1
GATE CSE 2021 Set 1
Numerical
+2
-0

A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

GATE CSE 2021 Set 1 Discrete Mathematics - Probability Question 15 English
If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______

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2
GATE CSE 2021 Set 1
Numerical
+1
-0

Consider the following expression

$$\mathop {\lim }\limits_{x \to -3} \frac{{\sqrt {2x + 22} - 4}}{{x + 3}}$$

The value of the above expression (rounded to 2 decimal places) is ______

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3
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67

Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and v}

Let M be the adjacency matrix of G.

Define graph G2 on the same set of vertices with adjacency matrix N, where

$$N_{ij} =\left\{ {\begin{array}{*{20}{c}} {1 \ \ \text{if} \ \ {M_{ij}} > 0 \ \ \text{or} \ \ P_{ij} > 0, \ \text{where} \ \ P = {M^2}}\\ {0, \ \ \ \ \ \text{otherwise}} \end{array}} \right.$$

Which one of the following statements is true?

A
diam(G) < diam(G2) ≤ diam(G)
B
$$\left\lceil {diam(G)/2} \right\rceil $$ < diam(G2) < diam(G)
C
diam(G2) ≤ $$\left\lceil {diam(G)/2} \right\rceil $$
D
diam(G2) = diam(G)
4
GATE CSE 2021 Set 1
Numerical
+2
-0

Consider the following matrix.

$$\left( {\begin{array}{*{20}{c}} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{array}} \right)$$

The largest eigenvalue of the above matrix is ______

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