GATE 2019 CS Computer Science and information technology
| Q1➡ | Digital Logic Design Which one of the following is NOT a valid identity? |
| i ➥ x ⊕ y = x + y, if xy = 0 |
| ii ➥ (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z) |
| iii ➥ x ⊕ y = (xy + x’y’)’ |
| iv ➥ (x + y) ⊕ z = x ⊕ (y + z) |
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Answer: IV
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| Q2➡ | Engineering Mathematics Let U = {1,2,…,n}. Let A = {(x,X)|x ∈ X, X ⊆ U}. Consider the following two statements on |A|. I.  II.  Which of the above statements is/are TRUE? |
| i ➥ Both I and II |
| ii ➥ Neither I nor II |
| iii ➥ Only I |
| iv ➥ Only II |
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Answer: I
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| Q3➡ | Digital Logic Design In 16-bit 2’s complement representation, the decimal number -28 is: |
| i ➥ 1000 0000 1110 0100 |
| ii ➥ 1111 1111 1110 0100 |
| iii ➥ 1111 1111 0001 1100 |
| iv ➥ 0000 0000 1110 0100 |
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Answer: II
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| Q4➡ | Compiler Design Which one of the following kinds of derivation is used by LR parsers? |
| i ➥ Rightmost |
| ii ➥ Leftmost in reverse |
| iii ➥ Rightmost in reverse |
| iv ➥ Leftmost |
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Answer: III
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| Q5➡ | Computer Organization The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal?  |
| i ➥ C800 to CFFF |
| ii ➥ DA00 to DFFF |
| iii ➥ CA00 to CAFF |
| iv ➥ C800 to C8FF |
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Answer: I
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| Q6➡ | Computer Organization A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor? |
| i ➥ 28 bits and 4 bits |
| ii ➥ 28 bits and 0 bits |
| iii ➥ 24 bits and 4 bits |
| iv ➥ 24 bits and 0 bits |
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Answer: II
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| Q7➡ | Engineering Mathematics Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to |
| i ➥ (n-1)! |
| ii ➥ (n-1)! /2 |
| iii ➥ n! |
| iv ➥ 1 |
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Answer: II or IV
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| Q8➡ | Database Management System Consider the following two statements about database transaction schedules: I. Strict two-phase locking protocol generates conflict serializable schedules that are also recoverable. II. Timestamp-ordering concurrency control protocol with Thomas Write Rule can generate view serializable schedules that are not conflict serializable. 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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Answer: IV
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| Q9➡ | Engineering Mathematics Let G be an arbitrary group. Consider the following relations on G: R1: ∀a,b ∈ G, aR1b if and only if ∃g ∈ G such that a = g-1bg R2: ∀a,b ∈ G, aR2b if and only if a = b-1 Which of the above is/are equivalence relation/relations? |
| i ➥ R1 only |
| ii ➥ Neither R1 and R2 |
| iii ➥ R2 only |
| iv ➥ R1 and R2 |
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Answer: I
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| Q10➡ | Engineering Mathematics Let X be a square matrix. Consider the following two statements on X. I. X is invertible. II. Determinant of X is non-zero. Which one of the following is TRUE? |
| i ➥ II implies I; I does not imply II. |
| ii ➥ I does not imply II; II does not imply I. |
| iii ➥ I implies II; II does not imply I. |
| iv ➥ I and II are equivalent statements. |
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Answer: IV
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| Q11➡ | Engineering Mathematics Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of: |
| i ➥ n – 1 bits |
| ii ➥ n + 1 bits |
| iii ➥ n bits |
| iv ➥ n + 2 bits |
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Answer: II
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| Q12➡ | Theory of Computation If L is a regular language over Σ = {a,b}, which one of the following languages is NOT regular? |
| i ➥ L∙LR = {xy │ x ∈ L, yR ∈ L} |
| ii ➥ Suffix (L) = {y ∈ Σ*|∃y ∈ Σ* such that xy ∈ L} |
| iii ➥ Prefix (L) = {x ∈ Σ*│∃y ∈ Σ* such that xy ∈ L} |
| iv ➥ {wwR │w ∈ L} |
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Answer: IV
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Q13➡ | Programming  The value printed by the program is __. |
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Answer: 26
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| Q14➡ | Operating System The following C program is executed on a Unix/Linux system:  The total number of child processes created is _____. |
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Answer: 31
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| Q15➡ | Computer Network Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)? |
| i ➥ IMAP, POP3 |
| ii ➥ IMAP, SMTP |
| iii ➥ SMTP, MIME |
| iv ➥ SMTP, POP3 |
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Answer: IV
Explanation:
SMTP: SMTP stands for Simple Mail Transfer Protocol and is a TCP/IP protocol used in sending e-mail . It’s a set of communication rules that allow software to send email over the Internet.
POP3(Post Office Protocol 3) and IMAP(Intractive Mail Access Protocol): POP3 and IMAP are two different protocols used to access email. POP3 and IMAP function very differently and each has its own advantages. POP3 is useful in checking emails from a computer that is in a specific location. IMAP is the better option when we need to check our emails from multiple locations, such as at work, from home, or on the road, using different computers.
MIME(Multipurpose Internet Mail Extensions): MIME is an Internet Standard that extends the format of e-mail to support-
• Text in character sets other than ASCII
• Non-Text Attachments.
• Message bodies with multiple parts
So, Option(IV) is correct.
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| Q16➡ | Theory of Computation For Σ = {a,b}, let us consider the regular language L = {x|x = a2+3k or x = b10+12k, k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L? |
| i ➥ 5 |
| ii ➥ 24 |
| iii ➥ 9 |
| iv ➥ 3 |
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Answer: II
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| Q17➡ | Database Management System Which one of the following statements is NOT correct about the B+ tree data structure used for creating an index of a relational database table? |
| i ➥ Non-leaf nodes have pointers to data records |
| ii ➥ B+ Tree is a height-balanced tree |
| iii ➥ Each leaf node has a pointer to the next leaf node |
| iv ➥ Key values in each node are kept in sorted order |
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Answer: I
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Q18➡ | Engineering Mathematics |
| i ➥ 108/7 |
| ii ➥ Limit does not exist |
| iii ➥ 1 |
| iv ➥ 53/12 |
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Answer: I
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| Q19➡ | Programming Consider the following C program:  The number that will be displayed on execution of the program is _______. |
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Answer: 6
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| Q20➡ | Operating Systems Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initialized to 100.  The process are executed on a uniprocessor system running a time-shared operating system. If the minimum and maximum possible values of D after the three processes have completed execution are X and Y respectively, then the value of Y–X is _________. |
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Answer: 80
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| Q21➡ | Digital Logic Design Two numbers are chosen independently and uniformly at random from the set {1, 2, …, 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ________. |
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Answer: 0.502 to 0.504
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| Q22➡ | Computer Network The value of 351 mod 5 is _______. |
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Answer: 2
Explanation:
Fermat’s Little Theorem:
If p is a prime and a is an integer then
ap-1 ≡ 1 (mod p) , if p does not divide a
else
ap ≡ a (mod p)
Caculation:
351 mod 5
here, p=5, a=3 and p does not divide
≡ 34*12 +3 mod 5
≡ ((34)12 mod 5) * (33 mod 5)
≡ (112 mod 5) * (33 mod 5) {* 35-1 ≡ 1 mod 5 *}
≡ 27 mod 5
≡ 2
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| Q23➡ | Algorithms An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ________. |
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Answer: 0.08
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| Q24➡ | Compiler Design Consider the grammar given below: S → Aa A → BD B → b | ε D → d | ε Let a, b, d and $ be indexed as follows:  Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210) |
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Answer: 31
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| Q25➡ | Algorithms Consider a sequence of 14 elements: A = [-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]. The subsequence sum S(i,j)=  Determine the maximum of S(i,j), where 0 ≤ i ≤ j < 14. (Divide and conquer approach may be used)___________. |
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Answer: 29
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| Q26➡ | Digital Logic Design Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms as f1 = Σ(0, 2, 5, 8, 14), f2 = Σ(2, 3, 6, 8, 14, 15), f3 = Σ(2, 7, 11, 14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:  |
| i ➥ Σ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15) |
| ii ➥ Σ (7, 8, 11) |
| iii ➥ Σ (2, 14) |
| iv ➥ Σ (2, 7, 8, 11, 14) |
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Answer: II
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| Q27➡ | Computer Network Suppose that in an IP-over-Ethernet network, a machine X wishes to find the MAC address of another machine Y in its subnet. Which one of the following techniques can be used for this? |
| i ➥ X sends an ARP request packet with broadcast IP address in its local subnet |
| ii ➥ X sends an ARP request packet to the local gateway’s MAC address which then finds the MAC address of Y and sends to X |
| iii ➥ X sends an ARP request packet with broadcast MAC address in its local subnet |
| iv ➥ X sends an ARP request packet to the local gateway’s IP address which then finds the MAC address of Y and sends to X |
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Answer: III
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| Q28➡ | Computer Network Consider three machines M, N and P with IP addresses 100.10.5.2, 100.10.5.5, and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true? |
| i ➥ Only M and N belong to the same subnet |
| ii ➥ Only N and P belong to the same subnet |
| iii ➥ M, N, and P all belong to the same subnet |
| iv ➥ M, N and P belong to three different subnets |
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Answer: II
Explanation:
Given,
IP addresses of M = 100.10.5.2
IP addresses of N = 100.10.5.5
IP addresses of P = 100.10.5.6
Subnet Mask = 255.255.255.252
Logic to solve,
We will find Network Id by X-ORing of IP Address of Machine with Subnet Mask. Same Network Id of Machine belong to same Subnet.Machine M:
100. 10 . 5 .0000 0010
255.255.255.1111 1100
——————————-
(100.10.5.0)Machine N:
100. 10 . 5 .0000 0101
255.255.255.1111 1100
———————————
(100.10.5.4)Machine P:
100. 10 . 5 .0000 0110
255.255.255.1111 1100
———————————-
(100.10.5.4)
Machine N and P belong to same subnet.
So, Option(II) is correct.
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| Q29➡ | Programming Consider the following C program:  Which one of the following values will be displayed on execution of the programs? |
| i ➥ 52 |
| ii ➥ 630 |
| iii ➥ 41 |
| iv ➥ 63 |
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Answer: I
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| Q30➡ | Programming Consider the following C function:  Which one of the following will happen when the function convert is called with any positive integer n as argument? |
| i ➥ It will print the binary representation of n and terminate. |
| ii ➥ It will print the binary representation of n in the reverse order and terminate. |
| iii ➥ It will print the binary representation of n but will not terminate. |
| iv ➥ It will not print anything and will not terminate. |
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Answer: IV
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| Q31➡ | Compiler Design Consider the following grammar and the semantic actions to support the inheritance type declaration attributes. Let X1, X2, X3, X4, X5 and X6 be the placeholders for the non-terminals D, T, L or L1 in the following table:  Which one of the following are the appropriate choices for X1, X2, X3 and X4? |
| i ➥ X1 = L, X2 = T, X3 = L1, X4 = L |
| ii ➥ X1 = T, X2 = L, X3 = T, X4 = L1 |
| iii ➥ X1 = T, X2 = L, X3 = L1, X4 = T |
| iv ➥ X1 = L, X2 = L, X3 = L1, X4 = T |
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Answer: I
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| Q32➡ | Engineering Mathematics Consider the first order predicate formula φ: ∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))] Here ‘a|b’ denotes that ‘a divides b’, where a and b are integers. Consider the following sets: S1. {1, 2, 3, …, 100} S2. Set of all positive integers S3. Set of all integers Which of the above sets satisfy φ? |
| i ➥ S2 and S3 |
| ii ➥ S1 and S3 |
| iii ➥ S1 and S2 |
| iv ➥ S1, S2 and S3 |
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Answer: I
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| Q33➡ | Theory of Computation Consider the following sets: S1. Set of all recursively enumerable languages over the alphabet {0,1} S2. Set of all syntactically valid C programs S3. Set of all languages over the alphabet {0,1} S4. Set of all non-regular languages over the alphabet {0,1} Which of the above sets are uncountable? |
| i ➥ S1 and S2 |
| ii ➥ S3 and S4 |
| iii ➥ S2 and S3 |
| iv ➥ S1 and S4 |
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Answer: II
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| Q34➡ | Operating System Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressable. The page size is 8 kB and the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss? |
| i ➥ 256×210 |
| ii ➥ 8×220 |
| iii ➥ 4×220 |
| iv ➥ 16×210 |
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Answer: I
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| Q35➡ | Database Management System Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS). Consider the two statements given below: I. Both Y and Z are in BCNF II. Decomposition of X into Y and Z is dependency preserving and lossless Which of the above statements is/are correct? |
| i ➥ Both I and II |
| ii ➥ I only |
| iii ➥ II only |
| iv ➥ Neither I nor II |
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Answer: III
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| Q36➡ | Theory of Computation Which one of the following languages over Σ = {a,b} is NOT context-free? |
| i ➥ {wanbnwR |w ∈ {a,b}*, n ≥ 0} |
| ii ➥ {anbi | i ∈ {n, 3n, 5n}, n ≥ 0} |
| iii ➥ {wanwRbn |w ∈ {a,b}*, n ≥ 0} |
| iv ➥ {wwR |w ∈ {a,b}*} |
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Answer: III
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| Q37➡ | Operating System The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointers. The disk block size is 4 kB, and the disk block address is 32-bits long. The maximum possible file size is (rounded off to 1 decimal place) ________ GB. |
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Answer: 4.0
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| Q38➡ | Operating System Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in milliseconds) as shown below:  These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling algorithm. If the average waiting time of the processes is 1 millisecond, then the value of Z is _______. |
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Answer: 2
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| Q39➡ | Data Structures Consider the following statements: I. The smallest element in a max-heap is always at a leaf node. II. The second largest element in a max-heap is always a child of the root node. III. A max-heap can be constructed from a binary search tree in Θ(n) time. IV. A binary search tree can be constructed from a max-heap in Θ(n) time. Which of the above statements are TRUE? |
| i ➥ I, II and III |
| ii ➥ I, III and IV |
| iii ➥ II, III and IV |
| iv ➥ I, II and IV |
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Answer: I
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| Q40➡ | Operating System Consider the following snapshot of a system running n concurrent processes. Process i is holding Xi instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R are currently in use. Further, for all i, process i can place a request for at most Yi additional instances of R while holding the Xi instances it already has. Of the n processes, there are exactly two processes p and q such that Yp = Yq = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution? |
| i ➥ Xp + Xq < Min {Yk | 1 ≤ k ≤ n, k ≠ p, k ≠ q} |
| ii ➥ Min (Xp, Xq) ≤ Max {Yk | 1 ≤ k ≤ n, k ≠ p, k ≠ q} |
| iii ➥ Min (Xp, Xq) ≥ Min {Yk | 1 ≤ k ≤ n, k ≠ p, k ≠ q} |
| iv ➥ Xp + Xq < Max {Yk | 1 ≤ k ≤ n, k ≠ p, k ≠ q} |
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Answer: I
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| Q41➡ | Engineering Mathematics Let G be any connected, weighted, undirected graph. I. G has a unique minimum spanning tree, if no two edges of G have the same weight. II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut. Which of the above statements is/are TRUE? |
| i ➥ Both I and II |
| ii ➥ I only |
| iii ➥ Neither I nor II |
| iv ➥ II only |
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Answer: I
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| Q42➡ | Algorithms There are n unsorted arrays: A1, A2, …, An. Assume that n is odd. Each of A1, A2, …, An contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A1, A2, …, An is |
| i ➥ O(n2) |
| ii ➥ Ω(n2 log n) |
| iii ➥ O(n) |
| iv ➥ O(n log n) |
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Answer: I
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| Q43➡ | Theory of Computation Let Σ be the set of all bijections from {1, …, 5} to {1, …, 5}, where id denotes the identity function i.e. id( j ) = j,∀j. Let º denote composition on functions. For a string x = x1 x2 … xn ∈ Σn, n ≥ 0. Let π(x) = x1 º x2 º … º xn. Consider the language L = {x ∈ Σ* | π(x) = id}. The minimum number of states in any DFA accepting L is _________. |
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Answer: 120
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| Q44➡ | Engineering Mathematics Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) ________. |
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Answer: 0.8
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| Q45➡ | Data Structure Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) __________. |
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Answer: 4.25
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| Q46➡ | Computer Organization A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60-MHz clock. To service a cache miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to fetch all the eight words of the block, and finally transmits the words of the requested block at the rate of 1 word per cycle. The maximum bandwidth for the memory system when the program running on the processor issues a series of read operations is _________ × 106 bytes/sec. |
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Answer: 160
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| Q47➡ | Engineering Mathematics Consider the following matrix:  The absolute value of the product of Eigen values of R is ________. |
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Answer: 12
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| Q48➡ | Engineering Mathematics Consider the augmented grammar given below: S’ → S S → 〈L〉 | id L → L,S | S Let I0 = CLOSURE ({[S’ → ·S]}). The number of items in the set GOTO (I0 , 〈 ) is: ___________. |
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Answer: 5
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| Q49➡ | Database Management System Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).  How many tuples will be returned by the following relational algebra query?  |
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Answer: 1
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| Q50➡ | Computer Network In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that Φ(n) = 2880, where Φ() denotes Euler’s Quotient Function, then the prime factor of n which is greater than 50 is ________. |
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Answer: 97
Explanation:
Given,
n = 3007
ϕ(n) = 2880
Calculation,
Let p and q be two prime number such that n=p*q = 3007
ϕ(n) = ϕ(p*q) = ϕ(p)* ϕ(q) = (p-1)*(q-1) = 2880
=> pq -p-q-1 =2880
=> 3007-p-q-1 =2880
=> p+q =128 ————(1)
=> pq =3007 ————(2)
put value of q in eq(1)
=> p+(3007/p) =128
=> p2 -128p + 3007 =0
The prime factor of n greater than 50 is 97.
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| Q51➡ | Programming Consider the following C program:  The output of the above C program is _______. |
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Answer: 10
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| Q52➡ | Programming Consider the following C program:  The number of times the variable sum will be printed, when the above program is executed, is ________. |
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Answer: 5
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| Q53➡ | Database Management System A relational database contains two tables Student and Performance as shown below:  The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together from the primary key. Consider the SQL query given below: SELECT S.Student_name, sum (P.Marks) FROM Student S, Performance P WHERE P.Marks > 84 GROUP BY S.Student_name; The number of rows returned by the above SQL query is ________. |
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Answer: 5
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| Q54➡ | Digital Logic Design What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of-minterms form as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. |
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Answer: 3
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| Q55➡ | Computer Network Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is ________. |
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Answer: 3
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