ALL MULTIPLE-CHOICE QUESTIONS:

13. The critical point of the curve y = - is at: X a. (0, 1) C. (e, 1) b. (1, e) d. ( - 1 , - -) 14. If y = cos x, then dy is : dx a. - sin x C. -2 cos x sin x b. e d. 2 cosx 15. If y = tan x sin x , then is. dx a. sec x cosx C. sec x sin x + sin x b. cos' x d. 3.14159 16. Which of the following quantities is a vector quantity? a. distance velocity b. volume speed17. If u . v =0 , then vectors u and v are: a. parallel C. collinear b perpendicular d. opposite 18. A vector equation of the line passing through the points P(2, 0, -3) and Q (-3, 2, -2) is: a. (x, y, z) = (2,0,-3) + 1(-5, 2, 1) C. (x, y, z) = (- 5, 2,1) +1(2,0,-3) b. (x, y, z) = (-3,2,-3)+1(5,2,1) d. (x, y, z) =(2,0,-3)+ 1(-3,2,-2) 19. The two lines (x, y, z) = (5,5,4) + s(7,1,-1) and (x, y, z) = (1,4,6) + t(14,2,-2) are: a. coincident b . C. skew intersecting d. parallel and distinct 20. If u = (3,1,5), v =(-2,0,4), and w =(-4,6,2) , then u - 2(v + w) is a. (-12,-11,-7) C. (15,-11,-7) b. (-12,1 1,7) d. (-12,7,17) 21. If u = (3,1,5), and v =(-2,0,4), then the angle O between u and v to the nearest degree is a. 90 C . 0o b 580 122022. If v = (3,1,2), and w = (5,4,0), then vx w is a. (-7,10,7) C. 19 b. (8, 7,17) d. (-8,10,7) 23. If u = (3,1,5), and v = (-24,-12,-12), then u . v is a. (-72,-12,-60) - 144 b. 0 d. 144 24. An object is dragged 8 m up a ramp by a constant force of 20 N applied at an angle of 20 to the ramp. The inclination of the ramp is 30 to the ground. At the top of the ramp, the object is dragged by the same force horizontally 13 m. The total work done is a. 394.7 J 347.2 J b. 317.5 J 406.4 J 25. The area of the parallelogram having u = (-2,-3,-1) and v = (0,1,2) as sides is a. V45 45 b. V135 d. 135