To begin, let's analyze the uploaded image to understand the style and complexity of the problems. Then, I'll generate a set of 30 random college-level math problems suitable for a test based on the format shown.

Analysis of Uploaded Image

The given problem is: $2x^2 + 4x = 0$

This is a quadratic equation, and it seems to be part of a set of algebra problems that involve solving for $x$. Given this, I will create a set of 30 problems that span a range of topics typically covered in college-level mathematics, such as algebra, calculus, linear algebra, and differential equations.

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[Algebra and Calculus] Test 1

Topics Covered: Quadratic Equations, Derivatives, Integrals, Limits, Linear Algebra, Differential Equations, Sequences and Series.

Section 1: Algebra (Quadratic Equations, Systems of Equations)

1. Solve for $x$: $3x^2 - 5x - 2 = 0$
2. Solve for $x$: $x^2 + 6x + 9 = 0$
3. Solve for $x$ and $y$: 2x + 3y = 6 \\ 4x - y = 5 \end{cases}$$
4. Solve for $x$: $x^3 - 2x^2 - x + 2 = 0$
5. Find the inverse of the matrix: $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$

Section 2: Calculus (Derivatives, Integrals, Limits)

6. Compute the derivative of $f(x) = 3x^2 + 5x - 7$.
7. Find the integral of $f(x) = 4x^3 - 2x + 1$ with respect to $x$.
8. Evaluate the limit: $\lim_{{x \to 0}} \frac{\sin(x)}{x}$.