Solve your IGNOU Doubts

Question:

Image ignouassignments-ignouacademy-com--p-ignou-14205

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Question:

Find the surface which is orthogonal to the one parameter system $z= cxy ( x^{2} +y^{2})$ and which passes through the hyperbola , $x^{2}-y^{2}= a^{2},z =0$

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Question:

Let an activation function be defined as , $\phi (v)=\frac{1}{1+e^{-av}},a> 0$ . Show that $\frac{d\phi }{dv}=a\phi (v)[1-\phi (v)]$ What is the value of $\phi$ ( v ) at the origin? Also, find the value of $\phi (v)$ as v approaches + $\infty$ and - $\infty$ .

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Question:

Find the general integral of the equation $(x-y )p+ (y- x- z ) q =z$

and the particular solution through the circle $z= 1, x^{2} + y^{2} =1$

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Question:

Find the value of n for which the equation $( n-1) u_{xx} - y^{^{2n}}u_{yy} = ny^{2n-1} u_{y}$ is parabolic or hyperbolic

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Question:

Find the length and order of the following schema:

i) S₁= (1 * * 0 0 * 1 * *)

ii) S₂ = (* 0 0 * 1 * *)

iii) S₃ = (* * * 1 * * *)

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Question:

Write any three terminating conditions used in learning of a neural network.

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Question:

Write any four activation function used in neural networks. Also, draw the graph of the output of these functions.

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Question:

What is competitive learning? How does it differ from Hebbian learning?

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Question:

Consider the problem of finding the shortest route through several cities, such that each city is visited only once and in the end traveler returns to the starting city (the travelling salesman problem). Suppose that in order to solve this problem we use a genetic algorithm, in which genes represent links between pairs of cities. For example, a link between Delhi and Mumbai is represented by a single gene DM : Also assume that the direction in which we travel is not important, so that DM = MD .

i) How many genes will be used in a chromosome of each individual if the number of cities is 10?

ii) How many genes will there be in the alphabet of the algorithm?

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Question:

Write a formula describing the function defined by a one-hidden-layer (already trained) MLP with a single output. Also, write the formula describing the function defined by a RBFN with a single output. How do they differ?

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Question:

Find max-average composition for R ( x , y ) and S ( x , y ) defined by the following relational matrices:

Image ignouassignments-ignouacademy-com--p-doubts-17821

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Question:

Find the differential equations of the space curve in which the two families of surfaces $u =x^{2} -y^{2} =c_{1} and v=y^{2} -z^{2} = c_{2}$ intersect.

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Question:

Verify that the equations

i) $z =\sqrt{2x+a}+ \sqrt{2y+b} and$

ii) $z^{2}+\mu = 2 ( 1 + \lambda ^{-1}) (x+\lambda y )$

are both complete integrals of the PDE $z =\frac{1}{p} + \frac{1}{q}$ Also show that the complete integral (ii) is the envelope of the one parameter sub-system obtained by taking $b=\frac{a}{\lambda } + \frac{\mu }{1+\lambda }$ in the solution i).

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Question:

Maximize f ( x , y ) = 8 x + 6 y

Subject to 2x + 3y $\leq$ 6

-3x + 2y $\leq$ 3

2x + y $\leq$ 4

0 $\leq$ x $\leq$ 2

Using genetic algorithm

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Question:

Two sensors based upon their detection levels and gain settings are compared. The following table of gain settings and sensor detection levels with a standard item being monitored provides typical membership values to represent the detection levels for each of the sensors.

Gain Setting	Sensor 1 detection levels	Sensor 2 detection levels
0	0	0
20	0.5	0.35
40	0.65	0.5
60	0.85	0.75
80	1	0.90
100	1	1

The universe of discourse is x = {0, 20 , 40 , 60 , 80 , 100 } . Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.

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Question:

Using the method of undetermined coefficients, find the general solution of the DE

$y^{iv} - 2y{}'' + 2y{}'' =3e^{-x}+ 2e^{-x }+ sin\: \: x$