Solve your IGNOU Doubts

Question:

Differentiate between bounded sum and algebraic sum of two fuzzy sets.

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Question:

If the input vectors are I₁ = [ -1, 0 ]^r , and I₂ [0 , 1]^r , and the initial values of two weight vectors are [0 , 1]^r and $\left [ \frac{2}{\sqrt{5}},\frac{-1}{\sqrt{5}} \right ],$ calculate the resulting weight found after training the competitive layer with the Kohonen’s rule and a learning rate $\alpha$ of 0 .4 on the input series in order I₁ , and I_2,.

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Question:

A certain population is known to be growing at a rate given by the logistic equation

$\frac{dx}{dt} =x ( b - ax)$

Show that the minimum rate of growth will occur when the population is equal to half the equilibrium size, that is, when the population is b / 2a

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Question:

Solve the differential equation

$X cos \left ( \frac{y}{x} \right ) (ydx + xdy ) = y sin \left ( \frac{y}{x} \right )( xdy - ydx )$

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Question:

Consider the ADALINE filter with three neurons in the input layer having weights w₁₁ = 3, w₁₂ = -2 and w₁₃ -2 and the input sequence {- - - , 0, 0, 0, -4, 5, 0, 0, 0 - - - - } What is the filter output?

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Question:

Define the following operations in Genetic algorithm with one example of each

i) Crossover

ii) Mutation

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Question:

Find a continuous solution of the IVP

$\frac{dy}{dx} + y = g (t) , y (0) =0$

Image ignouassignments-ignouacademy-com--p-doubts-83942

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Question:

Describe the Binary Hopfield network with the help of an example.

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Question:

Use a binary-coded Genetic algorithm (GA) to minimize the function f ( x₁ , x₂) = x₁+ x₂ + 2x₁²- x₂²+ x₁ , x₂, in the range of 0 $\leq$ x₁, x₂ $\leq$ 5 . Use a random population of size N = 6 , a single point crossover with probability P_c=1 and neglect mutation. Assume 3 bits for each variable and thus the GA-string will be 6- bits long. Show only one iteration by hand calculation.

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Question:

For these two fuzzy sets find the union, intersection, complement of $\varrho$ difference $\varrho$ - C , and verify any one of Demorgan’s law.

i) graphically and

ii) numerically

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Question:

Suppose the temperature of a body when discovered is 85° F. Two hours later, the temperature is 74° F and the room temperature is 68°F. Find the time when the body was discovered after death (assume the body temperature to be 98.6° F at the time of death.)

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Question:

Solve the following differential equations

a) $sin ^{-1} ( dy/dx) =x+y$

b) $( 1+ y^{2}) dx = ( tan^{-1} y -x ) dy$

c) $( D -1)^{2} ( D^{2} + 1)^{2} y= sin ^{2} \left ( \frac{x}{2} \right ) +e^{x} + x$

d) $2 x^{2}y \left ( \frac{d^{2}y}{dx^{2}} \right ) + 4y^{2}=x^{2}\left ( \frac{dy}{dx} \right )^{2} + 2xy \left ( \frac{dy}{dx} \right )$

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Question:

$If \frac{d^{2}y}{dt^{2}} + \frac{g}{b} ( x-a) =0,$ ( a,b,g being positive constants) and x=a ${}'$ and $\frac{dx}{dt} =0$ when t=0 show that $x =a + ( a{}' -a) cos \left \{ \frac{\sqrt{g}}{b}t \right \}$

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Question:

What is the order of

$(i)14 \; in^{^{\mathbb{Z}_{24}}}/\left \langle \bar{8} \right \rangle?$

$(ii)(\mathbb{Z}_{10}\oplus \cup (10)/< (2,9)> ?$

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Question:

A solution of the IVP $( 1 -t^{2} ) \frac{d^{2}y}{dt} -2y =0 ,y{}' (o) =-4$ is $y_{1}=t$ Use the method of reduction of order to find a general solution of IVP on the interval $-1< t< 1$ .

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Question:

Do the functions y₁ (t) = $\sqrt{t}$ and $y_{2}(t) = \frac{1}{t}$ form a fundamental set of solutions of the equation $2t^{2}y{}''+ 3t y{}' -y =0$ , on the interval $0< t< \infty$ ? Justify your answer.

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Question:

Let R and S be rings and f : R → S be a homomorphism. If x is an idempotent in R, show that f(x) is an idempotent in S. Hence, or otherwise, determine all ring homorphisms from $\mathbb{Z}$ × $\mathbb{Z}$ to $\mathbb{Z}$ .

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Question:

Prove that $\mathbb{Z}[\sqrt{2}]$ is isomorphic to $H=\left \{\begin{bmatrix} a &2b \\ b& a \end{bmatrix}\mid a,b\epsilon \mathbb{Z} \right \}$ as rings.