Which of the following functions y = f(x) satisfy y'= 32y, f (0) = 
?(I)y = 32e1/2x(II)y = e16x(III)y = 
e32x(IV)y = 
x32
A. IV only
B. I only
C. I and II
D. III only
E. none of these
Answer: D
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Find the required quantity given the wire that lies along the curve r and has density ?.Moment of inertia Iz about the z-axis, where r(t) = (6 sin 2t)i + (6 cos 2t)j + e3tk, 0 ? t ? 1; 
A. Iz = 4(e6 - 1)
B. Iz = 
C. Iz = 
D. Iz = 
[(144 + 9e6)3/2 - (144 + 9)3/2 ]
Reverse the order of integration and then evaluate the integral.
A. e25 - 1
B. 5e25 - 130
C. 
D. e25 - 
Evaluate the line integral of f(x,y) along the curve C.f(x, y) = cos x + sin y, C: y = x, 0 ? x ? 
A. 2
B. 
C. 2
D. 0
If the height, n, of a trapezoid equals the length of its shorter base and the longer base is twice the shorter base, then the area of the trapezoid is
(a) 2n (b) 3n2 (c) 1.5n3 (d) 1.5n2 (e) None of these is correct.