1
GATE CSE 2022
+1
-0.33

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

A
The diagonal entries of A2 are the degrees of the vertices of the graph.
B
If the graph is connected, then none of the entries of An $$-$$ 1 + In can be zero.
C
If the sum of all the elements of A is at most 2(n $$-$$ 1), then the graph must be acyclic.
D
If there is at least a 1 in each of A's rows and columns, then the graph must be connected.
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following is/are the eigen vector(s) for the matrix given below?

$$\left( {\matrix{ { - 9} & { - 6} & { - 2} & { - 4} \cr { - 8} & { - 6} & { - 3} & { - 1} \cr {20} & {15} & 8 & 5 \cr {32} & {21} & 7 & {12} \cr } } \right)$$

A
$$\left( {\matrix{ { - 1} \cr 1 \cr 0 \cr 1 \cr } } \right)$$
B
$$\left( {\matrix{ 1 \cr 0 \cr { - 1} \cr 0 \cr } } \right)$$
C
$$\left( {\matrix{ { - 1} \cr 0 \cr 2 \cr 2 \cr } } \right)$$
D
$$\left( {\matrix{ 0 \cr 1 \cr { - 3} \cr 0 \cr } } \right)$$
3
GATE CSE 2022
+1
-0.33

Consider the following threads, T1, T2 and T3 executing on a single processor, synchronized using three binary semaphore variables, S1, S2 and S3, operated upon using standard wait( ) and signal( ). The threads can be context switched in any order and at any time.

$${T_1}$$ $${T_2}$$ $${T_3}$$
while (true) {
wait ($${S_3}$$);
print ("C");
signal ($${S_2}$$); }
while (true) {
wait ($${S_1}$$);
print ("B");
signal ($${S_3}$$); }
while (true) {
wait ($${S_2}$$);
print ("A")
signal ($${S_1}$$); }

Which initialization of the semaphores would print the sequence BCABCABCA....... ?

A
S1 = 1; S2 = 1; S3 = 1
B
S1 = 1; S2 = 1; S3 = 0
C
S1 = 1; S2 = 0; S3 = 0
D
S0 = 1; S2 = 1; S3 = 1
4
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following statements is/are TRUE with respect to deadlocks?

A
Circular wait is a necessary condition for the formation of deadlock.
B
In a system where each resource has more than one instance, a cycle in its wait for graph indicates the presence of a deadlock.
C
If the current allocation of resources to processes leads the system to unsafe state, then deadlock will necessarily occur.
D
In the resource-allocation graph of a system, if every edge is an assignment edge, then the system is not in deadlock state.
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