Given total number of students = 80

Total teachers = 5

Number of coupons each student got = 15 x 80/100 = 12

Number of coupons each teacher got = 25 x 80/100 = 20

Therefore, total number of shopping coupons = 80 x 12 + 5 x 20 = 960 + 100 = 1060.

Here given formula is 

a2 + b2 + c2 -ab- bc - ca = 0

and it is possible if and only if a = b = c.

From the trial and error method, 

1) Let a = b = c = 1

Now substitute these values of a, b, c in the above formula.

We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0

2) Now, let a = b = c = 4

Now substitute these values of a, b, c in the above formula.

We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0.

Hence, it is possible that 

a2 + b2 + c2 -ab- bc - ca = 0 iff a = b = c.

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

Given that the waste tap can empty the filled tank in 32 min.

Now, the rate at which the waste tap can empty the tank = (40 + 60)8/32 = 100/4 = 25 lit/min.

Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively.

Now, required time after which they met for the first time = LCM of (16, 24 & 36) min

Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.

All the above given options are the examples of social interaction. In sociology, interactions are of five types.They are :

1) Exchange

2) Competition

3) Cooperation

4) Coercion

5) Conflict

CH3COOH, chemically known as Acetic acid, is not a strong acid among the given acids like Sulphuric acid, Hydrochloric acid,...

In DNA, the chemicals are Adenine, thymine, guanine and cytosine. They always pair as basepairs like Adenine with Thymine and Guanine with Cytosine.