# Recent questions tagged gate2004

1
Consider a parity check code with three data bits and four parity check bits. Three of the code words are 0101011, 1001101 and 1110001. Which of the following are also code words? 0010111 0110110 1011010 0111010 plz give the solution in detail I and III I, II and III II and IV I, II, III and IV
2
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ $bytes$ of application data to a host $H_C$ in network $C$. The TCP layer prefixes $20$ byte header to the message. This passes through an intermediate network $B$. The maximum packet ... other overheads. $325.5$ $\text{Kbps}$ $354.5$ $\text{Kbps}$ $409.6$ $\text{Kbps}$ $512.0$ $\text{Kbps}$
3
Consider the following program segment for a hypothetical CPU having three user registers $R_1, R_2$ and $R_3.$ \begin{array}{|l|l|c|} \hline \text {Instruction} & \text{Operation }& \text{Instruction size (in Words)} \\\hline \text{MOV $R_1,5000$} & \text{$R1$} \ ... text{2 clock cycles }\\\hline \end{array} The total number of clock cycles required to execute the program is $29$ $24$ $23$ $20$
4
Consider the grammar rule $E \rightarrow E1 - E2$ for arith­metic expressions. The code generated is targeted to a CPU having a single user register. The sub­traction operation requires the first operand to be in the register. If $E1$ and $E2$ do not have any com­mon ... first Evaluation of $E1$ and $E2$ should necessarily be interleaved Order of evaluation of $E1$ and $E2$ is of no consequence
5
Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2. ... $P-3\quad Q-4 \quad R-1\quad S-2$ $P-3\quad Q-4\quad R-2\quad S-1$
6
$L_1$ is a recursively enumerable language over $\Sigma$. An algorithm $A$ effectively enumerates its words as $\omega_1, \omega_2, \omega_3, \dots .$ Define another language $L_2$ over $\Sigma \cup \left\{\text{#}\right\}$ ... $S_1$ is true but $S_2$ is not necessarily true $S_2$ is true but $S_1$ is not necessarily true Neither is necessarily true
7
Consider the following grammar G: $S \rightarrow bS \mid aA \mid b$ $A \rightarrow bA \mid aB$ $B \rightarrow bB \mid aS \mid a$ Let $N_a(w)$ and $N_b(w)$ denote the number of a's and b's in a string $\omega$ respectively. The language $L(G)$ over $\left\{a, b\right\}^+$ generated by $G$ ... $\left\{w \mid N_b(w) = 3k, k \in \left\{0, 1, 2, \right\}\right\}$
8
The language $\left\{a^mb^nc^{m+n} \mid m, n \geq1\right\}$ is regular context-free but not regular context-sensitive but not context free type-0 but not context sensitive
9
The following finite state machine accepts all those binary strings in which the number of $1$’s and $0$’s are respectively: divisible by $3$ and $2$ odd and even even and odd divisible by $2$ and $3$
10
A program takes as input a balanced binary search tree with $n$ leaf nodes and computes the value of a function $g(x)$ for each node $x$. If the cost of computing $g(x)$ is: $\Large \min \left ( \substack{\text{number of leaf-nodes}\\\text{in left-subtree of$ ... the worst-case time complexity of the program is? $\Theta (n)$ $\Theta (n \log n)$ $\Theta(n^2)$ $\Theta (n^2\log n)$
11
The recurrence equation $T(1) = 1$ $T(n) = 2T(n-1) + n, n \geq 2$ evaluates to $2^{n+1} - n - 2$ $2^n - n$ $2^{n+1} - 2n - 2$ $2^n + n$
12
The time complexity of the following C function is (assume $n > 0$) int recursive (int n) { if(n == 1) return (1); else return (recursive (n-1) + recursive (n-1)); } $O(n)$ $O(n \log n)$ $O(n^2)$ $O(2^n)$
13
Let $A[1,\ldots,n]$ be an array storing a bit ($1$ or $0$) at each location, and $f(m)$ is a function whose time complexity is $\Theta(m)$. Consider the following program fragment written in a C like language: counter = 0; for (i=1; i<=n; i++) { if a[i] == 1) counter++; ... 0;} } The complexity of this program fragment is $\Omega(n^2)$ $\Omega (n\log n) \text{ and } O(n^2)$ $\Theta(n)$ $o(n)$
14
Let $G_1=(V,E_1)$ and $G_2 =(V,E_2)$ be connected graphs on the same vertex set $V$ with more than two vertices. If $G_1 \cap G_2= (V,E_1\cap E_2)$ is not a connected graph, then the graph $G_1\cup G_2=(V,E_1\cup E_2)$ cannot have a cut vertex must have a cycle must have a cut-edge (bridge) has chromatic number strictly greater than those of $G_1$ and $G_2$
15
A point is randomly selected with uniform probability in the $X-Y$ plane within the rectangle with corners at $(0,0), (1,0), (1,2)$ and $(0,2).$ If $p$ is the length of the position vector of the point, the expected value of $p^{2}$ is $\left(\dfrac{2}{3}\right)$ $\quad 1$ $\left(\dfrac{4}{3}\right)$ $\left(\dfrac{5}{3}\right)$
16
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k\\$ $^{\left(\frac{n^2-n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
17
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
18
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
19
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
20
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
21
An examination paper has $150$ multiple choice questions of one mark each, with each question having four choices. Each incorrect answer fetches $-0.25$ marks. Suppose $1000$ students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is $0$ $2550$ $7525$ $9375$
22
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\}$ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by set containment? $\{1\}$ $\{1\}, \{2, 3\}$ $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
23
The following is the incomplete operation table of a $4-$ ... $c\;a\;e\; b$ $c\; b\; a\; e$ $c\; b\; e\; a$ $c\; e\; a\; b$
24
How many solutions does the following system of linear equations have? $-x + 5y = -1$ $x - y = 2$ $x + 3y = 3$ infinitely many two distinct solutions unique none
25
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above
26
A 4-stage pipeline has the stage delays as $150$, $120$, $160$ and $140$ $nanoseconds$, respectively. Registers that are used between the stages have a delay of $5$ $nanoseconds$ each. Assuming constant clocking rate, the total time taken to process $1000$ data items ... will be: $\text{120.4 microseconds}$ $\text{160.5 microseconds}$ $\text{165.5 microseconds}$ $\text{590.0 microseconds}$
27
A hard disk with a transfer rate of $10$ Mbytes/second is constantly transferring data to memory using DMA. The processor runs at $600$ MHz, and takes $300$ and $900$ clock cycles to initiate and complete DMA transfer respectively. If the size of the transfer is $20$ Kbytes, what is the percentage of processor time consumed for the transfer operation? $5.0 \%$ $1.0\%$ $0.5\%$ $0.1\%$
The microinstructions stored in the control memory of a processor have a width of $26$ bits. Each microinstruction is divided into three fields: a micro-operation field of $13$ bits, a next address field $(X),$ and a MUX select field $(Y).$ There are $8$ status bits in the input of the MUX. ... the size of the control memory in number of words? $10, 3, 1024$ $8, 5, 256$ $5, 8, 2048$ $10, 3, 512$
Let $A = 1111 1010$ and $B = 0000 1010$ be two $8-bit$ $2’s$ complement numbers. Their product in $2’s$ complement is $1100 0100$ $1001 1100$ $1010 0101$ $1101 0101$
Consider a small two-way set-associative cache memory, consisting of four blocks. For choosing the block to be replaced, use the least recently used (LRU) scheme. The number of cache misses for the following sequence of block addresses is: $8, 12, 0, 12, 8$. $2$ $3$ $4$ $5$