Question: from pakistan Q2: (a) Evaluate ( x + y) ds where C is the straight line segment x = t, y = (1-1), z= 0

from pakistan

Q2: (a) Evaluate ( x + y) ds where C is the straight line segment x = t, y = (1-1), z= 0 from (0, 1, 0 ) to ( 1, 0,0) (b) Define line integral (8+2=10) Q3: (a) Find the centre and radius of the sphere 5x + 5y +5z +3x -4z +10 = 0 also sketch it (b) Give a geometric description of the set of points in space whose coordinates satisfy x2 + (y - 1)? + z' =4, y =5 and sketch that surface . (3+2+3+2) Q4: Find the Fourier series associated with the function f (x) = ]x _ 2/7 X ITS XS 217 (10) Q5: (a) Find the volume of the region bounded by the paraboloid z = x + y and below the given triangle enclosed by the lines y = x , x= 0 and xty=2 in the xy-plane, (b) How are the constants a,b and c related if the following differential form (ay* + 2czx) dx + y(bx + cz) dy + (ay' + cx ) z is exact (5+5=10)

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