1
GATE CSE 2021 Set 1
Numerical
+2
-0.67

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 7 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
+2
-0.67

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
Numerical
+2
-0.67

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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4
GATE CSE 2021 Set 1
Numerical
+2
-0.67
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______
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