If a > b and m < 0, then which of the following is correct :

1. am < bm
2. am = bm
3. am > bm
4. am and bm cannot be compared

Given:

a > b

m < 0 means m is negative.

Let's evaluate each:

1. am < bm

Multiplying an inequality by a negative number (m < 0) requires reversing the inequality sign. It is correct.

2. am = bm

Multiplying by a non-zero number (m < 0) maintains a difference between unequal values; they cannot become equal. It is incorrect.

3. am > bm

This is incorrect because, m is negative number and multiplying an inequality by a negative number requires reversing the inequality sign. But here the sign remains same.

4. am and bm cannot be compared

Since the relationship between a, b and the sign of m is known, their products are strictly comparable. It is incorrect.

Among all four options, option 1 is correct.

Hence, option 1 is the correct option.