**BMAT Prep Question Analysis - Q78 & Q136**

**Q78 A student arranges four 6**Ω** resistors. How many functionally different resistors can be made if all resistors are used in each circuit configuration?**

a. 3

b. 4

c. 5

d: 6

e. 7

**Q136 The nuclei of a radioactive element decay into the nuclei of another element at a rate proportional to the number of nuclei in the first element.**

**Consider that a radioactive element X decays into another radioactive element Y, which further decays into a non-radioactive element Z.**

**If you start with a pure sample of element X, and a plot of the number of the nuclei of Y as a function of time (t), which of the following graphs do you expect to obtain?**

**Answer and Explanation**

**Q78 Answer: **d. 6

**Explanation**: Because resistors in parallel and in series would give a different resistance, we can see that we can arrange the four resistors into different configurations of circuits to get six functionally different circuits.

**Q136 Answer: **Figure C

**Explanation: **Unstable nuclei disintegrate spontaneously and at random. The more un-decayed nuclei there are, the more frequently disintegrations are likely to occur.

As X decays into Y exponentially, you would expect to see an exponential decrease of X nuclei (similar to figure A); this corresponds to an exponential increase of Y as well. But since Y is also unstable and will also decay, it will undergo an exponential decay too. Thus we see figure C is the answer.

Initially when X decays into Y, Y increases, but when there is more and more Y, there is also a component of Y decay into Z (which is stable). Thus Y decreases exponentially.

Drafed by Quincy (BMAT Prep)