1. The determinant of a 3×3 matrix \(A\) is 5. What is the determinant of \(3A\)?

1. 15
2. 45
3. 135
4. None of the above

2. Find the inverse of the matrix \( \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \).

1. \( \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix} \)
2. \( \begin{bmatrix} 4 & -1 \\ -3 & 2 \end{bmatrix} \)
3. \( \begin{bmatrix} 2 & -1 \\ 1 & 4 \end{bmatrix} \)
4. Non-invertible

3. What is the principal value of \( \arcsin(-1) \)?

1. \(-\pi\)
2. \(-\frac{\pi}{2}\)
3. 0
4. \(\frac{\pi}{2}\)

4. Solve the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \).

1. \(y = Ce^{-2x} + \frac{1}{2}e^{-x}\)
2. \(y = Ce^{-2x} – e^{-x}\)
3. \(y = Ce^{2x} + e^{-x}\)
4. \(y = Ce^{2x} – \frac{1}{2}e^{-x}\)

5. Evaluate the integral \( \int \frac{dx}{x^2 + 1} \).

1. \(\arctan(x) + C\)
2. \(\arcsin(x) + C\)
3. \(\ln|x| + C\)
4. \(\frac{1}{x} + C\)

6. Which is the equation of a parabola with focus at (2,3) and directrix y=1?

1. \((x-2)^2 = 4(y-2)\)
2. \((y-3)^2 = 8(x-2)\)
3. \((y-2)^2 = 4(x-2)\)
4. \((x-2)^2 = 8(y-3)\)

7. Calculate the area enclosed by the curve \(y=x^3\) and the x-axis from x=0 to x=2.

1. 4 square units
2. 6 square units
3. 8 square units
4. None of the above

8. What is the volume of the solid obtained by rotating the area between \(y=x^2\) and \(y=x\) around the x-axis from x=0 to x=1?

1. \(\frac{\pi}{10}\) cubic units
2. \(\frac{\pi}{30}\) cubic units
3. \(\pi\) cubic units
4. \(\frac{\pi}{15}\) cubic units

9. A linear programming problem has an objective function \(F = 2x + 3y\) to maximize, with constraints \(x \geq 0\), \(y \geq 0\), \(x + y \leq 10\), and \(2x + 3y \leq 18\). The maximum value of \(F\) is:

1. 36
2. 30
3. 48
4. 54

10. The solution set for the inequality \(3x – 7 \leq 2x + 8\) is:

1. \(x \leq 15\)
2. \(x \geq 15\)
3. \(x \leq -15\)
4. \(x \geq -15\)