STUPIDSID
1(a)
Evaluate the following:
3 M
1(b)
Solve (D2-1)(D-1)2y=0
3 M
1(c)
Prove that E=1+Δ=ehD
3 M
1(d)
Solve the following:
3 M
1(e)
Change into polar co-ordinates and evaluate:
4 M
1(f)
Evaluate the following:
4 M
2(a)
Solve (x3y3-xy)dy=dx
6 M
2(b)
Change the order of Integration and evaluate:
6 M
2(c)(1)
Prove that:
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2(c)(2)
Evaluate 
, where a>0
, where a>0
4 M
3(a)
Evaluate the following:
6 M
3(b)
Find the area bounded by 9xy=4 and 2x+y=2
6 M
3(c)(1)
Solve the following:
4 M
3(c)(2)
Solve the equation by variation of parameters:
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4(a)
Show that for the parabola
from θ=0 to θ=π/2, length of the arc is
6 M
4(b)
Solve the following:
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4(c)
Apply Runge-Kutta method of fourth order to find an approximation value of y at x=0.2, if dy/dx=x+y2, given y=1 when x=0, in steps of h=0.1
8 M
5(a)
Solve: (2xy4ey+2xy3+y)dx+(x2y4ey-x2y2-3x)dy=0
6 M
5(b)
Solve dy/dx=2x+y with x0=0,y0=0 by Taylor’s method. Obtain y as a series in power of x. Find approximation value of y for x=0.2,0.4. Compare your result with exact values.
6 M
5(c)
Evaluate the following equation
by Trapezoidal method, Simpson's 1/3rd and 3/8th methods. Compare result with exact values.
by Trapezoidal method, Simpson's 1/3rd and 3/8th methods. Compare result with exact values.
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6(a)
In a circuit containing inductance L, resistance R, voltage E, the current i is given by L(di/dt)+Ri=E. Find i at a time t if at t=0,i=0, and if L, R, E are constants.
6 M
6(b)
Evaluate ∫∫xy dxdy bounded by y=x, x2+y2-2x=0, and y2=2x
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6(c)(1)
Find the volume of a tetrahedron bounded by the plane x=0,y=0,z=0 and x+y+z=a
4 M
6(c)(2)
Find the volume bounded by the cone z2=x2+y2 and paraboloid z=x2+y2.
4 M
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