Computer Science Gate 2016 Set 2 Questions

All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.

a) (i) only
b) (ii) only
c) both (i) and (ii)
d) neither (i) nor (ii)

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required. Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions

a) (i) only
b) (ii) only
c) both (i) and (ii)
d) neither (i) nor (ii)

Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.

a) 35
b) 45
c) 65
d) 90

Pick the odd one from the following options.

a) CADBE
b) JHKIL
c) XVYWZ
d) ONPMQ

Find the odd one in the following group of words.

mock, deride, praise, jeer

a) mock
b) deride
c) jeer
d) praise

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

a) put up with
b) put in with
c) put down to
d) put up against

The man who is now Municipal Commissioner worked as ______________.

a) the security guard at a university
b) a security guard at the university
c) a security guard at university
d) the security guard at the university

The number of states in the minimum sized DFA that accepts the language defined by the regular expression

(0+1)*(0+1)(0+1)*


is __________________

A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example,

int a[10][3];
The grammars use D as the start symbol, and use six terminal symbols int ; id [ ] num.

Grammar G1
D → int L;
L → id [E
E → num]
E → num] [E

Grammar G2
D → int L;
L → id E
E → E[num]
E → [num]

Which of the grammars correctly generate the declaration mentioned above?

a) Both G1 and G2
b) Only G1
c) Only G2
d) Neither G1 nor G2

Which one of the following grammars is free from left recursion?

a) S → AB
A → Aa | b
B → c
b) S → Ab | Bb | c
A → Bd | ε
B → e
c) S → Aa | B
A → Bb | Sc | ε
B → d
d) S → Aa | Bb | c
A → Bd | ε
B → Ae | ε

Consider the following languages.

L₁ = {(M) | M takes at least 2016 steps on some input},
L₂ = {(M) | M takes at least 2016 steps on all inputs} and
L₃ = {(M) | M accepts ε},

where for each Turing machine M, denotes a specific encoding of M. Which one of the following is TRUE?

a) L₁ is recursive and L₂, L₃ are not recursive
b) L₂ is recursive and L₁, L₃ are not recursive
c) L₁, L₂ are recursive and L₃ is not recursive
d) L₁, L₂,L₃ are recursive

Consider the following languages:

L₁= {aⁿb^mc^n+m : m, n >= 1}
L₂= {aⁿbⁿc²ⁿ : n >= 1}

Which one of the following is TRUE?

a) Both L₁ and L₂ are context-free.
b) L₁ is context-free while L₂ is not context-free.
c) L₂ is context-free while L₁ is not context-free.
d) Neither L₁ nor L₂ is context-free.

Consider the following two statements:

I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ* .
II. There exists a regular language A such that for all languages B, A ∩ B is regular.

Which one of the following is CORRECT?

a) Only I is true
b) Only II is true
c) Both I and II are true
d) Both I and II are false

Consider the following types of languages:

L1 Regular,
L2: Context-free,
L3: Recursive,
L4: Recursively enumerable.

Which of the following is/are TRUE?

I. L3' U L4 is recursively enumerable
II. L2 U L3 is recursive
III. L1* U L2 is context-free
IV. L1 U L2' is context-free

a) I only
b) I and III only
c) I and IV only
d) I, II and III only

Language L1 is defined by the grammar:
S1 -> aS1b | ε
Language L2 is defined by the grammar:
S2 -> abS2 | ε
Consider the following statements:

P: L1 is regular
Q: L2 is regular

Which one of the following is TRUE?

a) Both P and Q are true
b) P is true and Q is false
c) P is false and Q is true
d) Both P and Q are false

Consider the following program:

The value printed by the following program is____________

The following function computes XY for positive integers X and Y.

a) X^Y= a^b
b) (res ∗ a) ^Y = (res ∗ X) ^b
c) X^Y = res ∗ a^b
d) X^Y = (res ∗ a) ^b

Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies τ₁, τ₂, and τ₃ such that τ₁ = 3τ₂/4 = 2τ₃. If the longest pipeline stage is split into two pipeline stages of equal latency, the new frequency is _________ GHz, ignoring delays in the pipeline registers.

Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units U_F and U_G , respectively. Given two instances of U_F and two instances of U_G , it is required to implement the computation F(G(X_i )) for 1 <= i <= 10. ignoring all other delays, the minimum time required to complete this computation is ________________ nanoseconds

A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is ____________

Match the following

a) P ↔ i, Q ↔ ii, R ↔ iv, S ↔ iii
b) P ↔ iii, Q ↔ i, R ↔ ii, S ↔ iv
c) P ↔ ii, Q ↔ iii, R ↔ i, S ↔ iv
d) P ↔ iv, Q ↔ i, R ↔ ii, S ↔ iii

Consider a 128×103 bits/second satellite communication link with one-way propagation delay of 150 milliseconds. Selective retransmission (repeat) protocol is used on this link to send data with a frame size of 1 kilobyte. Neglect the transmission time of acknowledgment. The minimum number of bits required for the sequence number field to achieve 100% utilization is ___________

A network has a data transmission bandwidth of 20 × 106 bits per second. It uses CSMA/CD in the MAC layer. The maximum signal propagation time from one node to another node is 40 microseconds. The minimum size of a frame in the network is _________

For the IEEE 802.11 MAC protocol for wireless communication, which of the following statements is/are TRUE?

I. At least three non-overlapping channels are available for transmissions.
II. The RTS-CTS mechanism is used for collision detection.
III. Unicast frames are ACKed.

a) All I, II, and III
b) I and III only
c) II and III only
d) II only

Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server, assuming that the host has just been restarted.

a) HTTP GET request, DNS query, TCP SYN
b) DNS query, HTTP GET request, TCP SYN
c) DNS query, TCP SYN, HTTP GET request
d) TCP SYN, DNS query, HTTP GET request

In an Ethernet local area network, which one of the following statements is TRUE ?

a) A station stops to sense the channel once it starts transmitting a frame.
b) The purpose of the jamming signal is to pad the frames that are smaller than the minimum frame size.
c) A station continues to transmit the packet even after the collision is detected.
d) The exponential backoff mechanism reduces the probability of collision on retransmissions

Anarkali digitally signs a message and sends it to Salim. Verification of the signature by Salim requires

a) Anarkali’s public key.
b) Salim’s public key.
c) Salim’s private key.
d) Anarkali’s private key.

Let A₁, A₂, A₃, and A₄ be four matrices of dimensions 10 x 5, 5 x 20, 20 x 10, and 10 x 5, respectively. The minimum number of scalar multiplications required to find the product A₁ A₂A₃A₄ using the basic matrix multiplication method is______________.

Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is ________

N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on which the operation is to be performed.

An algorithm performs the following operations on the list in this order: Θ(N) delete, O(log N) insert, O(log N) find, and Θ(N) decrease-key What is the time complexity of all these operations put together

a) O(Log²N)
b) O(N)
c) O(N²)
d) Θ(N² Log N)

The Floyd-Warshall algorithm for all-pair shortest paths computation is based on

a) Greedy paradigm.
b) Divide-and-Conquer paradigm.
c) Dynamic Programming paradigm.
d) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.

Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order, which of the following are TRUE ?

I. Quicksort runs in Θ(n²) time
II. Bubblesort runs in Θ(n²) time
III. Mergesort runs in Θ(n) time
IV. Insertion sort runs in Θ(n) time

a) I and II only
b) I and III only
c) II and IV only
d) I and IV only

The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary search tree, such that the resulting tree has height 6, is _____________.
Note: The height of a tree with a single node is 0.

A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________

In an adjacency list representation of an undirected simple graph G = (V, E), each edge (u, v) has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of v. These are called twins of each other. A twin pointer is a pointer from an adjacency list entry to its twin. If |E| = m and |V| = n, and the memory size is not a constraint, what is the time complexity of the most efficient algorithm to set the twin pointer in each entry in each adjacency list?

a) Θ(n²)
b) Θ(m+n)
c) Θ(m²)
d) Θ(n⁴)

Consider the following New-order strategy for traversing a binary tree:

Visit the root;
Visit the right subtree using New-order
Visit the left subtree using New-order

The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 - 2 ˆ 6 7 * 1 + - is given by:

a) + - 1 6 7 * 2 ˆ 5 - 3 4 *
b) - + 1 * 6 7 ˆ 2 - 5 * 3 4
c) - + 1 * 7 6 ˆ 2 - 5 * 4 3
d) 1 7 6 * + 2 5 4 3 * - ˆ -

B+ Trees are considered BALANCED because

a) the lengths of the paths from the root to all leaf nodes are all equal.
b) the lengths of the paths from the root to all leaf nodes differ from each other by at most 1.
c) the number of children of any two non-leaf sibling nodes differ by at most 1.
d) the number of records in any two leaf nodes differ by at most 1.

Consider the following database schedule with two transactions, T₁ and T₂.

S = r₂(X); r₁(X); r₂(Y); w₁(X); r₁(Y); w₂(X); a₁; a₂;

where r_i(Z) denotes a read operation by transaction T_i on a variable Z, w_i(Z) denotes a write operation by T_i on a variable Z and a_i denotes an abort by transaction T_i . Which one of the following statements about the above schedule is TRUE?

a) S is non-recoverable
b) S is recoverable, but has a cascading abort
c) S does not have a cascading abort
d) S is strict

Suppose a database schedule S involves transactions T1, ....Tn. Construct the precedence graph of S with vertices representing the transactions and edges representing the conflicts. If S is serializable, which one of the following orderings of the vertices of the precedence graph is guaranteed to yield a serial schedule?

a) Topological order
b) Depth-first order
c) Breadth-first order
d) Ascending order of transaction indices

The width of the physical address on a machine is 40 bits. The width of the tag field in a 512 KB 8-way set associative cache is ____________ bits.

Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is _________

Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________

Let, x₁⊕x₂⊕x₃⊕x₄= 0 where x₁, x₂, x₃, x₄ are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE ?

a) x₁x₂x₃x₄=0
b) x₁x₃+x₄=0
c) x'₁⊕x'₃=x'₂⊕x'₄
d) x₁+x₂+x₃+x₄=0

The minimum number of colours that is sufficient to vertex-colour any planar graph is _______________

Consider the following expressions:

(i) false
(ii) Q
(iii) true
(iv) P ∨ Q
(v) ¬Q ∨ P

The number of expressions given above that are logically implied by P ∧ (P ⇒ Q) is ______________

Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:

I. Each compound in U S reacts with an odd number of compounds.
II. At least one compound in U S reacts with an odd number of compounds.
III. Each compound in U S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

a) Only I
b) Only II
c) Only III
d) None

Which one of the following well-formed formulae in predicate calculus is NOT valid?

a) (∀x p(x) ⇒ ∀x q(x)) ⇒ (∃x¬p(x) ∨ ∀x q(x))
b) (∃x p(x) ∨ ∃x q(x)) ⇒ ∃x (p(x) ∨ q(x))
c) ∃x (p(x) ∧ q(x)) ⇒ (∃x p(x) ∧ ∃x q(x))
d) ∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x))

A binary relation R on N x N is defined as follows:

(a, b) R (c, d) if a <= c or b <= d.

Consider the following propositions:

P: R is reflexive
Q: R is transitive

Which one of the following statements is TRUE?

a) Both P and Q are true.
b) P is true and Q is false.
c) P is false and Q is true.
d) Both P and Q are false.

Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A⁻¹)^T is _________.

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is_________.

Let f (x) be a polynomial and g(x) = f^^(x) be its derivative. If the degree of (f(x) + f(−x)) is 10, then the degree of (g(x) − g(−x)) is ___________ .

The value of the expression 13⁹⁹(mod 17), in the range 0 to 16, is

a) 4
b) 13
c) 8
d) 16

Consider the systems, each consisting of m linear equations in n variables.

I. If m < n, then all such systems have a solution
II. If m > n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution

Which one of the following is CORRECT?

a) I, II and III are true
b) Only II and III are true
c) Only III is true
d) None of them is true

Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S) increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in some order. The largest initial value of S for which at least one P(S) operation will remain blocked is ________.

Consider the following processes, with the arrival time and the length of the CPU burst given in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time first.

Consider the following two-process synchronization solution.

Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;

Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;

The shared variable turn is initialized to zero. Which one of the following is TRUE?

a) This is a correct two-process synchronization solution.
b) This solution violates mutual exclusion requirement.
c) This solution violates progress requirement.
d) This solution violates bounded wait requirement.

In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?

a) LRU (Least Recently Used)
b) OPT (Optimal Page Replacement)
c) MRU (Most Recently Used)
d) FIFO (First In First Out)