Solve your IGNOU Doubts

Question:

Find by Newton’s method the roots of the following equations correct to three places of decimals

i) $x log_{10}x = 4.772393 \: \: \: \: near x =6$

ii) $f (x) = x- 2 sin \: \: \: x\: \: \: near x =2$

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Question:

Using $x_{a} = -2$ as an initial approximation find an approximation to one of the zeros of

$p (x) = 2 x^{4} - 3 x^{2}+ 3 x -4$

by using Birge-Vieta method. Perform two iterations.

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Question:

Solve $x^{3}- 9 x + 1 = 0$ for the root lying between 2 and 4 by the method of false position. Perform two iterations.

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Question:

Find the number of positive and negative roots of the polynomial $P (x)= x^{3}- 3 x^{2} + 4 x -5$ Find P(2) and P(2) using synthetic division method

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Question:

Find the largest real root a of $f (x) = x^{6}- x - 1 =0$ lying between 1 and 2. Perform three iterations by

i) bisection method

ii) secant method ( 2, 1

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Question:

Denote by a, b and c the column vectors

$a=\begin{pmatrix} 1& \\ 2& \\ 3& \end{pmatrix},b=\begin{pmatrix} -2\\ 1 \\ -3, \end{pmatrix}c= \begin{pmatrix} -2\\ -1 \\ 1 \end{pmatrix}$

Calculate 2a - 5b, 2a- 5b +c, a / .b,

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Question:

Use the principle of mathematical induction to prove that

$(1+3+3^{2}+...+\frac{3^{n+1}-1}{2})\forall n\epsilon N.$

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Question:

Let the production function by a b Q = AL^a K ^b . Find the elasticity of production with respect to labour (L).

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Question:

Give an example of a mathematical statement that is not true. Also disprove the statement.

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Question:

What are the four different types of statements that make up a proof? Give an example of each kind.

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Question:

Explain the concept of maximum value function.

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Question:

Give an example, with justification, of each of the following:

i) a 2D figure which has reflection symmetry;

ii) a 2D figure with at least 30 lines of symmetry;

iii) a 2D figure with no rotational symmetry;

iv) a net of a wall-paper pattern;

v) a motif for a regular tessellation.

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Question:

Evaluate $\int ( 7 x-2 ) \sqrt{3x+2}\: \: \: \: \: \: dx$

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Question:

Singular matrix

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Question:

Decomposable matrix

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Question:

Give an activity, in detail, to help a Class 4 child develop the ability to estimate the difference of two fractions. Also give an activity, not involving paper and pencil, to help you assess the efficacy of the activity you gave.

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Question:

Adjugate of a matrix

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Question:

If Z = f(x,y) = xy

Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is, x +y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.

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Question:

Solve the following differential equation

$\frac{d^{2}y}{dx^{2}}-\frac{dy}{dx}+10y=0,$

given $Y ( 0) = 4\: \: \: \: \frac{dy}{dx} ( 0) =1$

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Question:

Is there a rule by which one can tell whether a number is divisible by 7? If yes, why does this rule work? If there is no such rule, give a rule for divisibility by 5.

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