Solve your IGNOU Doubts

Question:

The average number of cars arriving at a particular red light each day is 4. Assuming a Poisson distribution, calculate the probability that on a given day, less than three cars will arrive at the red light.

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Question:

For the vectors $\vec{a} ,\vec{b},\dot{c}$ and $\vec{d}$ show that:

$( \vec{a} \times \vec{b} ) ,(\vec{c}\times \vec{d} ) +( \vec{b}\times \vec{c} ) .\: \: (\vec{a} \times \vec{d} )+( \vec{c} \times \vec{a}) .(\vec{b} \times \vec{d} ) =0$

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Question:

The following readings were recorded in an experiment to determine the Young’s modulus for a steel bar.

Load (g)	0	10	20	30	40	50
Shift (cm)	0	0.6	1.25	2.05	2.6	3.2

Determine the correlation coefficient, the regression equation and the standard error of estimate for the data.

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Question:

What do you understand by wave impendence? Derive an expression for the impedance offered to sound waves propagating in a gaseous medium.

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Question:

Calculate the fundamental frequency and the first 3 overtones of a pipe of length 1.7 m and closed at one end.

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Question:

Standing waves are produced by the superposition of the following two waves:

y1 (x, t) = 0.2 sin $\pi$ (t - 2) and t2 (x,t) = 0.2 sin $\pi$ (t+ 2x)

a) Obtain the resultant displacement of the particle at x at time t.

b) Calculate the value(s) of x for which displacement is zero.

c) Calculate the difference between two nearest values of x for which the displacement is zero. Is it related to the wavelength?

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Question:

Determine the value of a constant $\alpha$ such that the projection of a vector

$\vec{A}=\alpha \hat{i} +\hat{j}+3\hat{k}$ on the vector $\vec{B}= 3\hat{i}+ 2\hat{j}+ 6\hat{k}$ units

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Question:

A vibrating turning fork of frequency 500 Hz is moved away from a stationary listener and towards a stationary wall at a speed of 3 ms⁻¹. The listener hears two frequencies; one due to direct sound and the other due to reflected wave. Calculate the number of beats heard by the listener per second. Take velocity of sound in air as 340 ms⁻¹ .

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Question:

A wave is expressed as: y = 0.5 sin $\pi$ (0.01x - 3t) Calculate the speed of propagation of the wave.

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Question:

The intensity ratio of two waves of same frequency and travelling in the same direction is 1:16. Calculate the ratio of their amplitudes.

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Question:

Two waves are represented by:

y = a sin $(\omega t-kx)$ and y = b cos $(\omega t-kx)$ Calculate the phase difference between the waves.

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Question:

Which of the following statements are true? Give reasons for your answer.

(i) F-distribution is always used in goodness of fit.

(ii) Measure of central tendency in a data set refers to the extent to which the observations are scattered.

(iii) A process is said to be under assignable cause when the points are above the VCL link of ( chart. X,R)

(iv) Simple random sampling is done by using random number tables where the probability of drawing a digit is .1 0⋅ (v) All time series have a trend.

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Question:

A researcher measures the temperature of a solution 5 times. The observations are 25, 32, 27, 29, 30 o C. Determine an unbiased estimate of the temperature.

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Question:

A box contains 10 screws, 3 of which are defective. Two screws are drawn at random. Find the probability that none of them is defective, if the sample is drawn (i) with replacement,

(ii) without replacement.

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Question:

A manufacture of rayon wants to compare that the yield strength of 5 11⋅ kg/ 2 mm is met or not at 5% level of significance. The manufacturer draws a sample and calculates the mean to be 8 12⋅ kg/ 2 mm and the standard derivation is known to be 2⋅0kg/ mm . 2 Carry out the statistical test appropriate for this.

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Question:

Suppose from a total of 120 guava trees, 5 clusters of 4 trees each selected and the yield (in kg) is recorded below:

Cluster	Trees
	1	2	3	4
1	5	4	2	15
2	11	1	4	7
3	26	10	19	11
4	7	15	12	10
5	2	22	8	6

Estimate the average yield per tree and its standard error.

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Question:

A shop manufacturer is trying to determine whether or not to market a new type of shop. It chooses a random samples of equivalent size in England and France. It asks each of the people in each sample to try the new soap, and see whether he or she likes it better than other soaps. The results are as follows:

	United States	England	France
Prefer new soap	81	43	26
Do not prefer it	219	257	274

Test the hypothesis that there are international difference in the proportion of people who prefer the new soap, using 5% level of significance.

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Question:

Write three advantage and three disadvantage of using a sampling approach instead of a census approach for studying a characteristic

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Question:

At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in weeks:

Time	Sample number
	1	2	3	4	5
9 a.m.	8	9	15	4	11
10	7	10	7	6	8
11	11	12	10	9	10
12	12	8	6	9	12
1 p.m.	11	10	6	14	11
2	7	7	10	4	11
3	10	7	4	10	10
4	8	11	11	11	7

Compute the control limits for x and R -charts. Draw the control charts for x and ,R and comments.

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Question:

The weight on a vertical spring undergoes forced vibrations according to the following equation:

$\frac{d^{2}x}{dt^{2}}+4x =8sin\; \omega t$

where x is the displacement from the equilibrium position and $\omega$ > 0 is a constant. If at t = 0, x = 0 and $\frac{dx}{dt}=0,$ calculate x as a function of t.