1
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: All film stars are playback singers. All film directors are film stars. Conclusions: All film directors are playback singers ... Only conclusion I follows. Only conclusion II follows. Neither conclusion I nor II follows. Both conclusions I and II follow.
2
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
3
Nodes A and B are connected with 100 Mbps ethernet segment with 6 microsec pop.delay between them.Suppose A,B send frames at t=0 and frames get collided.after first collision A draws k=0 and bdraws k=1.if jam signal is ignored and timeout is 1 RTT then at what time A's packet gets completely delivered to B...assume packet size 1000 bits. a)28 microsec b)16 microsec c)22 microsec d)38 microsec
4
If a graph has k-independent components, it it n-k+1 colorable
5
There are 16072016 users in Facebook. A graph is formed where an edge(u,v) is defined when a male is friend to a female and vice versa. Estimate the number of simple cycle of length 1607 formed in the graph?
6
Number of distinct BFS, DFS trees in a complete graph ?
7
If a real number x is chosen at random in the interval [0, 3], and a real number y is chosen at random in the interval [0, 4],what is the probability that x < y ? (A) 1/2 (B) 7/12 (C) 5/8 (D) 2/3
8
Let x1 x2 x3 be three independent and identically distribuyed random variables with uniform distrbution on (0,1) find probability p(x1+x2<=x3)
9
10
If $n$ and $m$ are positive integers and $n^{9}=19m+r$, then the possible values for $r$ modulo 19 are. Only 0 Only 0, $\pm$ 1. Only $\pm$ 1. None of the above.
11
Let M be a single-tape deterministic TM with tape alphabet { blank, 0, 1 }, and let C denote the ( possibly infinite ) computation of M starting with a blank tape. The input to each problem is M, together with a positive integer n. Which of the following problems is(are) decidable ? I. ... distinct tape cells during the company C (A). III only (B). I and II only (C).I and III only (D).I,II and III
1 vote
12
S-> S+S | S*S | a | € Which is false? a) G is ambiguous b) L is ambiguous c) both a and b d) none
1 vote
13
Which of the following problems is(are) decidable ? I. Given a (finite) string W, is W a prefix of the decimal expansion of $\pi$ II. Given a Program and an input, is the programs output the decimal expansion of $\pi$ III. Given a Program and an input a prifix of the decimal ... , the prorams output always the same for every prifix (A). I only (B). II only (C). I and II only (D). III only
14
15
Consider a simple graph with unit edge costs. Each node in the graph represents a router. Each node maintains a routing table indicating the next hop router to be used to relay a packet to its destination and the cost of the path to the destination through that router. Initially, the routing table is empty. ... to node $A$ at time $(t + 100)$ is : $>100$ but finite $\infty$ $3$ $>3$ and $\leq 100$
16
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... maximum value of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
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 $\Theta\left(n\right)$ $\Theta\left(n\log n\right)$ $\Theta\left(n\log^2 n\right)$ $\Theta\left(n^2\right)$
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.
How many term will be computed to determine the value of $10C8$ Using a divide and conquer algorithms ? 45 46 90 89
A computer uses $32-bit$ virtual address, and $32-bit$ physical address. The physical memory is byte addressable, and the page size is $4$ $\text{kbytes}$ . It is decided to use two level page tables to translate from virtual address to physical ... entries that can be contained in each page? How many bits are available for storing protection and other information in each page table entry?