# Recent questions tagged gate2011

1
An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$ are connected if and only if $0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below. The length of the path from $v_5$ to $v_6$ in the MST of previous question with $n=10$ is $11$ $25$ $31$ $41$
2
Consider the following recursive C function that takes two arguments. unsigned int foo(unsigned int n, unsigned int r) { if (n>0) return ((n%r) + foo(n/r, r)); else return 0; } What is the return value of the function $\text{foo}$ when it is called as $\text{foo(513, 2)}$? $9$ $8$ $5$ $2$
3
Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If all the flip-flops were reset to $0$ at power on, what is the total number of distinct outputs (states) represented by $PQR$ generated by the counter? $3$ $4$ $5$ $6$
4
Consider a network with five nodes, $N1$ to $N5$, as shown as below. The network uses a Distance Vector Routing protocol. Once the routes have been stabilized, the distance vectors at different nodes are as follows. N1: $(0, 1, 7, 8, 4)$ N2: $(1, 0, 6, 7, 3)$ ... $N1$ in the distance vector of $N3$ ? $3$ $9$ $10$ $\infty$
5
Let $P$ be a regular language and $Q$ be a context-free language such that $Q \subseteq P$. (For example, let $P$ be the language represented by the regular expression $p^*q^*$ and $Q$ be $\{p^nq^n \mid n \in N\})$. Then which of the following is ALWAYS regular? $P \cap Q$ $P-Q$ $\Sigma^*-P$ $\Sigma^*-Q$
6
A container originally contains $10$ litres of pure spirit. From this container, $1$ litre of spirit replaced with $1$ litre of water. Subsequently, $1$ litre of the mixture is again replaced with $1$ litre of water and this process is repeated one more time. How much spirit is now left in the container? $7.58$ litres $7.84$ litres $7$ litres $7.29$ litres
7
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses $7$ trucks, then at the end of the $4^{th}$ day he can clear all the orders. Alternatively, if he uses only $3$ trucks, then all the orders are ... minimum number of trucks required so that there will be no pending order at the end of $5^{th}$ day? $4$ $5$ $6$ $7$
8
The variable cost $(V)$ of manufacturing a product varies according to the equation $V=4q$, where $q$ is the quantity produced. The fixed cost $(F)$ of production of same product reduces with $q$ according to the equation $F=\dfrac{100}{q}$. How many units should be produced to minimize the total cost $(V+F)$? $5$ $4$ $7$ $6$
9
$P, Q, R$ and $S$ are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within $24$ hours of entering the body. The ... a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt? $P$ $Q$ $R$ $S$
10
Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting. Based on the above passage which topic would not be included in a unit on ... emotional stages are passed through in the healing process what the leading causes of death are how to give support to a grieving friend
11
Choose the word from the options given below that is most nearly opposite in the meaning to the given word Amalgamate merge split collect separate
12
Choose the most appropriate word from the options given below to complete the following sentence. If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or ________. hyperbolic restrained argumentative indifferent
13
Choose the most appropriate word(s) from the options given below to complete the following sentence. I contemplated _________ Singapore for my vacation but decided against it. to visit having to visit visiting for a visit
14
If $\log (\text{P}) = (1/2)\log (\text{Q}) = (1/3)\log (\text{R})$, then which of the following options is TRUE? $\text{P}^2 = \text{Q}^3\text{R}^2$ $\text{Q}^2=\text{P}\text{R}$ $\text{Q}^2 = \text{R}^3\text{P}$ $\text{R}=\text{P}^2\text{Q}^2$
15
Which of the following options is the closest in the meaning to the word below: Inexplicable Incomprehensible Indelible Inextricable Infallible
16
An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$ are connected if and only if $0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with $n$ nodes? $\frac{1}{12} (11n^2 - 5 n)$ $n^2-n+1$ $6n-11$ $2n+1$
17
Consider a network with five nodes, $N1$ to $N5$, as shown as below. The network uses a Distance Vector Routing protocol. Once the routes have been stabilized, the distance vectors at different nodes are as follows. N1: $(0, 1, 7, 8, 4)$ N2: $(1, 0, 6, 7, 3)$ N3: $(7, 6, 0, 2, 6)$ N4: $(8, 7, 2, 0, 4)$ ... at node, $N3$? $(3, 2, 0, 2, 5)$ $(3, 2, 0, 2, 6)$ $(7, 2, 0, 2, 5)$ $(7, 2, 0, 2, 6)$
18
Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If at some instance prior to the occurrence of the clock edge, $P, Q$ and $R$ have a value $0$, $1$ and $0$ respectively, what shall be the value of $PQR$ after the clock edge? $000$ $001$ $010$ $011$
19
Consider the following recursive C function that takes two arguments. unsigned int foo(unsigned int n, unsigned int r) { if (n>0) return ((n%r) + foo(n/r, r)); else return 0; } What is the return value of the function $\text{foo}$ when it is called as $\text{foo(345, 10)}$? $345$ $12$ $5$ $3$
20
The following is the comment written for a C function. /* This function computes the roots of a quadratic equation a.x^2 + b.x + c = 0. The function stores two real roots in *root1 and *root2 and returns the status of validity of roots. It handles four different kinds of cases. (i) When coefficient a is ... box testing? (A) T1, T2, T3, T6 (B) T1, T3, T4, T5 (C) T2, T4, T5, T6 (D) T2, T3, T4, T5
21
Database table by name $\text{Loan_Records}$ ... Borrower, Bank_Manager FROM Loan_Records) AS S NATURAL JOIN (SELECT Bank_Manager, Loan_Amount FROM Loan_Records) AS T ); $3$ $9$ $5$ $6$
22
A deterministic finite automaton ($\text{DFA}$) $D$ with alphabet $\Sigma = \{a, b\}$ is given below. Which of the following finite state machines is a valid minimal $\text{DFA}$ which accepts the same languages as $D$?
23
An application loads $100$ libraries at startup. Loading each library requires exactly one disk access. The seek time of the disk to a random location is given as $10$ ms. Rotational speed of disk is $6000$ rpm. If all $100$ libraries are loaded from random locations on the disk, how long does it take ... at the start of the block may be neglected.) $0.50 \ s$ $1.50 \ s$ $1.25 \ s$ $1.00 \ s$
24
An $8KB$ direct-mapped write-back cache is organized as multiple blocks, each size of $32$-$bytes$. The processor generates $32$-$bit$ addresses. The cache controller contains the tag information for each cache block comprising of the following. $1$ valid bit $1$ modified bit As ... cache controller to store meta-data (tags) for the cache? $4864$ $bits$ $6144$ $bits$ $6656$ $bits$ $5376$ $bits$
25
Definition of a language $L$ with alphabet $\{a\}$ is given as following.$L = \left\{a^{nk} \mid k > 0, \:\: and \:\: n \text{ is a positive integer constant} \right\}$What is the minimum number of states needed in a DFA to recognize $L$? $k+1$ $n+1$ $2^{n+1}$ $2^{k+1}$
26
Consider an instruction pipeline with four stages $\text{(S1, S2, S3 and S4)}$ each with combinational circuit only. The pipeline registers are required between each stage and at the end of the last stage. Delays for the stages and for the pipeline registers are as given ... steady state under ideal conditions when compared to the corresponding non-pipeline implementation? $4.0$ $2.5$ $1.1$ $3.0$
27
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
Consider a relational table $r$ with sufficient number of records, having attributes $A_1, A_2, \dots ,A_n$ and let $1 \leq p \leq n$. Two queries $Q1$ and $Q2$ are given below. $Q1: \pi_{A_1, \dots ,A_p} \left(\sigma_{A_p=c}\left(r\right)\right)$ ... for both queries Hashing will outperform ordered indexing on $Q1$, but not on $Q2$ Hashing will outperform ordered indexing on $Q2$, but not on $Q1$
Four Matrices $M_1, M_2, M_3$ and $M_4$ of dimensions $p \times q, \:\:q \times r, \:\:r \times s$ and $s \times t$ ... $t=80$, then the minimum number of scalar multiplications needed is $248000$ $44000$ $19000$ $25000$
Which of the given options provides the increasing order of asymptotic complexity of functions $f_1, f_2, f_3$ and $f_4$? $f_1(n) = 2^n$ $f_2(n) = n^{3/2}$ $f_3(n) = n \log_2 n$ $f_4(n) = n^{\log_2 n}$ $f_3, f_2, f_4, f_1$ $f_3, f_2, f_1, f_4$ $f_2, f_3, f_1, f_4$ $f_2, f_3, f_4, f_1$