Discrete Mathematics
Q131.
Let G be the non-planar graph with the minimum possible number of edges. Then G hasQ133.
Choose the correct alternatives ( more than one may be correct) and write the corresponding letters only:A non-planar graph with minimum number of vertices hasQ134.
For the distributions given below :Which of the following is correct for the above distributions?Q135.
A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?Q136.
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\in\{H,L\}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7. If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is __________.Q138.
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x^2+6xY+3Y+6 has only real roots is (rounded off to 1 decimal place) _________.Q139.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is _________Q140.
For n\gt2, let a \in \{0,1\}^n be a non-zero vector. Suppose that x is chosen uniformly at random from \{0,1\}^n. Then, the probability that \sum_{i=1}^{n}a_ix_i is an odd number is______