STUPIDSID
Answer any one question from Q1 and Q2
1 (a)
Solve any two:
i) (D2+6D+9) y=x-3 e-3x
ii) (D2-2D+2) y =ex tan x ( by variation of parameters method) iii) x2d2ydx2−3xdydx+5y=x2sin(logx)iii) x2d2ydx2−3xdydx+5y=x2sin(logx)
i) (D2+6D+9) y=x-3 e-3x
ii) (D2-2D+2) y =ex tan x ( by variation of parameters method) iii) x2d2ydx2−3xdydx+5y=x2sin(logx)iii) x2d2ydx2−3xdydx+5y=x2sin(logx)
8 M
1 (b)
Find the Fourier sine cosine transforms of e-mx m > 0.
4 M
2 (a)
The currents x and y in the coupled circuits are given by:
(LD + 2R)x - Ry=E
(LD + 2R)y- Rx =0.
Find the general values of x and y in terms of t.
(LD + 2R)x - Ry=E
(LD + 2R)y- Rx =0.
Find the general values of x and y in terms of t.
4 M
2 (b)
Find the inverse z-transform (any one): i) F(z)=10z(z−1)(z−2) (by inversion integral method)ii) F(z)=z(z−14)(z−15), |z|>14.
4 M
2 (c)
Solve the difference equation:
f(K+1)- f(K)=1, K≥0, f(0)=0.
f(K+1)- f(K)=1, K≥0, f(0)=0.
4 M
Answer any one question from Q3 and Q4
3 (a)
The first four moments about 44.5 of a distribution are -0.4, 2.99, -0.08 and 27.63. Calculate moments about means, coefficients of Skewness and Kurtosis.
4 M
3 (b)
The incidence of certain disease is such that on the average 20% of workers suffer from it. If 10 workers are selected at random, find the probability that:
i) exactly 2 workers suffer from disease.
ii) not more than 2 workers suffer.
i) exactly 2 workers suffer from disease.
ii) not more than 2 workers suffer.
4 M
3 (c)
Find the directional derivative of:
ϕ=4xz3 - 3x2y2z
at (2, -1, 2) along a line equally inclined with coordinate axes.
ϕ=4xz3 - 3x2y2z
at (2, -1, 2) along a line equally inclined with coordinate axes.
4 M
4 (a)
A random sample of 200 screws is drawn from a population which represents size of screws. If a sample is normally distributed with a mean 3.15 cm and S.D. 0.025 cm, find expected number of screws whose size falls between 3.12 cm and 3.2 cm.
[Give: For z=12, area =0.3849; for z=2, area = 0.4772]
[Give: For z=12, area =0.3849; for z=2, area = 0.4772]
4 M
4 (b)
show that (any one): i) ∇⋅(¯aׯrr)=0ii) ∇4(r2logr)=6r2
4 M
4 (c)
A fluid notaion is given by: ¯v=(ysinz−sinx)ˆi+(xsinz+2yz)ˆj+(xycosz+y2)ˆh Is the motion irrotational? If so, find the scalar velocity potential.
4 M
Answer any one question from Q5 and Q6
5 (a)
Find the work done by the force: ¯F(x2−yz)i+(y2−zx)j+(z2−xy)k in taking a particle from (1,1,1) to (3, -5, 7).
4 M
5 (b)
Use divergence theorem to evaluate: \iins(y2z2i+z2x2j+x2y2k)⋅overlineds where s is the upper half of the sphere x2+y2+z2=9 above the xoy plane.
5 M
5 (c)
Apply Stoke's theorem to evaluate: ∫c(4y dx+2z dy +6y dz Where C is the curve x2+y2+z2=6z, z=x+3.
4 M
6 (a)
Find the work done in moving a particle from (0, 1, -1) to (π2,−1,2)inaforcefield:\[¯F(y2cosx+z3)i+(2ysinx−4)j+(3xz2+2)k.
4 M
6 (b)
Evaluate: ∬s[(x+y2)i−2x j+2yz k]⋅¯ds Where s is the plane 2x+y+2z-6=0 considered as one of the bounding planes of the tetrahedron x=0, y=0, z=0, 2x+y+2z=6.
5 M
6 (c)
Verify Stoke's theorem for: F= -y3i + x3 j and closed curve c is the boundary of the circle x2+y2=1.
4 M
Answer any one question from Q7 and Q8
7 (a)
Find the condition under which:
u=ax3+ bx2y+cxy2+dy3 is harmonic.
u=ax3+ bx2y+cxy2+dy3 is harmonic.
4 M
7 (b)
Evaluate: ∮c4z2+zz2−1dz, where C: |z-1|=3.
5 M
7 (c)
Show that: w=z−i1−iz \] maps upper half of z-plane onto interior of unit circle in w-plane.
4 M
8 (a)
Find the harmonic conjugate of:
u=r3 cos 3θ + r sin θ.
u=r3 cos 3θ + r sin θ.
4 M
8 (c)
Evaluate: ∮csin2z(z+π3)4dz, where C: |z|=2.
5 M
8 (c)
Find the bilinear transformation which maps the points 1, 0, i of the z-plane onto the points \[ \infty, -2, -\dfrac {1}{2} (1+i) of the w-plane.
4 M
More question papers from Engineering Maths 3