GATE 2010 Computer Science & Information Technology (CS&IT) Question Paper and Solutions

# Recent questions tagged gate2010

1
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? A) 0 B) 1 C) (n-1)/2 D) (n-1)
2
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 $2 \hspace{0.1cm} \text{nanoseconds}$ ... $888 \hspace{0.1cm} \text{nanoseconds}$ $902 \hspace{0.1cm} \text{nanoseconds}$ $968 \hspace{0.1cm} \text{nanoseconds}$
3
Consider a complete undirected graph with vertex set $\{0, 1, 2, 3, 4\}$. Entry $W_{ij}$ in the matrix $W$ below is the weight of the edge $\{i, j\}$ ... 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? $7$ $8$ $9$ $10$
4
A hash table of length $10$ uses open addressing with hash function $h(k) = k \: mod \: 10$, and linear probing. After inserting $6$ ... insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above? $10$ $20$ $30$ $40$
5
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 are changed to $2$ and the distance vector algorithm is used again until all routing tables stabilize. How many links will now remain unused? $0$ $1$ $2$ $3$
6
Given digits$2, 2, 3, 3, 3, 4, 4, 4, 4$ how many distinct $4$ digit numbers greater than $3000$ can be formed? $50$ $51$ $52$ $54$
7
$5$ skilled workers can build a wall in $20$ days; $8$ semi-skilled workers can build a wall in $25$ days; $10$ unskilled workers can build a wall in $30$ days. If a team has $2$ skilled, $6$ semi-skilled and $5$ unskilled workers, how long it will take to build the wall? $20$ days $18$ days $16$ days $15$ days
8
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 ... Use of chemical agents in warfare would be undesirable. People in military establishments like to use chemical agents in war.
9
Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than three years. Given the following facts: Hari's age + Gita ... and Saira is not the youngest. There are no twins. In what order they were born (oldest first)? $HSIG$ $SGHI$ $IGSH$ $IHSG$
10
If $137 + 276 = 435$ how much is $731+672?$ $534$ $1403$ $1623$ $1513$
11
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 fallow : land unaware : sleeper wit : jester renovated : house
12
$25$ 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: $2$ $17$ $13$ $3$
13
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. uphold restrain cherish conserve
14
Which of the following options is the closest in meaning to the word given below: Circuitous cyclic indirect confusing crooked
15
Choose the most appropriate word from the options given below to complete the following sentence: His rather casual remarks on politics ________ his lack of seriousness about the subject. masked belied betrayed suppressed
16
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 ... tables stabilize, how many links in the network will never be used for carrying any data? $4$ $3$ $2$ $1$
17
A hash table of length $10$ uses open addressing with hash function $h(k) = k \mod 10$, and linear probing. After inserting $6$ ... $46, 42, 34, 52, 23, 33$ $34, 42, 23, 52, 33, 46$ $46, 34, 42, 23, 52, 33$ $42, 46, 33, 23, 34, 52$
18
Consider a complete undirected graph with vertex set $\{0, 1, 2, 3, 4\}$. Entry $W_{ij}$ in the matrix $W$ below is the weight of the edge $\{i, j\}$ ... $T$ in this graph such that vertex 0 is a leaf node in the tree $T$? $7$ $8$ $9$ $10$
19
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 $2 \hspace{0.1cm} nanoseconds$ ... this transfer? $2 \hspace{0.1cm} nanoseconds$ $20 \hspace{0.1cm} nanoseconds$ $22 \hspace{0.1cm}nanoseconds$ $88 \hspace{0.1cm} nanoseconds$
20
Suppose computers $A$ and $B$ have $IP$ addresses $10.105.1.113$ and $10.105.1.91$ respectively and they both use same netmask $N$. Which of the values of $N$ given below should not be used if $A$ and $B$ should belong to the same network? $255.255.255.0$ $255.255.255.128$ $255.255.255.192$ $255.255.255.224$
21
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 $P_i$ ... $n=40,\: k=26$ $n=21,\:k=12$ $n=20,\:k=10$ $n=41,\:k=19$
22
The following program consists of $3$ concurrent processes and $3$ binary semaphores. The semaphores are initialized as $S0=1, S1=0$ and $S2=0.$ ... $P0$ print '$0$'? At least twice Exactly twice Exactly thrice Exactly once
23
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 ... = d Which of the test suites given below ensures coverage of statements S1, S2, S3 and S4? T1, T2, T3 T2, T4 T3, T4 T1, T2, T4
24
The following functional dependencies hold for relations $R(A, B, C)$ and $S(B, D, E).$ $B \to A$ $A \to C$ The relation $R$ contains $200$ tuples and the relation $S$ contains $100$ tuples. What is the maximum number of tuples possible in the natural join $R \bowtie S$? $100$ $200$ $300$ $2000$
25
Consider the following schedule for transactions $T1, T2$ and $T3:$ ... below is the correct serialization of the above? $T1 \to T3 \to T2$ $T2 \to T1 \to T3$ $T2 \to T3 \to T1$ $T3 \to T1 \to T2$
26
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 non-deterministic finite automation that accepts $L$? $n-1$ $n$ $n+1$ $2^{n-1}$
27
Consider the languages $L1=\{0^i1^j\ \mid i \neq j\},$ $L2=\{0^i1^j\mid i=j\},$ $L3=\{0^i1^j \mid i=2j+1\},$ $L4=\{0^i1^j \mid i\neq2j\}$ Only $L2$ is context free. Only $L2$ and $L3$ are context free. Only $L1$ and $L2$ are context free. All are context free
Let $L=\{ w \in \:(0+1)^* \mid w\text{ has even number of }1s \}$. i.e., $L$ is the set of all the bit strings with even numbers of $1$s. Which one of the regular expressions below represents $L$? $(0^*10^*1)^*$ $0^*(10^*10^*)^*$ $0^*(10^*1)^*0^*$ $0^*1(10^*1)^*10^*$
The grammar $S \to aSa \mid bS \mid c$ is LL(1) but not LR(1) LR(1) but not LL(1) Both LL(1) and LR(1) Neither LL(1) nor LR(1)
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? $2$ $3$ $4$ $6$