The 2n vertices of graph G correspond to all subsets of a set of size n,for n≥6. Two vertices of G are adjacent if and only if the corresponding sets intersect inexactly two elements.The number of connected components in G is _______
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Solution
Number of connected component of G is determined by the degree and edges of vertices there are n + 1 vertices whose degree is zero,so they can form n + 1 connected component. The remaining vertices of the graph G are all connected as a single component. So total number of connected component is n +2.
Consider the following recurrence relation:
T(1) = 1
\(T(n+1)-T(n)+\left \lfloor \sqrt{n+1} \right \rfloor\) for all n ≥ 1
he value of T(m)2 for m≥1 is
The rank of the matrix given below is ______
\(\begin{bmatrix} 1 & 4 & 8 & 7\\ 0 & 0 & 3 & 0\\ 4 & 2 & 3 & 1\\ 3 & 12 & 24 & 2 \end{bmatrix}\)-
Solution
R4 = 3R1.
∴ Rank > 4
\(and \begin{bmatrix} 1 & 4 & 8\\ 0 & 0 & 3\\ 4 & 2 & 3 \end{bmatrix} = 48 \not\equiv 0\)
∴ Rank = 3
Two friends agree to meet at a park with the following conditions. Each will reach the park between 4.00 p.m. and 5.00 p.m. and will see if the other has already arrived.If not,they will wait for 10 minutes or the end of the hour which ever is earlier and leave. What is the probability that the two will not meet ?
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Solution
0.6944
Suppose X and Y are sets and |X| and |Y| are their respective cardinalities. It is given that there are exactly 97 functions from X to Y.From this one can conclude that
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Solution
Given 97 functions from X to Y is
So,|X| = 1, |Y| = 97.
You are given the following IP address and subnet mask
192.168.1.58255.
255.255.240.
Identify the original range of subnet address is that this IP address belong to
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Solution
First 4 bits are borrowed from host ID, hence subnet IDs are 0, 16, 32, 48, ....., 240 and each subnet contains 24– 2 = 14 hosts, hence it should bein 48 subnet.
∴Host ID range is
00110001 – 49
01000000 – 64
Consider a Packet Switching network which uses a Random Routing Algorithm
Ri: is the data rate on link
and Pi: is the probability of selecting the link
What is the value of P1 for some j?
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Solution
The random routing algorithm assigns a probability to each out going link and to select the link.So,
\(P_{i}=\frac{R_{i}}{\underset{j}{\sum }Rj}\)
Given the following state table of an FSM with two states A and B, one input and one output.
If the initial state is A = 0, B = 0, what is the minimum length of an input string,_________. which will take the machine to state A =0, B = 1 with output = 1?
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Solution
The initial state= 00
Final state required = 01
Let us construct the transition diagram for the given truth tableNow,construct the transition diagram for the required final state and output by using above transition diagram.
Hence, the minimal string is 101 to get the final state 01,with output 1 and its length is 3.
Consider a given schema R(ABCD) with primary key AB.Under which set of FD’s, the schema R is in 2NF but not in 3 NF.
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Solution
The FD AB →CD
BC →D is in 2NF but not in 3NF
Which of the following is private IP address?
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Solution
Class A private Address range is
10.0.0.0 – 10.255.255.255
Class B private Address range is
172.16.0.0 – 172.31.255.255
Class C private Address range is
192.168.0.0 – 192.168.255.255