes and the size of tree/disk pointer is 8 bytes. Assume that the database has one million records. Also assume that no node of the B+ tree and no records are present initially in main memory. Consider that each record fits into one disk block. The minimum number of disk accesses required to retrieve any record in the database is ________. |

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Q53➡ | Operating SystemConsider a paging system that uses a 1-level page table residing in main memory and a TLB for address translation. Each main memory access takes 100 ns and TLB lookup takes 20 ns. Each page transfer to/from the disk takes 5000 ns. Assume that the TLB hit ratio is 95%, page fault rate is 10%. Assume that for 20% of the total page faults, a dirty page has to be written back to disk before the required page is read in from disk. TLB update time is negligible. The average memory access time in ns (round off to 1 decimal places) is _______. |

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Q54➡ | Engineering MathematicsGraph G is obtained by adding vertex s to K _{3,4} and making s adjacent to every vertex of K_{3,4}. The minimum number of colours required to edge-colour G is ________. |

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Q55➡ | Theory of Computation Consider the following language. L = {x ∈ {a,b}* | number of a’s in x is divisible by 2 but not divisible by 3} The minimum number of states in a DFA that accepts L is ______. |

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