1. The unit normal is given by which of the following? 1. 2. 3. 4.

2. Find a unit normal to the plane 4x + y – 2z = 3 1. 2. 3. 4.

3. Find a unit vector normal to the sphere (x + 3)² + (y – 1)² + 2z² = 5 at (0, 0, 1). 1. 2. 3. 4.

4. Which of the following vector fields are conservative? 1.F=xyi + 2y²zj + 3xyzk 2.F=y²i + 2xyj + 2zk 3.F=2x²zi + xyzj - 2xyk 4.F=2yzi + 2xzj + 2xyk

5. Which of the following statements are true? 1. only depends on the end points of A and B 2. for all C 3. for a conservative field F 4.All gradient fields are conservative

6. represents: 1.The area beneath the surface z=F(x,y) but above the curve C. 2.The area beneath the surface z=F(x,y) and below the curve C. 3.The area above the surface z=F(x,y) and above the curve C. 4.The area above the surface z=F(x,y) but below the curve C.

7. Which of the following statements is true? 1. evaluates to a scalar 2. evaluates to a scalar 3.Both of the above evaluate to scalars 4.Neither of the above evaluate to scalars

8. Find where C is the curve y=x²+2 starting from x=0, y=0 and ending at x=1, y=1 1.½ + y 2.1 + 2y 3.3 4.7

9. Find where, on C, x and y are given in terms of the parameter t by x=2t and y=t²+1 for t varying from 0 to 1. 1.7/3 2.14/3 3.½ + y

10. In general 1.True 2.False 3.Don’t Know

11. F = xyi + y²j Find from (0,0) to (1,3) where C is the curve y = 3x 1.10 2.270 3.½y + 9 4.(9/2)y + 1

12. F = 3xyzi + x²yj – 2xyz²k C is a curve from A=(0,0,0) to B=(1,1,1) given by x=y=z=t, 0≤t≤1. Find. 1.3/10 2.3/5 3.i/4 + j/4– k/5 4.3i/4 + j/4 – 2k/5

13. Evaluate where C represents the contour y=x²+1 from (0,1) to (1,2) 1. 2. 3. 4.

14. Find where F = 2x²i + xy²j + xzk and C is the curve y = x², z = x³ from (0,0,0) to (1,1,1) 1. 2. 3. 4.

15. Evaluate where A represents the surface of the unit cube 0≤x≤1, 0≤y≤1, 0≤z≤1 and r = xi + 2yj + 3zk 1.15 2.6 3.3 4.0

16. When an electric current flows at a constant rate through a conductor, then the current continuity equation states that. 1.True 2.False 3.Don’t Know

17. Evaluate where F = 2xyi + xy²zj + z²k and S is the surface of the unit cube 0≤x≤1, 0≤y≤1, 0≤z≤1 1. 2. 3. 4.

18. F = y²i + 3xyj Evaluate where V is the volume under the plane z=x+y+ 1 and above z=0 for -1≤x≤2, -1≤y≤2 1. 2. 3. 4.

19. Which of the following is Stokes’ Theorem? 1. 2. 3. 4.

20. Which of the following can be obtained from Gauss’ Law? 1. 2. 3. 4.

21. Evaluate around the rectangle 0≤x≤4, 0≤y≤2 using Green’s Theorem 1.0 2.8 3.-2 4.None of the above