STUPIDSID
1(a)
prove that:\(\Gamma({\dfrac {3}{4}-x}).\Gamma({\dfrac {3}{4}+x})=(\dfrac{1}{4}-x^2)\pi\sec x.\) Provided -1<2x<1
5 M
1(b)
Solve (D4 - 4D3 + 8D2 - 8D + 4)y = ex + 1.
5 M
1(c)
Find the length of the curve y = log(ex + 1) - log(ex - 1) from x=1 to x=2.
5 M
1(d)
Find the area bounded by the curves : xy =2, 4y = x2, y=4
5 M
2(a)
Change the order of integration:
6 M
2(b)
Solve by the method of variation of parameters:
6 M
2(c)
Solve dy/dx = 2 + (xy)xy with x0 = 1.2 and y0 =1.6403 by Euler's modifies formula for x = 1.6. Correct the four places of decimal. Take h = 0.2
8 M
3(a)
Evaluate:
6 M
3(b)
Change to polar co-ordinates:
6 M
3(c)
Solve the differential equation dy/dx = x + y2, y(0) = 1 by Runge-Kutta method of fourth order, for the interval (0,0.2) in steps of h =0.1
8 M
4(a)
Solve (D2 - 2D + 1)y = xexsin(x)
6 M
4(b)
Evaluate:
6 M
4(c)
Solve:
8 M
5(a)
Solve dy/dx = ex-y(ex-ey)
6 M
5(b)
Solve:
6 M
5(c)
Find the volume of the tetrahedron bounded by the planes x = 0, y = 0, z=a,x + y + z = a
8 M
6(a)
Find the mass of the lamina bounded by the curves ay2 = x3 and the line by=x, if the density at a point varies as the distance of the point from the x-axis.
6 M
6(b)
Using Duplication Formula prove:
6 M
6(c)
Solve: (D2 - 1)y = x2sin(3x).
8 M
7(a)
Evaluate ∫ ∫ (x2 + y2)dxdy over the area of a triangle whose vertices are (0,1) (1,1) and (1,2).
6 M
7(b)
Solve the following:
6 M
7(c)
Evaluate the following:
and hence deduce that:
and hence deduce that:
8 M
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