GATE 2014 SET-1 CS Computer Science and information technology
[Q1 – Q25 carry ONE mark each ]
Q1➡| Engineering Mathematics Consider the statement “Not all that glitters is gold” Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?
Q2➡| Engineering Mathematics Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is____________.
Q3➡| Engineering Mathematics Let G = (V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?
i ➥ G1=(V,E1) where E1={(u,v)|(u,v)∉E}
ii ➥ G2=(V,E2 )where E2={(u,v)│(u,v)∈E}
iii ➥ G3=(V,E3) where E3={(u,v)|there is a path of length≤2 from u to v in E}
iv ➥ G4=(V4,E) where V4 is the set of vertices in G which are not isolated
Q4➡| Engineering Mathematics Consider the following system of equations: 3x + 2y = 1 4x + 7z = 1 x + y + z = 3 x – 2y + 7z = 0 The number of solutions for this system is _.
Q5➡| Engineering Mathematics The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is __.
Q6➡| Engineering Mathematics Let the function where and f'(θ) denote the derivative of f with respect to θ. Which of the following is/are TRUE? (I) There exists θ ∈ such that f'(θ)=0. (II) There exists θ ∈ such that f'(θ)≠0.
Q9➡| Computer Organization A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is .
Q11➡| Data Structure Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time of Depth First Search on G, when G is represented as an adjacency matrix?
Q12➡| Data Structure Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes is O(na logb n). Then the value of a+10b is __.
Q14➡| Data Structure Let P be a quicksort program to sort numbers in ascending order using the first elements as the pivot. Let t1 and t2 be the number of comparisons made by P for the inputs [1 2 3 4 5] and [4 1 5 3 2] respectively. Which one of the following holds?
Q19➡| Operating-Systems Suppose a disk has 201 cylinders, numbered from 0 to 200. At some time the disk arm is at cylinder 100, and there is a queue of disk access requests for cylinders 30, 85, 90, 100, 105, 110, 135 and 145. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access, the request for cylinder 90 is serviced after servicing __ number of requests.
Q21➡| Database Management System Consider the relation scheme R = (E, F, G, H, I, J, K, L, M, N) and the set of functional dependencies {{E,F} → {G}, {F} → {I,J}, {E,H} → {K,L}, {K} → {M}, {L} → {N}} on R. What is the key for R?
Q22➡| Database Management System Given the following statements: S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL. S2: Given the table R(a,b,c) where a and b together form the primary key. the following is a valid table definition. CREATE TABLE S ( a INTEGER, d INTEGER, e INTEGER, PRIMARY KEY (d), FOREIGN KEY (a) references R) Which one of the following statements is CORRECT?
Q23➡| Computer Network Consider the following three statements about link state and distance vector routing protocols, for a large network with 500 network nodes and 4000 links. [S1] The computational overhead in link state protocols is higher than in distance vector protocols. [S2] A distance vector protocol (with split horizon) avoids persistent routing loops, but not a link state protocol. [S3] After a topology change, a link state protocol will converge faster than a distance vector protocol. Which one of the following is correct about S1, S2, and S3 ?
Q24➡| Computer Network Which of the following are used to generate a message digest by the network security protocols? (P) RSA (Q) SHA-1 (R) DES (S) MD5
Q25➡| Computer Network Identify the correct order in which the following actions take place in an interaction between a web browser and a web server. 1. The web browser requests a webpage using HTTP. 2. The web browser establishes a TCP connection with the web server. 3. The web server sends the requested webpage using HTTP. 4. The web browser resolves the domain name using DNS.
Q26➡| Computer Network Consider a token ring network with a length of 2 km having 10 stations including a monitoring station. The propagation speed of the signal is 2×108 m/s and the token transmission time is ignored. If each station is allowed to hold the token for 2 µsec, the minimum time for which the monitoring station should wait (in µsec) before assuming that the token is lost is______.
Q27➡|Computer Network Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs. The round trip time of the connection is 100 msec and the maximum segment size used is 2 KB. The time taken (in msec) by the TCP connection to get back to 32 KB congestion window is _.
Show Answer With Best Explanation
Answer: 1000 To 1300
Explanation: Given, size of congestion window = 32KB Round Trip Time = 100ms Maximum segment size = 2KB
Logic to solve, When Time-out occurs in TCP slow start phase, Thresold value is calculated by Thresold = (Congestion window size)/2
So, start with 1MSS (or 2KB) as sender window size. Slow start phase will begin and window size will grow exponentially till Thresod reached. After that congestion avaidance phase will begin. Now window size will grow linearly till 16MSS (or 32KB).
Slow start phase: window size is 1 MSS (or 2KB) After 1st Round Trip, window size is 2 MSS (or 4KB) After 2nd Round Trip, window size is 4 MSS (or 8KB) After 3rd Round Trip, window size is 8 MSS (or 16KB) (Thresold reached) Congestion avaodance phase: After 4th Round Trip, window size is 9 MSS (or 18KB) After 5th Round Trip, window size is 10 MSS (or 20KB) After 6th Round Trip, window size is 11 MSS (or 22KB) After 7th Round Trip, window size is 12 MSS (or 24KB) After 8th Round Trip, window size is 13 MSS (or 26KB) After 9th Round Trip, window size is 14 MSS (or 28KB) After 10th Round Trip, window size is 15 MSS (or 30KB) After 11th Round Trip, window size is 16 MSS (or 32KB)
Total Round Trip = 11 Total Round Trip Time = 11* 100 ms = 1100ms The time taken (in msec) by the TCP connection to get back to 32 KB congestion window is 1100.
Q28➡| Computer Network Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send data on a 1.5 Mbps link with a one-way latency of 50 msec. To achieve a link utilization of 60%, the minimum number of bits required to represent the sequence number field is __.
Sequence Number = sender window size + receiver window size = N+N =2N Minimum number of bits required for the sequence number = ceil of(2N)
Calculation, Efficiency (η) = => 0.6 = => N = 0.6(1+2a) => N = 0.6(1+2*9.15) = 11.58 = 12(approximate)
Sequence Number = sender window size + receiver window size = N+N = 12+12 = 24 Minimum number of bits required for the sequence number = ceil of(2N) =ceil of (24) = 5bits
Q29➡| Database Managemnt System Consider the following four schedules due to three transactions (indicated by the subscript) using read and write on a data item x, denoted by r(x) and w(x) respectively. Which one of them is conflict serializable?
Q30➡|Database Managemnt System Given the following two statements: S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF. S2: AB->C, D->E, E->C is a minimal cover for the set of functional dependencies AB->C, D->E, AB->E, E->C. Which one of the following is CORRECT?
Q31➡| Operating Systems An operating system uses the Banker’s algorithm for deadlock avoidance when managing the allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution. There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system is currently in a safe state. Consider the following independent requests for additional resources in the current state:
REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z Which one of the following is TRUE?
Q32➡| Operating Systems Consider the following set of processes that need to be scheduled on a single CPU. All the times are given in milliseconds. Using the shortest remaining time first scheduling algorithm, the average process turnaround time (in msec) is .
Q33➡| Operating Systems Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is .
Q37➡|Algorithms There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is .
Q38➡|Algorithms Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?
Q40➡| Data Structure Consider a hash table with 9 slots. The hash function is ℎ(k) = k Nod 9. The collisions are resolved by chaining. The following 9 keys are inserted in the order: 5, 28, 19, 15, 20, 33, 12, 17, The maximum, minimum, and average chain lengths in the hash table, respectively, are
Q41➡|Programming in C Consider the following C function in which size is the number of elements in the array E: The value returned by the function MyX is the
i ➥ maximum possible sum of elements in any sub-array of array E.
ii ➥ maximum element in any sub-array of array E.
iii ➥ sum of the maximum elements in all possible sub-arrays of array E.
Q43➡| Computer Organization Consider a 6-stage instruction pipeline, where all stages are perfectly balanced.Assume that there is no cycle-time overhead of pipelining. When an application is executing on this 6-stage pipeline, the speedup achieved with respect to non-pipelined execution if 25% of the instructions incur 2 pipeline stall cycles is .
Q44➡| Computer Organization An access sequence of cache block addresses is of length N and contains n unique block addresses. The number of unique block addresses between two consecutive accesses to the same block address is bounded above by k. What is the miss ratio if the access sequence is passed through a cache of associativity A ≥ k exercising least-recently-used replacement policy?
Q45➡|Digital Logic Design Consider the 4-to-1 multiplexer with two select lines S1 and S0 given below. The minimal sum-of-products form of the Boolean expression for the output F of the multiplexer is
Q47➡|Engineering Mathematics A function f(x) is continuous in the interval [0,2]. It is known that f(0) = f(2) = −1 and f(1) = 1. Which one of the following statements must be true?
i ➥ There exists a y in the interval (0,1) such that f(y) = f(y + 1)
ii ➥ For every y in the interval (0,1), f(y) = f(2− y)
iii ➥ The maximum value of the function in the interval (0,2) is 1
iv ➥ There exists a y in the interval (0,1) such that f(y) = −f(2− y)
Q49➡|Engineering Mathematics A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)}and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10- pennants is .
Q50➡| Engineering Mathematics Let S denote the set of all functions f: {0,1}4 → {0,1}. Denote by N the number of functions from S to the set {0,1}. The value of log2 log2 N is .
Q51➡| Engineering Mathematics Consider an un-directed graph G where self-loops are not allowed. The vertex set of G is {(i, j):1 ≤ i ≤ 12, 1 ≤ j ≤ 12}. There is an edge between (a, b) and (c, d) if |a − c| ≤ 1 and |b − d| ≤ 1. The number of edges in this graph is .
and f'(θ) denote the derivative of f with respect to θ. Which of the following is/are TRUE?
such that f'(θ)=0.
