For each question, X indicates a correct choice. ANSWER SHEET - BLUE. Question a b c d e Do not write in this column 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X
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1 For each question, X indicates a correct choice. ANSWER SHEET - BLUE X ANSWER SHEET - GREEN X ANSWER SHEET - WHITE X
2 ANSWER SHEET - YELLOW For each question, place an X in the box of your choice. X
3 QUESTION SHEET - BLUE 1. If f(x, y) = e sin x + x y + ln(), then 2 f x 4 (b) x + 1 () 2 (e) e sin x cos x+x 1 2. The radius of curvature ρ(s) of the helix which parametred by r(t) = The directional derivative of f(x, y) = x 3 y + 12x 2 8y at the point (1, ) (b) 1 (c) 3 (9, 7) (e) The value of the triple integral V x2 y 2 dxdydz where V the cylinder 8π (b) 2π (c) 0 2π (e) 8π.. If f = (xyz, yz 2, y + zx 2 ) then f equal to yz+z 2 +x 2 (b) (1 2yz, xy 2zx, xz) (c) (1 2yz, xy+2zx, xz) ( + 2xz, y + zx, xz) (e) yz + z 2 + x 2 + y. 6. The line integral C 1 (b) π 2 7. The vector field f = (2xy yz + z, x 2 xz, x xy) expressible as φ xyz+x 2 (b) xyz+xy (c) xy+yz+zx x 2 y xyz+xz (e) x 2 y xz. 8. The work done in moving a particle against the force field given by F(x, y, z) = (2z, 3x, y + 2x) along the curve described parametrically by r(t) = 3 (b) 17 (c) (e) 280.
4 QUESTION SHEET - GREEN 1. If f(x, y) = e sin x + x y + ln(), then 2 f x 4 (b) x + 1 () 2 (e) e sin x cos x+x 1 2. The line integral C 1 (b) π 2 3. The work done in moving a particle against the force field given by F(x, y, z) = (2z, 3x, y + 2x) along the curve described parametrically by r(t) = 3 (b) 17 (c) (e) The value of the triple integral V x2 y 2 dxdydz where V the cylinder 8π (b) 2π (c) 0 2π (e) 8π.. If f = (xyz, yz 2, y + zx 2 ) then f equal to yz+z 2 +x 2 (b) (1 2yz, xy 2zx, xz) (c) (1 2yz, xy+2zx, xz) ( + 2xz, y + zx, xz) (e) yz + z 2 + x 2 + y. 6. The vector field f = (2xy yz + z, x 2 xz, x xy) expressible as φ xyz+x 2 (b) xyz+xy (c) xy+yz+zx x 2 y xyz+xz (e) x 2 y xz. 7. The directional derivative of f(x, y) = x 3 y + 12x 2 8y at the point (1, ) (b) 1 (c) 3 (9, 7) (e) The radius of curvature ρ(s) of the helix which parametred by r(t) = 1 2
5 QUESTION SHEET - WHITE 1. If f = (xyz, yz 2, y + zx 2 ) then f equal to yz+z 2 +x 2 (b) (1 2yz, xy 2zx, xz) (c) (1 2yz, xy+2zx, xz) ( + 2xz, y + zx, xz) (e) yz + z 2 + x 2 + y. 2. The line integral C 1 (b) π 2 3. The value of the triple integral V x2 y 2 dxdydz where V the cylinder 8π (b) 2π (c) 0 2π (e) 8π. 4. The directional derivative of f(x, y) = x 3 y + 12x 2 8y at the point (1, ) (b) 1 (c) 3 (9, 7) (e) 1.. If f(x, y) = e sin x + x y + ln(), then 2 f x 4 (b) x + 1 () 2 (e) e sin x cos x+x 1 6. The work done in moving a particle against the force field given by F(x, y, z) = (2z, 3x, y + 2x) along the curve described parametrically by r(t) = 3 (b) 17 (c) (e) The vector field f = (2xy yz + z, x 2 xz, x xy) expressible as φ xyz+x 2 (b) xyz+xy (c) xy+yz+zx x 2 y xyz+xz (e) x 2 y xz. 8. The radius of curvature ρ(s) of the helix which parametred by r(t) = 1 2
6 QUESTION SHEET - YELLOW 1. The vector field f = (2xy yz + z, x 2 xz, x xy) expressible as φ xyz+x 2 (b) xyz+xy (c) xy+yz+zx x 2 y xyz+xz (e) x 2 y xz. 2. If f = (xyz, yz 2, y + zx 2 ) then f equal to yz+z 2 +x 2 (b) (1 2yz, xy 2zx, xz) (c) (1 2yz, xy+2zx, xz) ( + 2xz, y + zx, xz) (e) yz + z 2 + x 2 + y. 3. The directional derivative of f(x, y) = x 3 y + 12x 2 8y at the point (1, ) (b) 1 (c) 3 (9, 7) (e) The line integral C 1 (b) π 2. The radius of curvature ρ(s) of the helix which parametred by r(t) = The work done in moving a particle against the force field given by F(x, y, z) = (2z, 3x, y + 2x) along the curve described parametrically by r(t) = 3 (b) 17 (c) (e) The value of the triple integral V x2 y 2 dxdydz where V the cylinder 8π (b) 2π (c) 0 2π (e) 8π. 8. If f(x, y) = e sin x + x y + ln(), then 2 f x 4 (b) x + 1 () 2 (e) e sin x cos x+x 1
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