GATE 2015 SET-2 CS Computer Science and information technology
[Q1 – Q25 carry ONE mark each ]
| Q1➡ | Engineering Mathematics Consider the following statements: S1: If a candidate is known to be corrupt, then he will not be elected. S2: If a candidate is kind, he will be elected. Which one of the following statements follows from S1 and S2 as per sound inference rules of logic? |
| i ➥ If a person is known to corrupt, he is kind |
| ii ➥ If a person is not known to be corrupt, he is not kind |
| iii ➥ If a person is kind, he is not known to be corrupt |
| iv ➥ If a person is not kind, he is not known to be corrupt |
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Answer: III
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| Q2➡ | Engineering Mathematics The cardinality of the power set of {0, 1, 2, … 10} is __________. |
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Answer: 2048
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| Q3➡ | Engineering Mathematics Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is true? |
| i ➥ R is symmetric and reflexive but not transitive |
| ii ➥ R is reflexive but not symmetric and not transitive |
| iii ➥ R is transitive but not reflexive and not symmetric |
| iv ➥ R is symmetric but not reflexive and not transitive |
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Answer: IV
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| Q4➡ | Engineering Mathematics The number of divisors of 2100 is ______. |
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Answer: 36
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| Q5➡ | Engineering Mathematics The larger of the two eigenvalues of the matrix  |
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Answer: 6
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| Q6➡ | Data Structure An unordered list contains n distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is |
| i ➥ Θ(nlog n) |
| ii ➥ Θ(n) |
| iii ➥ Θ(log n) |
| iv ➥ Θ(1) |
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Answer: IV
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| Q7➡ | Digital Logic Design The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0, 0, 1, 1, 2, 2, 3, 3, 0, 0,……) is _______. |
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Answer: 3
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| Q8➡ | Computer Organization Assume that for a certain processor, a read request takes 50 nanoseconds on a cache miss and 5 nanoseconds on a cache hit. Suppose while running a program, it was observed that 80% of the processors read requests result in a cache hit. The average and access time in nanoseconds is ________. |
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Answer: 14
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| Q9➡ | Operating Systems A computer system implements a 40-bit virtual address, page size of 8 kilobytes, and a 128-entry translation look-aside buffer (TLB organized into 32 sets each having four ways. Assume that the TLB tag does not store any process id. The minimum length of the TLB tag in bits is _________. |
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Answer: 22
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| Q10➡ | Theory of Computation Consider the following statements: I. The complement of every Turning decidable language is Turning decidable II. There exists some language which is in NP but is not Turing decidable III. If L is a language in NP, L is Turing decidable Which of the above statements is/are True? |
| i ➥ Only II |
| ii ➥ Only III |
| iii ➥ Only I and II |
| iv ➥ Only I and III |
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Answer: IV
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| Q11➡ | Programming Consider the following function written the C programming language.  The output of the above function on input “ABCD EFGH” is |
| i ➥ ABCD EFGH |
| ii ➥ ABCD |
| iii ➥ HGFE DCBA |
| iv ➥ DCBA |
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Answer: IV
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| Q12➡ | Data Structure Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is |
| i ➥ Ω(logn) |
| ii ➥ Ω(n) |
| iii ➥ Ω(nlog n) |
| iv ➥ Ω(n2) |
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Answer: I
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| Q13➡ | Data Structure A binary tree T has 20 leaves. The number of nodes in T having two children is ________. |
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Answer: 19
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| Q14➡ | Programming Consider the following C functions  The return value of fun(5) is ________. |
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Answer: 51
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| Q15➡ | Software Engineering A software requirements specification(SRS) document should avoid discussing which one of the following? |
| i ➥ User interface issues |
| ii ➥ Non-functional requirements |
| iii ➥ Design specification |
| iv ➥ Interfaces with third party software |
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Answer: III
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| Q16➡ | Algorithms Consider two decision problems Q1, Q2 such that Q1 reduces in polynomial time to 3-SAT and 3 -SAT reduces in polynomial time to Q2. Then which one of following is consistent with the above statement? |
| i ➥ Q1 is in NP, Q2 in NP hard |
| ii ➥ Q1 is in NP, Q2 is NP hard |
| iii ➥ Both Q1 and Q2 are in NP |
| iv ➥ Both Q1 and Q2 are NP hard |
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Answer: I
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| Q17➡ | Compiler Design Match the following:  |
| i ➥ P-2, Q-3, R-1, S-4 |
| ii ➥ P-2, Q-1, R-4, S-3 |
| iii ➥ P-2, Q-4, R-1, S-3 |
| iv ➥ P-2, Q-3, R-4, S-1 |
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Answer: III
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| Q18➡ | Compiler Design In the context of abstract-syntax-tree (AST) and control-flow-graph (CFG), which one of the following is TRUE? |
| i ➥ In both AST and CFG, let node, N2 be the successor of node N1. In the input program, the code corresponding to N2 is present after the code corresponding in N1. |
| ii ➥ For any input program, neither AST nor CFG will contain a cycle |
| iii ➥ The maximum number of successors of a node in an AST and a CFG depends on the input program |
| iv ➥ Each node is AST and CFG corresponds to at most one statement in the input program |
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Answer: III
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| Q19➡ | Software Engineering Consider the basic COCOMO model where E is the effort applied in person-months, D is the development time in chronological months, KLOC is the estimated number of delivered lines of code (in thousands) and ab, bb, cb, db have their usual meanings. The basic COCOMO equations are of the form |
| i ➥ E = ab(KLOC) exp (bb) , D = cb (E) exp (db) |
| ii ➥ E = ab(KLOC)exp (bb) , D = cb(E) exp (db) |
| iii ➥ E = ab exp(bb), D = cb(KLOC) exp (db) |
| iv ➥ E = ab exp(Db), D = cb(KLOC) exp (bb) |
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Answer: I
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| Q20➡ | Operating System A system has 6 identical resources and N processes competing for them. Each process can request atmost 2 resources. Which one of the following values of N could lead to a deadlock? |
| i ➥ 1 |
| ii ➥ 2 |
| iii ➥ 3 |
| iv ➥ 6 |
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Answer: IV
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| Q21➡ | Database Management System Consider the following transaction involving two bank account x and y. read(x); x:= x-50; write(x); read(y); y:= y+50; write(y) The constraint that the sum of the accounts x and y should remain constant is that of |
| i ➥ Atomicity |
| ii ➥ Consistency |
| iii ➥ Isolation |
| iv ➥ Durability |
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Answer: IV
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| Q22➡ | Database Management System With reference to the B+ tree index of order 1 shown below, the minimum number of nodes (including the Root node) that must be fetched in order to satisfy the following query:”Get all records with a search key grater than or equal to 7 and less than 15″ is _______.  |
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Answer: 5
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| Q23➡ | Computer Network Identify the correct order in which a server process must invoke the function calls accept, bind, listen, and recv according to UNIX socket API. |
| i ➥ listen, accept, bind recv |
| ii ➥ bind, listen, accept, recv |
| iii ➥ bind, accept, listen, recv |
| iv ➥ accept, listen, bind recv |
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Answer: II
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| Q24➡ | Computer Network A link has a transmission speed of 106 bits/sec. It uses data packets of size 1000 bytes each. Assume that the acknowledgement has negligible transmission delay, and that its propagation delay is the same as the data propagation delay. Also assume that the processing delays at the nodes are negligible. The efficiency of the stop-and-wait protocol in this setup is exactly 25%. The value of the one-way propagation delay (in milliseconds) is ________. |
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Answer: 12
Explanation:
Given,
Bandwidth = 106 bps
Frame size = 1000 B = 1000* 8 bits
Efficiency = 25% = 1/4
Ask,
Propogation Delay = ?
Formula,
For stop-wait protocol,
Efficiency (η) = 
where,
Tp = Propogation Delay
Tt = Transmission Delay = 
Calculation,
=> η =
=> 1/4 =
=> 1+2a = 4
=> Tp =3*Tt /2
=> Tp = 3*8ms/2
=> Tp = 12ms
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| Q25➡ | Computer Network Which one of the following statements is NOT correct about HTTP cookies? |
| i ➥ A cookie is a piece of code that has the potential to compromise the security of an internet user |
| ii ➥ A cookie gains entry to the user’s work area through an HTTP header |
| iii ➥ A cookie has an expiry date and time |
| iv ➥ Cookies can be used to track the browsing pattern of a user at a particular site |
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Answer: I
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[Q26 – Q55 carry TWO mark each ]
| Q26➡ | Computer Network Consider the following routing table at an IP router:  For each IP address in Group I identify the correct choice of the next hop from Group II using the entries from the routing table above.  |
| i ➥ i-a, ii-c, iii-e, iv-d |
| ii ➥ i-a, ii-d, iii-b, iv-e |
| iii ➥ i-b, ii-c, iii-d, iv-e |
| iv ➥ i-b, ii-c, iii-e, iv-d |
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Answer: I
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| Q27➡ | Computer Network Host A sends a UDP datagram containing 8880 bytes of user data to host B over an Ethernet LAN. Ethernet frames may carry data up to 1500 bytes (i.e. MTU = 1500 bytes). Size of UDP header is 8 bytes and size of IP heard is 20 bytes. There is no option field in IP header. How many total number of IP fragments will be transmitted and what will be the contents of offset field in the last fragment? |
| i ➥ 6 and 925 |
| ii ➥ 6 and 7400 |
| iii ➥ 7 and 1110 |
| iv ➥ 7 and 8880 |
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Answer: III
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| Q28➡ | Computer Network Assume that the bandwidth for a TCP connection is 1048560 bits/sec. Let α be the value of RTT in milliseconds (rounded off to the nearest integer) after which the TCP window scale option is needed. Let β be the maximum possible window size the window scale option. Then the values of α and β are |
| i ➥ 63 milliseconds, 65535×214 |
| ii ➥ 63 milliseconds, 65535×216 |
| iii ➥ 500 milliseconds, 65535×214 |
| iv ➥ 500 milliseconds, 65535×216 |
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Answer: III
Explanation:
RTT: Round-trip delay (RTD) or round-trip time (RTT) is the amount of time it takes for a signal to be sent plus the amount of time it takes for acknowledgement of that signal having been received.
Bandwidth-Delay Product(BDP): The bandwidth-delay product is the product of a data link’s capacity (in bits per second) and its round-trip time (in seconds). BDP = RTT * bandwidth
Given,
Bandwidth(or data link capacity) = 1048560 bits/sec
TCP window scale option is needed. It is needed for efficient transfer of data when the Bandwidth-Delay Product (BDP) is greater than 64 KB
{* BDP = 64KB (BDP is maximum 216-1 =65535 B )*}
Calculation,
BDP = RTT * bandwidth
=> 65,535 B = α * 1048560 bits/sec
=> 
=> α = 0.5 sec = 500 milliseconds
By using the window scale option, the receiver window size increased up to a maximum of 1GB.
Receiver window size from 64KB to 1GB i.e. 216B to 230B.
a 14bits shift count is used in TCP Header. So, the maximum possible window size gets increased from 216-1 to (216-1 * 214) or 65,535 to 65,535 * 214.
So, Option(III) is correct.
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| Q29➡ | Database Management System Consider a simple check-pointing protocol and the following set of operations in the log. (start, T4); (write, T4, y, 2, 3); (start, T1); (commit, T4); (write, T1, z, 5, 7); (checkpoint); (start, T2); (write, T2, x, 1, 9); (commit, T2); (start, T3); (write, T3, z, 7, 2); If a crash happens now and the system tries to recover using both undo and redo operations, what are the contents of the undo list and the redo list |
| i ➥ Undo T3, T1; Redo T2 |
| ii ➥ Undo T3, T1; Redo T2, T4 |
| iii ➥ Undo: none; redo: T2, T4, T3, T1 |
| iv ➥ Undo T3, T1; T4; Redo: T2 |
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Answer: I
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| Q30➡ | Database Managemnt System Consider two relations R1(A,B) with the tuples (1,5), (3,7) and R2(A,C) = (1,7), (4,9). Assume that R(A,B,C) is the full natural outer join of R1 and R2. Consider the following tuples of the form (A,B,C): a = (1.5,null), b = (1,null,7), c = (3,null,9), d = (4,7,null), e = (1,5,7), f = (3,7,null), g = (4,null,9). Which one of the following statements is correct? |
| i ➥ R contains a,b,e,f,g but not c, d. |
| ii ➥ R contains all of a,b,c,d,e,f,g |
| iii ➥ R contains e,f,g but not a,b |
| iv ➥ R contains e but not f,g |
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Answer: III
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| Q31➡ | Operating Systems Consider six memory partitions of sizes 200 KB, 400 KB, 600 KB, 500 KB, 300 KB and 250 KB, where KB refers to kilobyte. These partitions need to be allotted to four processes of sizes 357 KB, 210KB, 468 KB and 491 KB in that order. If the best fit algorithm is used, which partitions are NOT allotted to any process? |
| i ➥ 200KBand 300 KB |
| ii ➥ 200KBand 250 KB |
| iii ➥ 250KBand 300 KB |
| iv ➥ 300KBand 400 KB |
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Answer: I
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| Q32➡ | Computer Oraganization Consider a typical disk that rotates at 15000 rotations per minute (RPM) and has a transfer rate of 50×106 bytes/sec. If the average seek time of the disk is twice the average rotational delay and the controller’s transfer time is 10 times the disk transfer time, the average time (in milliseconds) to read or write a 512-byte sector of the disk is ________. |
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Answer: 6.1 to 6.2
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| Q33➡ | Operating Systems A computer system implements 8 kilobyte pages and a 32-bit physical address space. Each page table entry contains a valid bit, a dirty bit, three permission bits, and the translation. If the maximum size of the page table of a process is 24 megabytes, the length of the virtual address supported by the system is _______ bits. |
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Answer: 36
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| Q34➡ | Compiler Design Consider the intermediate code given below. (1) i = 1 (2) j = 1 (3) t1 = 5 * i (4) t2 = t1 + j (5) t3 = 4 * t2 (6) t4 = t3 (7) a[t4] = –1 (8) j = j + 1 (9) if j <= 5 goto(3) (10) i = i + 1 (11) if i < 5 goto(2) The number of nodes and edges in the control-flow-graph constructed for the above code, respectively, are |
| i ➥ 5 and 7 |
| ii ➥ 6 and 7 |
| iii ➥ 5 and 5 |
| iv ➥ 7 and 8 |
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Answer: II
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| Q35➡ | Theory of Computation The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1) * (10) is ________. |
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Answer: 3
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| Q36➡ | Theory of Computation Which of the following language is/are regular ? L1: {wxwR ⎪ w, x ∈ {a, b}* and ⎪w⎪, ⎪x⎪ >0} wR is the reverse of string w L2: {anbm ⎪m ≠ n and m, n≥0} L3: {apbqcr ⎪ p, q, r ≥ 0} |
| i ➥ L1 and L3 only |
| ii ➥ L2 only |
| iii ➥ L2 and L3 only |
| iv ➥ L3 only |
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Answer: I
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| Q37➡ | Algorithms Given below are some algorithms, and some algorithm design paradigms  Match the above algorithms on the left to the corresponding design paradigm they follow Codes: |
| i ➥ 1-i, 2-iii, 3-i, 4-v. |
| ii ➥ 1-iii, 2-iii, 3-i, 4-v. |
| iii ➥ 1-iii, 2-ii, 3-i, 4-iv. |
| iv ➥ 1-iii, 2-ii, 3-i, 4-v. |
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Answer: III
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| Q38➡ | Data Structure A Young tableau is a 2D array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with ∞, and hence there cannot be any entry to the right of, or below a ∞. The following Young tableau consists of unique entries.  When an element is removed from a Young tableau, other elements should be moved into its place so that the resulting table is still a Young tableau (unfilled entries may be filled in with a ∞). The minimum number of entries (other than 1) to be shifted, to remove 1 from the given Young tableau is __________. |
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Answer: 5
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| Q39➡ | Algorithms Suppose you are provided with the following function declaration in the C programming language. int partition (int a[], int n); The function treats the first element of a[] as a pivot, and rearranges the array so that all elements less than or equal to the pivot is in the left part of the array, and all elements greater than the pivot is in the right part. In addition, it moves the pivot so that the pivot is the last element of the left part. The return value is the number of elements in the left part. The following partially given function in the C programming language is used to find the kth smallest element in an array a[ ] of size n using the partition function. We assume k ≤ n  The missing argument lists are respectively |
| i ➥ (a, left_end, k) and (a + left_end + 1, n – left_end – 1, k – left_end – 1) |
| ii ➥ (a, left_end, k) and (a, n – left_end – 1, k – left_end – 1) |
| iii ➥ (a + left_end + 1, n – left_end – 1, k – left_end – 1) and (a, left_end, k) |
| iv ➥ (a, n – left_end – 1, k – left_end – 1) and (a, left_end, k) |
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Answer: I
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| Q40➡ | Data Structure Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for i ranging from 0 to 2020? |
| i ➥ h(i) = i2 mod 10 |
| ii ➥ h(i) = i3 mod 10 |
| iii ➥ h(i) = (11 *i2) mod 10 |
| iv ➥ h(i) = (12 * i) mod 10 |
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Answer: II
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| Q41➡ | Engineering Mathematics The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xa and xb for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xb is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method? Secant  |
| i ➥ xb – (fb–f(xa)) fb /(xb–xa) |
| ii ➥ xa – (fa–f(xa)) fa /(xb–xa) |
| iii ➥ xb – (xb–xa) fb /(fb–f(xa)) |
| iv ➥ xa – (xb–xa) fa /(fb–f(xa)) |
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Answer: III
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| Q42➡ | Programming Consider the C program below.   The value printed by the above program is __________. |
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Answer: 15
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| Q43➡ | Computer Organization Consider the sequence of machine instructions given below: MUL R5, R0, R1 DIV R6, R2, R3 ADD R7, R5, R6 SUB R8, R7, R4 In the above sequence, R0 to R8 are general purpose registers. In the instructions shown, the first register stores the result of the operation performed on the second and the third registers. This sequence of instructions is to be executed in a pipelined instruction processor with the following 4 stages: (1) Instruction Fetch and Decode (IF), (2) Operand Fetch (OF), (3) Perform Operation (PO) and (4) Write back the Result (WB). The IF, OF and WB stages take 1 clock cycle each for any instruction. The PO stage takes 1 clock cycle for ADD or SUB instruction, 3 clock cycles for MUL instruction and 5 clock cycles for DIV instruction. The pipelined processor uses operand forwarding from the PO stage to the OF stage. The number of clock cycles taken for the execution of the above sequence of instructions is |
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Answer: 13
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| Q44➡ | Computer Organization Consider a processor with byte-addressable memory. Assume that all registers, including Program Counter (PC) and Program Status Word (PSW), are of size 2 bytes. A stack in the main memory is implemented from memory location (0100)16 and it grows upward. The stack pointer (SP) points to the top element of the stack. The current value of SP is (016E)16. The CALL instruction is of two words, the first word is the op-code and the second word is the starting address of the subroutine (one word = 2 bytes). The CALL instruction is implemented as follows: • Store the current value of PC in the stack. • Store the value of PSW register in the stack. • Load the starting address of the subroutine in PC. The content of PC just before the fetch of a CALL instruction is (5FA0)16. After execution of the CALL instruction, the value of the stack pointer is |
| i ➥ (016A)16 |
| ii ➥ (016C)16 |
| iii ➥ (0170)16 |
| iv ➥ (0172)16 |
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Answer: IV
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| Q45➡ | Digital Logic Design The number of min-terms after minimizing the following Boolean expression is ________. [D′ + AB′ + A′C + AC′D + A′C′D]′ |
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Answer: 1
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| Q46➡ | Engineering Mathematics Let f(x) = x -(1/3) and A denote the area of the region bounded bu f(x) and the X-axis, when x varies from -1 to 1. Which of the following statements is/are TRUE? I) f is continuous in [-1,1] II) f is not bounded in [-1,1] III) A is nonzero and finite |
| i ➥ II only |
| ii ➥ III only |
| iii ➥ II and III only |
| iv ➥ I, II and III |
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Answer: III
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| Q47➡ | Engineering Mathematics Perform the following operations on the matrix  (i) add the third row to the second row (ii) Subtract the third column from the first column The determinant of the resultant matrix is ____________. |
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Answer: 0
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| Q48➡ | Engineering Mathematics The number of onto function (surjective function) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is _______. |
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Answer: 36
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| Q49➡ | Engineering Mathematics Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X to Y. Let f be randomly chosen from F. The probability of f being one-to-one is ________. |
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Answer: 0.95
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| Q50➡ | Theory of Computation Consider alphabet ∑ = {0, 1}, the null/empty string λ and the sets of strings X0, X1 and X2 generated by the corresponding non-terminals of a regular grammar. X0, X1 and X2 are related as follows: X0 = 1 X1 X1 = 0 X1 + 1 X2 X2 = 0 X1 + {λ} Which one of the following choices precisely represents the strings in X0? |
| i ➥ 10(0* + (10)*) 1 |
| ii ➥ 10(0* + (10)*)*1 |
| iii ➥ 1(0 + 10)* 1 |
| iv ➥ 10(0 + 10)* 1 + 110(0 + 10)* 1 |
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Answer: III
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| Q51➡ | Engineering Mathematics A graph is self-complementary if it is isomorphic to its complement for all self-complementary graphs on n vertices, n is |
| i ➥ A multiple of 4 |
| ii ➥ Even |
| iii ➥ Odd |
| iv ➥ Congruent to 0 mod 4, or, 1 mod 4 |
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Answer: IV
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| Q52➡ | Engineering Mathematics In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is true? |
| i ➥ A tree has no bridges |
| ii ➥ A bridge cannot be part of a simple cycle |
| iii ➥ Every edge of a clique with size 3 is a bridge (A clique is any complete sub graph of a graph) |
| iv ➥ A graph with bridges cannot have a cycle |
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Answer: II
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| Q53➡ | Engineering Mathematics Which one of the following well formed formulae is a tautology? |
| i ➥ ∀x ∃y R(x,y) ↔ ∃y ∀x R(x,y) |
| ii ➥ (∀x [∃y R(x,y) → S(x,y)]) → ∀x∃y S(x,y) |
| iii ➥ [∀x ∃y (P(x,y) → R(x,y)] ↔ [∀x ∃y (¬ P(x,y)∨R(x,y)] |
| iv ➥ ∀x ∀y P(x,y) → ∀x ∀y P(y,x) |
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Answer: III
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| Q54➡ | Software Engineering Which one of the following assertions concerning code inspection and code walkthrough is true? |
| i ➥ Code inspection is carried out once the code has been unit tested |
| ii ➥ Code inspection and code walkthrough are synonyms |
| iii ➥ Adherence to coding standards is checked during code inspection |
| iv ➥ Code walkthrough is usually carried out by an independent test team |
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Answer: III
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| Q55➡ | Digital Logic Design A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate. The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit ripple-carry binary adder is implemented by using four full adders. The total propagation time of this 4-bit binary adder in microseconds is _________. |
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Answer: 19.2
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