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1. Choose the correct answer for the questions 1-15 (2 pts. each) 1. The curl of the vector field Fei-siny] + cos²z kis (a) ze (b)-rev (e) ze 1-cosy 3-2 cosy sina k (d) ze-cosy-2 cosy sinz 2. If the gradient of f(x, y, z) at (1,2,3) is 21-23+k, then the maximum value for a directional derivative of f(x,y,z) at (1,2,3) is (a) -3 (b) 3 (c) 9 (d) -9 3. If a,b and care nonzero real numbers such that the vector field F-yi+yj is a conservative vector field, then c= (a) 7 (b) 6 (c) 5 (d) 1 4. The value of feF.dr where F-1+23 and = sint 1-3, Osts (a) (b) 0 (c) 1 (d)-1 5. The value of a so that the vectors -1-oj and u-1-35 are orthogonal is (a) 3 (b) (d) = 6. Using the double integral, the area of the region R enclosed between the prabola yer and the line y = 3r is 3-a-dyda (b) fol dydz (a) a (c) ²-3 dydir (d) ff dydz 7. The angle between the vectors -(1,0,3) and = (0,2√3) is (b) (c) (d) 5. Using the chain rule, the value of at -1₁ (a)-9 =1 where z=81²y-2+3y, z, y=-* (c) 9 (b) 5 9. The system of ordinary differential equations corresponding to the PDE -2,0 <=<1, y>0 is (a) r"-2A=0 and + Ar=0 (b) "+A=0 and Ar-0 (c) r" 2r-A-0azid "-1-0 (d) -2-A=0 and A 10. Let (-2,3). The unit vector in the direction of u is (b) (1,1) (Ⓒ) (.) 11. fff dydada - (b) g () 12. The total differential de for the function er at (10) is (a) 2 dy (b) 2 dr+2 dy (c) 2 13. Let i and i be vectors with i-(-1,1,0) then (a) (0.-1,1) (b) (1,-1,0) (c) (0,0,0) 14. Let (z.) then /(2,1)= (0)1 (d) 2 dz (d) (-1,1,0) (d)