Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (= 106 bits per second). The aggregate number of transmissions across all the nodes (in-cluding new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is  

Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

Consider the following two statements about regular languages:

S₁: Every infinite regular language contains an undecidable language as a subset.

S₂: Every finite language is regular.

Which one of the following choices is correct?

If $${\left( {x - {1 \over 2}} \right)^2} - {\left( {x - {3 \over 2}} \right)^2} = x + 2$$, then the value of x is :