GATE 2009 Computer Science & Information Technology Question Paper with Solution

# Recent questions tagged gate2009

1
Consider this question and its selected answer: https://gateoverflow.in/3690/gate2004-it-47 And this question: https://gateoverflow.in/1314/gate2009-28 Both questions are somewhat similar. In the first one's answer, instruction $I_1$ (when i = 2), the $S_2$ stage is ... there any point that I am missing? PS. From where can I study this? Hamacher book doesn't contain pipelining in this much detail.
2
A hard disk has $63$ sectors per track, $10$ platters each with $2$ recording surfaces and $1000$ cylinders. The address of a sector is given as a triple $\langle c, h, s \rangle$, where $c$ is the cylinder number, $h$ is the surface number and $s$ is the sector number. Thus, the ... is $\langle 0, 15, 31 \rangle$ $\langle 0, 16, 30 \rangle$ $\langle 0, 16, 31 \rangle$ $\langle 0, 17, 31 \rangle$
3
A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences $X[m]$ and $Y[n]$ of lengths $m$ and $n$, respectively with indexes of $X$ and $Y$ starting from $0$. We wish to find the length of the longest common ... major order of $L[M, N]$. $L[p, q]$ needs to be computed before $L[r, s]$ if either $p<r$ or $q < s$.
4
Consider the following relational schema: $\text{Suppliers}(\underline{\text{sid:integer}},\text{ sname:string, city:string, street:string})$ $\text{Parts}(\underline{\text{pid:integer}}, \text{ pname:string, color:string})$ ... is in $3NF$ but not in $\text{BCNF}$ The schema is in $2NF$ but not in $3NF$ The schema is not in $2NF$
5
Frames of $1000\text{ bits}$ are sent over a $10^6$ bps duplex link between two hosts. The propagation time is $25ms$. Frames are to be transmitted into this link to maximally pack them in transit (within the link). Let $I$ be the minimum number of ... wait before starting transmission of the next frame? (Identify the closest choice ignoring the frame processing time) $16ms$ $18ms$ $20ms$ $22ms$
6
Consider a binary max-heap implemented using an array. What is the content of the array after two delete operations on $\left\{25,14,16,13,10,8,12\right\}$ $\left\{14,13,12,10, 8\right\}$ $\left\{14,12,13,8,10\right\}$ $\left\{14,13,8,12,10\right\}$ $\left\{14,13,12,8,10\right\}$
7
Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap? $\left\{25,12,16,13,10,8,14\right\}$ $\left\{25,14,13,16,10,8,12\right\}$ $\left\{25,14,16,13,10,8,12\right\}$ $\left\{25,14,12,13,10,8,16\right\}$
8
Frames of $\text{1000 bits}$ are sent over a $10^6$ $\text{bps}$ duplex link between two hosts. The propagation time is $\text{25 ms}$. Frames are to be transmitted into this link to maximally pack them in transit (within the link). What is the minimum number of bits ... numbers distinctly? Assume that no time gap needs to be given between transmission of two frames. $I=2$ $I=3$ $I=4$ $I=5$
9
Consider the following relational schema: $\text{Suppliers}(\underline{\text{sid:integer}},\text{ sname:string, city:string, street:string})$ $\text{Parts}(\underline{\text{pid:integer}}, \text{ pname:string, color:string})$ ... the names of all suppliers who have supplied only non-blue part. Find the names of all suppliers who have not supplied only blue parts.
10
A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences $X[m]$ and $Y[n]$ of lengths $m$ and $n$, respectively with indexes of $X$ and $Y$ starting from $0$. We wish to find the length of the longest ... $\text{expr2} = \max\left(l\left(i-1, j-1\right), l\left(i,j\right)\right)$
11
A hard disk has $63$ sectors per track, $10$ platters each with $2$ recording surfaces and $1000$ cylinders. The address of a sector is given as a triple $\langle c, h, s \rangle$, where $c$ is the cylinder number, $h$ is the surface number and $s$ is the sector ... $\langle 400, 16, 29 \rangle$ corresponds to sector number: $505035$ $505036$ $505037$ $505038$
12
Consider the following statements about the cyclomatic complexity of the control flow graph of a program module. Which of these are TRUE? The cyclomatic complexity of a module is equal to the maximum number of linearly independent circuits in the graph. The cyclomatic complexity of ... paths that should be tested during path coverage testing. I and II II and III I and III I, II and III
13
Which of the following statements are TRUE? The context diagram should depict the system as a single bubble. External entities should be identified clearly at all levels of DFDs. Control information should not be represented in a DFD. A data store can be connected wither to another data store or to an external entity. II and III II and III I and III I, II and III
14
Let $G(x)$ be the generator polynomial used for CRC checking. What is the condition that should be satisfied by $G(x)$ to detect odd number of bits in error? $G(x)$ contains more than two terms $G(x)$ does not divide $1+x^k$, for any $k$ not exceeding the frame length $1+x$ is a factor of $G(x)$ $G(x)$ has an odd number of terms.
15
While opening a $TCP$ connection, the initial sequence number is to be derived using a time-of-day (ToD) clock that keeps running even when the host is down. The low order $32$ bits of the counter of the ToD clock is to be used for the initial sequence numbers. The clock counter ... at which sequence numbers used for packets of a connection can increase? $0.015$/s $0.064$/s $0.135$/s $0.327$/s
16
In the RSA public key cryptosystem, the private and public keys are $(e, n)$ and $(d, n)$ respectively, where $n=p \times q$ and $p$ and $q$ are large primes. Besides, $n$ is public and $p$ and $q$ are private. Let $M$ be an integer such that $0<M<n$ ... Which of the above equations correctly represents RSA cryptosystem? I and II I and III II and IV III and IV
17
Let $R$ and $S$ be relational schemes such that $R=\{a,b,c\}$ and $S=\{c\}.$ Now consider the following queries on the database: $\pi_{R-S}(r) - \pi_{R-S} \left (\pi_{R-S} (r) \times s - \pi_{R-S,S}(r)\right )$ ... Select R.a,R.b From R,S Where R.c = S.c Which of the above queries are equivalent? $1$ and $2$ $1$ and $3$ $2$ and $4$ $3$ and $4$
18
The following key values are inserted into a $B+$ - tree in which order of the internal nodes is $3$, and that of the leaf nodes is $2$, in the sequence given below. The order of internal nodes is the maximum number of tree pointers in each node, and the order of leaf nodes is ... $2$, $1$ The maximum number of times leaf nodes would get split up as a result of these insertions is $2$ $3$ $4$ $5$
19
Consider two transactions $T_1$ and $T_2$, and four schedules $S_1, S_2, S_3, S_4$, of $T_1$ and $T_2$ as given below: $T_1: R_1[x]W_1[x]W_1[y]$ $T_2: R_2[x]R_2[y]W_2[y]$ $S_1: R_1[x]R_2[x]R_2[y] W_1[x] W_1[y] W_2[y]$ ... $S_1 \text{ and } S_2$ $S_2 \text{ and } S_3$ $S_3$ only $S_4$ only
20
Which of the following statements are TRUE? There exist parsing algorithms for some programming languages whose complexities are less than $\Theta(n^3)$ A programming language which allows recursion can be implemented with static storage allocation. No L-attributed definition can be ... performed at both source language and intermediate code level. I and II I and IV III and IV I, III and IV
21
The above DFA accepts the set of all strings over $\{0,1\}$ that begin either with $0$ or $1$. end with $0$. end with $00$. contain the substring $00$.
22
Let $L = L_1 \cap L_2$, where $L_1$ and $L_2$ are languages as defined below: $L_1= \left \{ a^m b^mca^nb^n \mid m,n \geq 0 \right \}$ $L_2=\left \{ a^i b^j c^k \mid i,j,k \geq 0 \right \}$ Then $L$ is Not recursive Regular Context free but not regular Recursively enumerable but not context free.
23
In quick-sort, for sorting $n$ elements, the $\left(n/4\right)^{th}$ smallest element is selected as pivot using an $O(n)$ time algorithm. What is the worst case time complexity of the quick sort? $\Theta(n)$ $\Theta(n \log n)$ $\Theta(n^2)$ $\Theta(n^2 \log n)$
24
Consider the following graph: Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal’s algorithm? $\text{(b, e) (e, f) (a, c) (b, c) (f, g) (c, d)}$ $\text{(b, e) (e, f) (a, c) (f, g) (b, c) (c, d)}$ $\text{(b, e) (a, c) (e, f) (b, c) (f, g) (c, d)}$ $\text{(b, e) (e, f) (b, c) (a, c) (f, g) (c, d)}$
25
What is the maximum height of any AVL-tree with $7$ nodes? Assume that the height of a tree with a single node is $0$. $2$ $3$ $4$ $5$
26
The keys $12, 18, 13, 2, 3, 23, 5$ and $15$ are inserted into an initially empty hash table of length $10$ using open addressing with hash function $h(k) = k \mod 10$ ...
27
The running time of an algorithm is represented by the following recurrence relation: $T(n) = \begin{cases} n & n \leq 3 \\ T(\frac{n}{3})+cn & \text{ otherwise } \end{cases}$ Which one of the following represents the time complexity of the algorithm? $\Theta(n)$ $\Theta(n \log n)$ $\Theta(n^2)$ $\Theta(n^2 \log n)$
The enter_CS() and leave_CS() functions to implement critical section of a process are realized using test-and-set instruction as follows: void enter_CS(X) { while(test-and-set(X)); } void leave_CS(X) { X = 0; } In the above solution, $X$ is a memory location associated with the $CS$ ... $CS$ at the same time Which of the above statements are TRUE? (I) only (I) and (II) (II) and (III) (IV) only
In the following process state transition diagram for a uniprocessor system, assume that there are always some processes in the ready state: Now consider the following statements: If a process makes a transition $D$, it would result in another process making transition $A$ ... uses non-preemptive scheduling. Which of the above statements are TRUE? I and II I and III II and III II and IV