In a geometric progression, the terms are numeric and follow a specific ratio; thus, non-numeric terms do not form a valid GP.

In a geometric series, the ratio between consecutive terms is constant, not the difference.

In a regular polygon, all sides and angles are equal, and the vertices are convex, not concave.

In a rhombus, while all sides are equal and diagonals bisect each other at right angles, the diagonals are not necessarily equal in length.

In a square, all angles are right angles (90 degrees), not acute.

The statement a^m + b^m = (a+b)^m is not a property of exponents; it is only true for m=1.

In a geometric progression, the common ratio cannot be zero, as it would invalidate the progression.

The sum of the terms in a harmonic progression is not necessarily an integer, as the terms can be fractions.

The sum of the first n terms of a harmonic progression diverges as n approaches infinity, hence it is not finite.

The last statement is incorrect as it does not follow the properties of logarithms.

Modular arithmetic is commutative for addition and multiplication, hence non-commutativity is not a property.

Polygons are defined as shapes made up of straight line segments, so having curved sides disqualifies a shape from being a polygon.

While coefficients can be negative in certain expansions, they are not always negative.

Not all triangles have all angles acute; for example, a right triangle has one angle that is 90 degrees.

The Binomial Theorem is specifically for polynomial expansions and does not apply to geometric series.

In base-3, only digits 0, 1, and 2 are valid. '30' is invalid.

In base 3, only digits 0, 1, and 2 are valid. '230' contains '3', which is invalid.

'22' cannot represent 10 in any base since it would require base 3 or higher.

The passage does not mention data compression techniques as an application of digital sum.

The base of the natural logarithm is e, approximately equal to 2.718.

A factor is defined as a number that divides another number without leaving a remainder.

The quadratic x^2 - 5x + 6 factors to (x - 2)(x - 3).

Binary is the simplest (base-2), followed by Decimal (base-10), and then Hexadecimal (base-16), making the correct order Binary, Decimal, Hexadecimal.

All the listed properties are correct and fundamental to logarithmic functions.

15 divided by 4 gives a remainder of 3, hence 15 mod 4 = 3.

The decimal number 15 is represented as '1111' in binary.

15 in decimal is represented as '33' in base-4 (3*4^1 + 3*4^0 = 12 + 3 = 15).

25 in decimal is represented as '31' in base-8 (3*8^1 + 1*8^0 = 24 + 1 = 25).

Using the quotient rule for exponents, (x^2y^3)/(xy^2) simplifies to x^(2-1)y^(3-2) = xy.

Using the property of exponents for division, we subtract the exponents: x^(3-2) * y^(2-1) = x^1 * y^1.