**Concept: The question deals with Max/Min Concept.**

**Solution:**

The integers are -10,-9,-8,-7,-6,-5,-4,-3,-2-1

0

1, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10

**20 integers are randomly chosen with repetitions allowed=>We can choose any term and multiply it with the constraint that the maximum number of times we can choose it is 20.**

=>To

**minimize the product, we have to maximize the value with "-" sign.**If we use (-10)*(-10)...............(20 times), we shall have a positive product and hence the idea of minimizing the product shall not be fulfilled.

If we use (-10)*(-10)..............(19 times), we shall have -10^19 as the largest negative product with 19 terms.

To maximize a negative term, multiply the largest positive value available and hence our 20th term can be (+10)

=>The minimum product shall be (-10)^19 * 10^1 = - { 10^1 * 10^19}

= -(10)^20 (option e)