### Computer Science (GATE Exam) 2010 - Previous Question Paper Solution

Description: GATE Exam Previous Year Question Paper Solution Computer Science(CS) - 2010 | |

Number of Questions: 65 | |

Created by: Aliensbrain Bot | |

Tags: Computer Science GATE CS Previous Year Paper |

Let G=(V, E) be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in G. If S and T are two different trees with $\xi(S) = \xi(T)$, then

Consider the set S = ${1, ω, ω^2}$, where $ω$ and $ω^2$ are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms

In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?

P is a 16-bit signed integer. The 2's complement representation of P is (F87B)_{16}. The 2's complement representation of 8*P is

Which data structure in a compiler is used for managing information about variables and their attributes?

A main memory unit with a capacity of 4 megabytes is built using 1M ^{× }1-bit DRAM chips. Each DRAM chip has 1K rows of cells with 1K cells in each row. The time taken for a single refresh operation is 100 nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is

Two alternative packages A and B are available for processing a database having 10^{k} records. Package A requires 0.0001n^{2} time units and package B requires 10nlog_{10}n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

Which languages necessarily need heap allocation in the runtime environment?

One of the header fields in an IP datagram is the Time to Live (TTL) field. Which of the following statements best explains the need for this field?

Which one of the following is not a client server application?

Consider a B^{+} -tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node?

What does the following program print?

```
#include
void f (int *p, int * g)
{
p = q;
* p = 2;
}
int i = 0, j = 1;
int main ( )
{
f(&i, &j);
print f ("%d%d n", i, j) ;
return 0;
}
```

Newton-Raphson method is used to compute a root of the equation x^{2} − 13 = 0 with 3.5 as the initial value. The approximation after one iteration is

Which of the following concurrency control protocols ensure(s) both conflict serializability and freedom from deadlock? I. 2-phase locking II. Time-stamp ordering

Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?

The cyclomatic complexity of each of the modules A and B shown below is 10. What is the cyclomatic complexity of the sequential integration shown on the right hand side?

What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?

A system uses FIFO policy for page replacement. It has 4 page frames with no pages loaded to begin with. The system first accesses 100 distinct pages in some order and then accesses the same 100 pages but now in the reverse order. How many page faults will occur?

A relational schema for a train reservation database is given below: Passenger (pid, pname, age)

Table: passenger

pid | pname | Age |
---|---|---|

0 | Sachin | 65 |

1 | Rahul | 66 |

2 | Sourav | 67 |

3 | Anil | 69 |

Table: Reservation

pid | class | tid |
---|---|---|

0 | AC | 8200 |

1 | AC | 8201 |

2 | SC | 8201 |

5 | AC | 8203 |

1 | SC | 8204 |

3 | AC | 8202 |

What pids are returned by the following SQL query for the above instance of the tables?

```
SELECT pid
FROM Reservation
WHERE class 'AC' AND
EXISTS (SELECT *
FROM Passenger
WHERE age 65 > AND
Passenger. pid = Reservation. pid)
```

What is the probability that divisor of 1099 is a multiple of 1096?

Which of the following statements are true?

I. Shortest remaining time first scheduling may cause starvation II. Preemptive scheduling may cause starvation III. Round robin is better than FCFS in terms of response time

Consider a company that assembles computers. The probability of a faulty assembly of any computer is *p. *The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of *q. *What is the probability of a computer being declared faulty?

Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\ x & y \end{array}\right]$$ If the eigenvalues of A are 4 and 8, then

Consider the methods used by processes P1 and P2 for accessing their critical sections whenever needed, as given below. The initial values of shared Boolean variables S1 and S2 are randomly assigned.

Method used by P1 | Method used by P2 |
---|---|

while (S1==S2); | while (S1!=S2); |

Critical Section | Critical Section |

S1=S2; | S2 = not(S1) |

Which one of the following statements describes the properties achieved?

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? I. 7, 6, 5, 4, 4, 3, 2, 1 II. 6, 6, 6, 6, 3, 3, 2, 2 III. 7, 6, 6, 4, 4, 3, 2, 2 IV. 8, 7, 7, 6, 4, 2, 1, 1

What is the appropriate pairing of items in the two columns listing various activities encountered in a software life cycle?

P. Requirements Capture | 1. Module Development and Integration |

Q. Design | 2. Domain Analysis |

R. Implementation | 3. Structural and Behavioral Modeling |

S. Maintenance | 4. Performance Tuning |

What is the possible number of reflexive relations on a set of 5 elements?

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. Which one of the statements below expresses best the meaning of the formula $∀x∃y∃t(¬F(x,y,t))$?

What is the value printed by the following C program?

```
#include
int f(int * a, int n) {
if (n <= 0) return 0;
else if ( * a % 2 = = 0) return *a + f(a + 1, n - 1);
else return *a - f(a + 1, n - 1);
}
int main() {
int a[] = {
12,
7,
13,
4,
11,
6
};
print f( % d, f(a, 6));
return 0;
}
```

In the sequential circuit shown below, if the initial value of the output Q_{1}Q_{0} is 00, what are the next four values of Q_{1}Q_{0}?

The weight of a sequence a_{0}, a_{1},…, a_{n-1} of real numbers is defined as a + a_{1} / 2 + …. + a_{n-1 }/ 2^{n-1}. A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of a_{0}, a_{1}, …., a_{n-1}. Then X is equal to

The grammar S $\rightarrow$ aSa|bS|c is

The following C function takes a simply-linked list as input argument. It modifies the list by moving the last element to the front of the list and returns the modified list. Some part of the code is left blank.

```
typedef struct node {
int value;
struct node * next;
}Node;
Node * move_to_front(Node * head) {
Node * p, * q;
if ((head = = NULL: || (head - > next = = NULL)) return head; q = NULL; p = head;
while (p - > next != NULL) {
q = P;
p = p - > next;
}
return head;
}
```

Choose the correct alternative to replace the blank line.

Suppose computers A and B have IP addresses 10.105.1.113 and 10.105.1.91 respectively and they both use the same net mask N. Which of the values of N given below should not be used if A and B should belong to the same network?

A 5-stage pipelined processor has Instruction Fetch (IF), Instruction Decode (ID), Operand Fetch (OF), Perform Operation (PO) and Write Operand (WO) stages. The IF, ID, OF and WO stages take 1 clock cycle each for any instruction. The PO stage takes 1 clock cycle for ADD and SUB instructions, 3 clock cycles for MUL instruction, and 6 clock cycles for DIV instruction respectively. Operand forwarding is used in the pipeline. What is the number of clock cycles needed to execute the following sequence of instructions?

Instruction Meaning of instruction $t_0: MUL :R_2,R_0,R_1$ $R_2 \gets R_0*R_1$ $t_1: DIV: R_5,R_3,R_4$ $R_5 \gets R_3 / R_4$ $t_2: ADD: R_2,R_5,R_2$ $R_2 \gets R_5 + R_2$ $t_3: SUB :R_5,R_2,R_6$ $R_5 \gets R_2 - R_6$

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry Wij in the matrix W below is the weight of the edge {i, j}. W =

What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

Consider a network with 6 routers R1 to R6 connected with links having weights as shown in the following diagram

All the routers use the distance vector based routing algorithm to update their routing tables. Each router starts with its routing table initialized to contain an entry for each neighbour with the weight of the respective connecting link. After all the routing tables stabilize, how many links in the network will never be used for carrying any data?

A system has $n$ resources $R_0, \dots,R_{n-1}$, and $k$ processes $P_0, \dots, P_{k-1}$. The implementation of the resource request logic of each process $P_i$ is as follows:

```
if (i%2==0) {
if (i
```

The program below uses six temporary variables a, b, c, d, e, f.

a = 1 |

b = 10 |

c = 20 |

d = a + b |

e = c + d |

f = c + e |

b = c + e |

e = b + f |

d = 5 + e |

return d + f |

Assuming that all operations take their operands from registers, what is the minimum number of registers needed to execute this program without spilling?

A computer system has an L1 cache, an L2 cache, and a main memory unit connected as shown below. The block size in L1 cache is 4 words. The block size in L2 cache is 16 words. The memory access times are 2 nanoseconds, 20 nanoseconds and 200 nanoseconds for L1 cache, L2 cache and main memory unit, respectively.

When there is a miss in L1 cache and a hit in L2 cache, a block is transferred from L2 cache to L1 cache. What is the time taken for this transfer?

A hash table of length 10 uses open addressing with hash function h(k)=k mod 10, and linear probing. After inserting 6 values into an empty hash table, the table is as shown below

0 | |
---|---|

1 | |

2 | 42 |

3 | 23 |

4 | 34 |

5 | 52 |

6 | 46 |

7 | 33 |

8 | |

9 |

How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above?

A computer system has an L1 cache, an L2 cache, and a main memory unit connected as shown below. The block size in L1 cache is 4 words. The block size in L2 cache is 16 words. The memory access times are 2 nanoseconds. 20 nanoseconds and 200 nanoseconds for L1 cache, L2 cache and main memory unit respectively.

When there is a miss in both L1 cache and L2 cache, first a block is transferred from main memory to L2 cache, and then a block is transferred from L2 cache to L1 cache. What is the total time taken for these transfers?

The following program consists of 3 concurrent processes and 3 binary semaphores. The semaphores are initialized as S0 = 1, S1 = 0, S2 = 0.

Process P0 | Process P1 | Process P2 |

while (true) { | wait (S1); | wait (S2); |

wait (S0); | release (S0); | release (S0); |

print '0'; | ||

release (S1); | ||

release (S2); | ||

} |

How many times will process P0 print ‘0’?

** Directions:** Choose the most appropriate word from the options given below to the complete the following sentence.

His rather casual remarks on politics ___________ his lack of seriousness about the subject.

Consider a network with 6 routers R1 to R6 connected with links having weights as shown in the following diagram

Suppose the weights of all unused links in the previous question are changed to 2 and the distance vector algorithm is used again until all routing tables stabilize. How many links will now remain unused?

** Directions:** Choose the most appropriate word from the options given below to complete the following sentence.

If we manage to ____________ our natural resources, we would leave a better planet for our children.

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.
**Unemployed : Worker**

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the above passage?

If 137 + 276 = 435 how much is 731 + 672?

Which of the following options is closest in meaning to the word Circuitous.

A hash table of length 10 uses open addressing with hash function h(k)=k mod 10, and linear probing. After inserting 6 values into an empty hash table, the table is as shown below

0 | |
---|---|

1 | |

2 | 42 |

3 | 23 |

4 | 34 |

5 | 52 |

6 | 46 |

7 | 33 |

8 | |

9 |

Which one of the following choices gives a possible order in which the key values could have been inserted in the table?

Consider the following schedule for transactions T1, T2 and T3:

$\underline {T1}$ $\underline{T2}$ $\underline{T1}$ Read(X) Read(Y) Read(Y) Write(Y) Write(X) Write(X) Read(X) Write(X)

Which one of the schedules below is the correct serialization of the above?

5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Let w be any string of length n in {0, 1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

Consider the languages L1 = {0^{i}1^{j} | i $\ne$ j}. L2 = {0^{i}1^{j} | i = j}. L3 = {0^{i}1^{j} | i = 2j +1}.
L4 = {0^{i}1^{j} | i $\ne$2j}. Which one of the following statements is true?

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry Wij in the matrix W below is the weight of the edge {i, j}. W =

What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1^{st} january. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i. Hari's age + Gita's age > Irfan's age + Saira's age
ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.

In what order were they born (oldest first)?

Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

The following program is to be tested for statement coverage: begin if (a = = b) {S1; exit;} else if (c = = d) {S2;} else {S3; exit;} S4; end The test cases T1, T2, T3 and T4 given below are expressed in terms of the properties satisfied by the values of variables a, b, c and d. The exact values are not given. T1 : a, b, c and d are all equal T2 : a, b, c and d are all distinct T3 : a=b and c !=d T4 : a !=b and c=d

Which of the test suites given below ensures coverage of statements S1, S2, S3 and S4?

The following functional dependencies hold for relations R(A, B, C) and S(B, D, E) B $\rightarrow$A, A $\rightarrow$C The relation R contains 200tuples and the relation S contains 100tuples. What is the maximum number of tuples possible in the natural join $R \bowtie S$

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is

The minterm expansion of f (P, Q, R) = PQ + Q^{$\bar R$} + P^{$\bar R$} is

The Boolean expression for the output f of the multiplexer shown below is

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?