Given:
Focal length of the lens, f = 10 cm
Size of the image, h'i = -30 cm (negative sign indicates that the image is inverted)

To find:
Magnification of the lens, m

Formula:
Magnification of the lens, m = h'i / h'o
where h'o is the size of the object

Calculation:
As the size of the object is not given, we cannot directly calculate the magnification. However, we can use the lens formula to find the size of the object.

Lens formula:
1/f = 1/di + 1/do
where di is the distance of the image from the lens and do is the distance of the object from the lens

As the lens formula involves distances, we assume that they are measured from the optical center of the lens.

Given that the image is formed on the same side as the object, i.e., it is a virtual image.

Therefore, di = -30 cm (negative sign indicates that the image is virtual)

Substituting the values in the lens formula, we get:

1/10 = 1/-30 + 1/do

Simplifying the equation, we get:

1/do = 1/10 + 1/30 = 2/30

do = 15 cm

Now, we can calculate the magnification using the formula:

m = h'i / h'o

As the image is inverted, the magnification will also be negative.

Substituting the values, we get:

m = -30 / (2 * h'o)

m = -15 / h'o

We cannot find the exact value of the magnification as the size of the object is not given. However, we can eliminate options (b), (c), and (d) as they have positive values, which is not possible for an inverted image.

Therefore, the correct option is (a), which has a negative value of 2. This indicates that the image is half the size of the object and is inverted.