I'll give you a few tips:

like the question say, you first need to write yourself the density function and the cumulative distribution function.

a.

it T is time in years, and T~Exp(0.2), then you are looking for P(3<T<5). There are 2 ways to do it, one is the use the cumulative distribution function, and the other is to use the density function.

P(3<T<5) = P(T<5) - P(T<3) , while P(T<5) and P(T<3) can be obtained from the CDF. Another way, is to calculate an Integral of the density function using the values 3 and 5.

b.

at first sight looks like a conditional probability, but look on the internet for the "Memorylessness" attribute of exponential distribution.

c.

define a "success" or "failure" to be a failure during the first 4 years. Calculate the probability of that to happen in a random TV set. Then you will have an experiment of 10 TV sets, while you know the probability p of each one of the 10 to "succeed" or "fail". Then what should be the distribution of N then ? ( Hint: It's discrete )