Question 96
If P(A) = 0.5, P(B) = 0.4, and P(A | B) = 0.6, what is P(A n B)?
Detailed Solution
$P(A∩B)=P(A|B)P(B)=0.6*0.4=0.24.$
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GATE CSE Discrete & Engineering Mathematics – Full Mock Test SET-1
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Question 97
What is the number of edges in a hypercube graph $Q_{4}$ (4-dimensional hypercube)?
Detailed Solution
$Q_{4}$ has $2^4$ vertices, each of degree 4, so edges = 16*4/2 = 32.
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Question 98
What is the number of vertices in a hypercube graph $Q_{4}$?
Detailed Solution
Formula for vertices in n-dimensional hypercube $Q_{n}$ is $2^n$. For $Q_{4}$: $2^4$ = 16.
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Question 99
What is the maximum number of edges in a simple graph with 5 vertices that does NOT contain any triangles ($K_{3}$)?
Detailed Solution
By Turán's theorem, the maximum number of edges in a triangle-free graph on 5 vertices is floor(25/4)=6.
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Question 100
Let G be a graph with 10 vertices and 25 edges. What is the sum of degrees of all vertices in G?
Detailed Solution
The handshaking lemma gives sum of degrees = 2|E| = 50.
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