CareerCup

L = { <M> | there is at least one input string on which the Turing machine M does not halt}

Here, for a Turing machine M, the notation <M> denotes an encoding, oversome alphabet, of the code of the Turing machine.to
which of the following language classes does L belong:

(1) Regular.

(2) Context-free but not Regular.

(3) Recursive but not Context-free.

(4) Recursively enumerable but not recursive.

(5) Not recursively enumerable.

Rockets are launched until the first successful launching
has taken place.if this does not occur within 5 attempts,the
experiment is halted and the equipment inspected.suppose that
there is a constant probability of 0.8 of having a successful
launching and that successive attempts are independent.Assume
that the cost of the first launching is K dollars while subsequent
launching cost K/3 dollars.whenever a successful launching take place,a certain amount of information
is obtained which may be expressed as financial gain of,say 'C' dollars.if 'T' is the net cost of this
experiment,find the probability distribution of T?

A factory produces 10 glass containers daily. It may be assumed that there is a constant probability p=0.1 of producing a defective container. Before these containers are stored they are inspected and the defectives ones are set aside. Suppose that there is a constant probability r=0.2 that a defective container is misclassified. Let X equal the number of containers classified as a defective at the end of a production day. (Suppose that all containers which are manufactured on a particular day are also inspected on that day.)

(1)P(X=k) = ?