1. **Find the second order partial derivative of** [tex]F(x,y) = x^3 + xy^3 - 2y^2[/tex] **with respect to** [tex]x[/tex] **at** [tex](2,1)[/tex]:
- a. 14
- b. 12
- c. 0
- d. 8

2. **Find the distance between the points with coordinates** [tex]P(3, -2, 3)[/tex] **and** [tex]Q(7, 0, 1)[/tex]:
- a. 4.899
- b. 6
- c. 0
- d. 8

3. **Value of** [tex]t[/tex] **such that vectors** [tex]\mathbf{a}=\langle1,1,1\rangle, \mathbf{b}=\langle2,-4, 0\rangle, \mathbf{c}=\langle1, t, 3\rangle[/tex] **are coplanar**:
- a. 10
- b. 5/3
- c. 0
- d. 12

4. **If vector** [tex]\mathbf{T} = (x + y + 1)\mathbf{i} + \mathbf{j} - (x + y)\mathbf{k}[/tex], **then** [tex]\mathbf{T} \cdot \text{curl}(\mathbf{T})[/tex] **is**:
- a. None
- b. 3
- c. 0
- d. [tex]\mathbf{i} + \mathbf{k}[/tex]

5. **The divergence of** [tex]\mathbf{F}[/tex] **where** [tex]\mathbf{F} = \nabla(x + y + z)[/tex]:
- a. [tex]3(x + y + z)[/tex]
- b. 0
- c. [tex]3(x + y + z - xy)[/tex]
- d. [tex]6(x + y + z)[/tex]

6. **Value of integral** [tex]\int \int S \, x \, dx \, dy[/tex] **is**:
- a. 3/8
- b. 20/40
- c. 32/40

7. **Evaluate the integral** [tex]\int \int \int [dz \, dx \, dy][/tex]:
- a. 1/3
- b. 2/8
- c. 3/2
- d. 3/4