1. Find the square root of -8 - 6i.

2. For

show that

.

3. Obtain the Maclaurin's series for

.

4. Solve:-

.

5. Find the intervals at which

is increasing or decreasing.

6. Prove by vector method that
cos(A+B) = cosAcosB - sinAsinB.

7. Find the vector and Cartesian equation of the plane through the points (1,2,3), (2,3,1) and perpendicular to the plane 3x - 2y + 4z - 5 = 0

8. Find the equation of the hyperbola if its asymptotes are parallel to x+2y-12 = 0 and x-2y+8 = 0, (2,4) is the center of the hyperbola and it passes through (2,0).

9. Find the common area enclosed by the parabola 4y² = 9x and 3x² = 16y.

10. Find the volume of the solid generated by revolution of the loop of the curve

about x-axis.