# Tutor profile: Lakshmi R.

## Questions

### Subject: TOEFL

"Deep in the Sierra Nevada, the famous General Grant giant sequoia tree is suffering its loss of stature in silence. What once was the world's No. 2 biggest tree has been supplanted thanks to the most comprehensive measurements taken of the largest living things on Earth." What does the word "supplanted" mean in this paragraph?

Answer - The word "supplanted" has a double-meaning both as a pun on the topic of plants and a literal meaning of "to replace". The part stating that it WAS the world's no. 2 biggest tree suggests that it is no more in the same position and has been replaced. The pun comes into the picture because of the word "supplanted" being used instead of directly stating that it has been replaced or superseded.

### Subject: GRE

A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

At the beginning, there are 34 students from two-year community colleges among a total of hundred students. Hence, the probability of choosing a community college student will be 34/100. For the second round of selection, since we have already obtained the probability for selecting a community college student in the first round, let us assume that a community college student has been chosen. Hence, the remaining number of community college students goes down by 1 to 33, and the total number of students also goes down by 1 to 99. So the probability of selecting a community college student in the second round would be 33/99. The question states that we need to find the probability that both students are from community colleges. Hence, the probability of the first round of selecting community college students needs to be multiplied by the probability of choosing a community college student in the second round. This is because the question is for an AND operation, wherein both conditions need to be satisfied, the final probability cannot be obtained without satisfying both conditions. The second condition cannot be fulfilled without first fulfilling the first condition. Hence the total probability of selecting community college students in both rounds would be (34/100) * (33/99), or (1122/9900).

### Subject: Electrical Engineering

With respect to analog receivers, what is the input third intercept point (IIP3)?

The concept of IP3 originates from the observation that if the amplitude of each of the input tones is raised by a certain amount, say 4 dB, then the amplitude of its corresponding intermodulation (IM) products also increases by a certain factor. Since the IM products are determined by the third order term in the input/output characteristic equation for non-linear terms, i.e. (3/4) * h3 * (A^3), the amplitude of the IM products will increase more sharply, by 12 dB here (gets multiplied by a factor of 3 in dB because of the term A^3). Thus, if we keep on increasing the amplitude of the inputs, after a certain point the amplitude of the intermodulation products would be equal to that of the input signal. The input level (on a logarithmic scale) at which this phenomenon takes place is called the IIP3, and it can be mathematically calculated by equating the fundamental with the IM amplitudes.

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