To solve these expressions, we can use the formulas for the sum of consecutive integers and the sum of consecutive squares.

1. (1+2+3+....+100).(1^2+2^2+....+10^2)
The sum of consecutive integers from 1 to 100 is given by the formula: n(n+1)/2, where n is the number of terms. In this case, n = 100.
So, the sum of consecutive integers from 1 to 100 is (100)(101)/2 = 5050.

The sum of consecutive squares from 1^2 to 10^2 is given by the formula: n(n+1)(2n+1)/6, where n is the number of terms. In this case, n = 10.
So, the sum of consecutive squares from 1^2 to 10^2 is (10)(11)(21)/6 = 385.

Therefore, (1+2+3+....+100).(1^2+2^2+....+10^2) = 5050 * 385 = 1,944,250.

2. (65.111-13.15.37)
To simplify this expression, we can perform the multiplication first:
13.15.37 = 13 * 15 * 37 = 7,185.

Now, we can substitute this value back into the expression:
65.111 - 7,185 = 57,926.

Therefore, (65.111-13.15.37) = 57,926.

3. (10^2+11^2+12^2):(13^2+14^2)
To simplify this expression, we can calculate the squares first:
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169
14^2 = 196

Now, we can substitute these values back into the expression:
(100 + 121 + 144) / (169 + 196) = 365 / 365 = 1.

Therefore, (10^2+11^2+12^2):(13^2+14^2) = 1.