# Tutor profile: Aviral S.

## Questions

### Subject: Microsoft Excel

Given huge piles of data, that have hundreds, or thousands of rows, while scrolling down a user tends to forget the column name, under which a particular cell or range of cells, falls under. Is there some way in which the headers can be frozen?

Let us assume a table, in which the headers are entered in row 1 and the first header is entered in cell A1. To freeze the panes follow the given steps: 1. Click on cell A2. 2. Go to the view tab on your options bar. (The bar at the top of the screen) 3, And Click on freeze pane. Try scrolling down on your table, you will now see that the headers are visible even if you scroll down on your table.

### Subject: Trigonometry

Prove the following: cos(t) / [ 1 + sin(t) ] = [ 1 - sin(t) ] / cos(t)

To prove the following we will follow the given steps : 1. The question requires the use of the formula: sin^2(t) + cos^2(t) = 1. 2. Such questions require one to prove that LHS = RHS, follow the given approach. 3. Multiply the numerator and denominator by [ 1 - sin(t) ] 4. We get the following expression : {cos(t) * [ 1 -sin(t) ]} / {[ 1 + sin(t) ] * [[1 - sin(t)]} 5. On multiplying, we get : {cos(t) * [ 1 -sin(t) ]} / [ 1 - sin^2(t) ] 6. From the equation given in step 1, we can say that : [ 1 - sin^2(t) ] = cos^2(t) 7. Hence the expression given in step 5 changes to ; {cos(t) * [ 1 -sin(t) ]} / cos^2(t) 8. On simplifying, we get : [ 1 -sin(t) ] / cos(t) 9. Hence we have proved that : cos(t) / [ 1 + sin(t) ] = [ 1 - sin(t) ] / cos(t)

### Subject: Statistics

In a test, out of the 500 new recruits, the ones who score in the bottom 16 percent on their exams are required to take a retest. If the test scores are normally distributed and have an arithmetic mean of 72, and it is given that 10 new recruits scored at least 82 on their tests, find out the score below which all recruits will have to take a retest.

In a normally distributed curve, the mean is given as 72, while the standard deviation can be a variable 's'. All values below 16% will be approximately at a distance of one standard deviation (s) from the mean, which will be 72 - s. It is also given that 10 recruits score at least 82 marks. Since 10 people are 2% of 500, and in a normal curve, the values in the top 2% of a normal curve are 2 standard deviations above the mean. Hence 72 + 2s = 82. Which gives s = 5. Hence the threshold value for the bottom 16% of the class will be 72 - 5 = 67. The score below which all recruits will have to take a retest is 67.