Solve your IGNOU Doubts

Question:

A string of length l is connected to a fixed point at one end and to a stick of mass m at the other. The stick is whirling in a circle at constant velocity v . Use dimensional analysis to find the equation of the force in the string.

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Question:

Consider the following system of equations ${\frac{\mathrm{d}\mathbf{x}}{\mathrm{dt}}}=\mathbf{y},\,{\frac{\mathrm{d}\mathbf{y}}{\mathrm{dt}}}=-\mathbf{k}^{2}\,\sin\mathbf{x}$

Find the nature of the critical point ,0( of the corresponding linear system.

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Question:

A particle moving in .H.S M has got the velocities cm8 /sec and cm6 /sec when it is at distance cm3 and cm4 respectively from the centre of its motion. Determine the period and the amplitude of motion.

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Question:

If a planet was suddenly stopped in its orbit, supposed circular, show that it will fall into the sun in a time which is $\frac{\sqrt{2}}{8}$ times the period of the planet’s revolution.

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Question:

A particle of mass m moves on a straight line towards the centre of attraction, starting from rest at a distance a from the centre. Its velocity at a distance x from the centre varies as $\sqrt{\frac{a^3-x^3}{x^3}}.$ . Find the law of force.

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Question:

Characterise the following as discrete or continuous giving reasons for your answers.

i) Effects of radiation treatment on a tumour when applied for short period of time but at regular intervals.

ii) Effects of chemotherapy drugs on a tumour when introduced into a patient for a given duration of time.

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Question:

Classify the following into linear and non-linear models, justifying your classification.

i) Simple harmonic motion for small amplitude of oscillation.

ii) Population growth model given by ${\frac{\mathrm{d}\mathbf{N}}{\mathrm{dt}}}=\mathbf{a}\mathbf{N}~(\mathbf{B}-\mathbf{k}\mathbf{N}),~\mathbf{a},\ \mathbf{B},\ \mathbf{k}$ are constants.

iii) Equation for velocity v of a particle at any time t, moving with a constant acceleration a, and initial velocity u.

iv) Equation describing dynamic stability of market equilibrium price given by $\mathbf{p}_{\mathrm{t}}=[1+\mathbf{k}\,(\mathbf{a}-\mathbf{A})\,\mathbf{p}_{\mathrm{t-1}}+\mathbf{k}\ (\mathbf{b}-\mathbf{B})],\,\mathbf{a},\,\mathbf{b},\,\mathbf{A},\,\mathbf{B},\,\mathbf{k}$ are constants and $p_t$ is the price in period t.

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Question:

State two real-world problems where you think that mathematical modelling is the only approach to find the solution of the problem. Give 4 essentials for each of the problems. Why do you think that there is no other scientific alternative for the treatment of these problems.

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Question:

What is the edge-chromatic number of the graph given in Fig. 3(ii)? Justify by giving an explicit coloring

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Question:

Prove that the graph given below is non-Hamiltonian. Image ignouassignments-ignouacademy-com--p-your-73007

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Question:

How many colors are needed to color the 15 balls in the below given triangular array so that no two touching balls get same color? Image ignouassignments-ignouacademy-com--p-solve-12553

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Question:

Can the following figures be drawn without lifting the pen from paper and without covering any line segment more than once? Give reasons in support of your answers. Image ignouassignments-ignouacademy-com--p-doubts-35750

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Question:

Write down the degree sequences of the graphs in Fig. 3: Image ignouassignments-ignouacademy-com--p-ignou-33293

Are these graphs isomorphic? Justify your answer.

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Question:

Using combinatorial arguments, prove tha $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r},$ where the notation $\binom{n}{k}$ is used for the number of ways to choose a subset of See Answer →

Question:

How will you define a complete bipartite graph? Give an example of it. Is every complete bipartite graph complete? Justify.

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Question:

Let See Answer →

Question:

Using combinatorial arguments, prove that $(a+b+c)^{n}=\Sigma_{r+s+t=n}\left(\!\!\!\begin{array}{c}{{n}}\\ {{r\,,\,\,s,\,\,t}}\end{array}\!\!\right)a^{r}b^{s}c^{t}.$ What is the coefficient of $x^{50}y^{12}z^{38}\stackrel{.}{\mathrm{in}}(x-y+2z)^{100}?$

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Question:

Using the method of generating functions, solve the recurrence relation $a_{n}=2a_{n-1}+2^{n},~~n\geq1~,a_{0}=1.$

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Question:

Check whether the graphs in Fig. 2 are planar or not. If yes, give their plane drawing, otherwise give a $K_{3,3}$ or $K_{5}$ subdivision. Image ignouassignments-ignouacademy-com--p-doubts-98082