# Recent questions tagged gate2007-it 1
Consider the $B^{+}$ tree in the adjoining figure, where each node has at most two keys and three links. Keys $K15$ and then $K25$ are inserted into this tree in that order. Now the key $K50$ is deleted from the $B^+$ tree resulting after the two insertions made ... Statements (i) and (ii) are true Statements (ii) and (iii) are true Statements (iii) and (i) are true All the statements are false
2
Consider the $B^+$ tree in the adjoining figure, where each node has at most two keys and three links. Keys $K15$ and then $K25$ are inserted into this tree in that order. Exactly how many of the following nodes (disregarding the links) will be present in the tree after the two insertions? $1$ $2$ $3$ $4$
3
The head of a hard disk serves requests following the shortest seek time first (SSTF) policy. What is the maximum cardinality of the request set, so that the head changes its direction after servicing every request if the total number of tracks are $2048$ and the head can start from any track? $9$ $10$ $11$ $12$
4
The head of a hard disk serves requests following the shortest seek time first (SSTF) policy. The head is initially positioned at track number $180$. Which of the request sets will cause the head to change its direction after servicing every request assuming that the head does not change direction if there ... $10, 139, 169, 178, 181, 184, 201, 265$ $10, 138, 170, 178, 181, 185, 200, 265$
5
Let $P_1, P_2,\dots , P_n$be $n$ points in the $xy$-plane such that no three of them are collinear. For every pair of points $P_i$ and $P_j$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the steepest gradient among all $n(n -1)/2$ lines. The ... and $P_b$ is $\Theta\left(n\right)$ $\Theta\left(n\log n\right)$ $\Theta\left(n\log^2 n\right)$ $\Theta\left(n^2\right)$
6
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the steepest ... the largest or the smallest $y$-coordinate among all the points The difference between $x$-coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
7
Consider the following expression $a\bar d + \bar a \bar c + b\bar cd$ Which of the following expressions does not correspond to the Karnaugh Map obtained for the given expression? $\bar c \bar d+ a\bar d + ab\bar c + \bar a \bar cd$ $\bar a\bar c + \bar c\bar d + a\bar d + ab\bar cd$ $\bar a\bar c + a\bar d + ab\bar c + \bar cd$ $\bar b\bar c \bar d + ac\bar d + \bar a \bar c + ab\bar c$
8
Consider the following expression $a\bar d + \bar a\bar c + b\bar cd$ Which of the following Karnaugh Maps correctly represents the expression?
9
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the sequence $x_n$ converges for all ... $a < x_0 < b$? $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
10
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n -2$, where $c > 0$. Suppose there exists a non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges to a limit. The sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$
11
Consider a token ring topology with N stations (numbered 1 to N) running token ring protocol where the stations are equally spaced. When a station gets the token it is allowed to send one frame of fixed size. Ring latency is tp, while the transmission time of a frame is tt. All other latencies ... maximum utilization of the token ring when tt = 5 ms, tp = 3 ms, N = 15 is: 0.545 0.655 0.9375 0.961
12
Consider a token ring topology with N stations (numbered 1 to N) running token ring protocol where the stations are equally spaced. When a station gets the token it is allowed to send one frame of fixed size. Ring latency is tp, while the transmission time of a frame is tt. All other latencies ... The maximum utilization of the token ring when tt =3 ms, tp = 5 ms, N = 10 is 0.545 0.6 0.857 0.961
13
Consider the regular expression $R = (a + b)^* \ (aa + bb) \ (a + b)^*$ Which one of the regular expressions given below defines the same language as defined by the regular expression $R$ ? $(a(ba)^* + b(ab)^*)(a + b)^+$ $(a(ba)^* + b(ab)^*)^*(a + b)^*$ $(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^*$ $(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^+$
14
Consider the regular expression $R = (a + b)^* (aa + bb) (a + b)^*$ Which deterministic finite automaton accepts the language represented by the regular expression $R$?
15
Consider the regular expression $R = (a + b)^* (aa + bb) (a + b)^*$ Which of the following non-deterministic finite automata recognizes the language defined by the regular expression $R$? Edges labeled $\lambda$ denote transitions on the empty string.
16
You are given the following four bytes : 10100011 00110111 11101001 10101011 Which of the following are substrings of the base $64$ encoding of the above four bytes? $\text{zdp}$ $\text{fpq}$ $\text{qwA}$ $\text{oze}$
17
Consider the following clauses: Not inherently suitable for client authentication. Not a state sensitive protocol. Must be operated with more than one server. Suitable for structured message organization. May need two ports on the serve side for proper operation. The option that has the maximum number of ... -v POP3-i; SMTP-ii; DNS-iii; IMAP-iv; HTTP-v SMTP-i; HTTP-ii; IMAP-iii; DNS-iv; FTP-v
18
Consider the following relation schemas : b-Schema = (b-name, b-city, assets) a-Schema = (a-num, b-name, bal) d-Schema = (c-name, a-number) Let branch, account and depositor be respectively instances of the above schemas. Assume that account and depositor relations are much bigger ... < 0 account) ⋈ depositor) Пc-name (σb-city = "Agra" branch ⋈ (σb-city = "Agra" ⋀ bal < 0 account ⋈ depositor))
19
Consider the following implications relating to functional and multivalued dependencies given below, which may or may not be correct. if $A \rightarrow \rightarrow B$ and $A \rightarrow \rightarrow C$ then $A \rightarrow \rightarrow BC$ if $A \rightarrow B$ and $A \rightarrow C$ then ... $A \rightarrow \rightarrow C$ Exactly how many of the above implications are valid? $0$ $1$ $2$ $3$
20
Consider the following two transactions : T1 and T2. T1 : read (A); T2 : read (B); read (B); read (A); if A = 0 then B ← B + 1; if B ≠ 0 then A ← A - 1; write (B); write (A); Which of the following schemes, using shared and exclusive locks, satisfy the requirements for strict two ... B ← B + 1; then A ← A - 1; write (B); write (A); unlock (A); unlock (A); unlock (B); unlock (B); commit; commit;
21
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are uniformly distributed in the interval $[0, 500].$ Which one of the following options is the best estimate of the number of tuples returned by the given selection query ? $50$ $100$ $150$ $200$
22
A broadcast channel has $10$ nodes and total capacity of $10$ Mbps. It uses polling for medium access. Once a node finishes transmission, there is a polling delay of $80$ μs to poll the next node. Whenever a node is polled, it is allowed to transmit a maximum of $1000$ bytes. The maximum throughput of the broadcast channel is: $1$ Mbps $100/11$ Mbps $10$ Mbps $100$ Mbps
23
A group of $15$ routers is interconnected in a centralized complete binary tree with a router at each tree node. Router $i$ communicates with router $j$ by sending a message to the root of the tree. The root then sends the message back down to router $j$. The mean number of hops per message, assuming all possible router pairs are equally likely is $3$ $4.26$ $4.53$ $5.26$
24
Let us consider a statistical time division multiplexing of packets. The number of sources is $10$. In a time unit, a source transmits a packet of $1000$ bits. The number of sources sending data for the first $20$ ... $5$ $4.45$ $3.45$ $0$
25
In the waveform (a) given below, a bit stream is encoded by Manchester encoding scheme. The same bit stream is encoded in a different coding scheme in wave form (b). The bit stream and the coding scheme ... Differential Manchester respectively $0111101000$ and Differential Manchester respectively $1000010111$ and Integral Manchester respectively $0111101000$ and Integral Manchester respectively
26
For the network given in the figure below, the routing tables of the four nodes $A$, $E$, $D$ and $G$ are shown. Suppose that $F$ has estimated its delay to its neighbors, $A$, $E$, $D$ and $G$ as $8$, $10$, $12$ and $6$ msecs respectively and updates its routing table using distance ...
27
The contents of the text file t1 txt containing four lines are as follows : a1 b1 a2 b2 a3 b2 a4 b1 The contents of the text file t2 txt containing five lines are as follows : a1 c1 a2 c2 a3 c3 a4 c3 a5 c4 Consider the following Bourne shell script : awk - F ' ' ' {Print ... the above script in run? (Note that the given strings may be substrings of a printed line.) "b1 c1" "b2 c3" "b1 c2" "b1 c3"
A demand paging system takes $100$ time units to service a page fault and $300$ time units to replace a dirty page. Memory access time is $1$ time unit. The probability of a page fault is $p$. In case of a page fault, the probability of page being dirty is also $p$. It is observed that the average access time is $3$ time units. Then the value of $p$ is $0.194$ $0.233$ $0.514$ $0.981$
In a multi-user operating system on an average, $20$ requests are made to use a particular resource per hour. The arrival of requests follows a Poisson distribution. The probability that either one, three or five requests are made in $45$ minutes is given by : $6.9 \times 10^6 \times e^{-20}$ $1.02 \times 10^6 \times e^{-20}$ $6.9 \times 10^3 \times e^{-20}$ $1.02 \times 10^3 \times e^{-20}$