III B.Tech. I-Semester Supplementary Examinations, November-2003. MATHEMATICS (Metallurgy and Material Technology)
1.a) b) c)
Max. Marks: 70
Answer any FIVE Questions All Questions carry equal marks ---State Axioms of probability. If A and B are any two events, then prove that P(AUB) = P(A) + P(B)−P(AYB) If BCA, then prove that P(b) ≤ P(A)
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Time: 3 hours
A problem in mechanics is given to three students A,B and C whose chances of 1 1 1 solving it are , and respectively. What is the probability that the problem 2 3 4 will be solved?
3.a)
From a lot of 10 items containing 3 defective , a sample of 4 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the sample is drawn without replecement (i)Find the probability distribution of X (ii) Find P(X 1) and P(0 < X < 2). Define nornal distribution. Find its mean and variance.
4.a)
b)
Define sampling distribution and its standard error. Explain the terms 'Parameter' and 'Statistic' A population consists of the four numbers 3,7,11 and 15. Consider all possible samples of size two that can be drawn with replacement from this population. Find (a) the population mean (b) the population standard deviation (c) the mean of the sampling distribution of means and (d) the standard deviation of the sampling distribution of means. Define point estimation, interval estimation and Baysian estimations with suitable examples. The average zinc contrition recovered from a sample of zinc measurements in 36 different locations is found to be 2.6 grams per milliliter. Find the 95% and 99% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3. And how large sample is required if we want to be 95% confident that out estimate of μ is off by less than 0.05?
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Code No:311851
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A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data: Brand A (%) 13.5 14 13.6 12.9 13 Brand B (%)
12.9
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12.4
13.5
12.7
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6.a)
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Test the null hypothesis μ1 = μ2 (where μ1 and μ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis μ1 μ2 at the level of significance α =0.05. Discuss the method of least squares. Fit a least square straight line for the following data x y
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Find y when x1 = 10 and x2 = 6 from the least square regress equation of y on x1 and x2 for the following data. x 90 72 54 42 30 12 x1 3 5 6 8 12 14 y2 16 10 7 4 3 2
Code No: 311851 III B.Tech. I-Semester Supplementary Examinations ...
b) The average zinc contrition recovered from a sample of zinc measurements in 36 · different locations is found to be 2.6 grams per milliliter. Find the 95% and ...
320256. III-B.Tech. II Semester Supplementary Examinations December 2002/January 2003 · MODELLING OF POWER SYSTEM COMPONENTS · (Electrical and Electronics Engineering) · Time: 3 hours · Max. Marks: 70 · Answer any FIVE questions · All questions carry
1011. 7.a) Discuss the generation and detection of pulse width modulation. b) Explain the principle transversal equiliber. 8. Write short notes on the following:.
... plate capacitor is · equal to the conduction current in the leads. b) Investigate the vector magnetic potential for the infinite, straight, current element · L in free space. 3. Find the magnetic field intensity due to the presence of a finite st
2.a) With a neat sketch explain the operation of a cupola, its charge composition and · control of the melt composition. b) Briefly explain the pressure die casting ...
b) Explain heat treatment given to high speed tool steels. 7. Explain structure, properties and applications of any THREE of the following: · (a) Al-Si alloys (b) ...
b) Draw a graph showing the refractive index distribution of central core cladded · optical fibre and explain the plot. 2.a) Give any three applications of optical ...
1.a) Explain with a neat sectional view the operation and advantages of hot blast · cupola. b) Discuss the various types of refractories used for cupola lining.
5.a) What is sine bar. Sketch an arrangement for any one of the applications. b) Describe the constructional features and working of optical collimator.
Explain in detail gas liquid contact in mechanically agitated vessels. ... b) Derive the expression for height of a water cooling tower by using HTU and NTU.
b) With the help of a neat sketch of psychometric chart show the various psychrometric · processes naming them clearly. c) Explain what effective temperature is ...
Write a short note on 'compressor surge and its prevention'. 6.a) In rocket propulsion, explain the following: · (i) Thrust coefficient (ii) Characteristic velocity (iii) Specific impulse. b) Derive the 'Generalised Thrust Equation, of a rocket from
c) What is the difference between the BSA instruction and the interrupt cycle? 8. Write short notes on any two: · a) RISC and CISC Processors. b) Priority interrupt ...
with 64 addressing modes. The computer has 500 instructions. In one of the · instruction format the First Field represents operator field, Second Field is Mode,.
1. a) With a schematic diagram explain the operation of a hot blast cupola. What is its · application? b) How are the refractories classified? Explain the factors in ...
Explain about harmonics generated in e.m.f of a synchronous machine. ... A â 3 â Phase star connected, 4- pole, 50Hz. Alternator develops an open circuit.
4.a) What are the advantages of barometric condenser over surface condenser in steam · jet refrigeration system. b) Explain the phenomenon of energy transfer ...
1. a) Define the role of each of the following components in the operation of an ... b) Compare and contrast the vertical and horizontal micro instructions.
Briefly discuss about Reflections and cross talk problems that affect digital PCBs. 6. Sketch the geometry of a screen fabric and explain about Monofile polyester.
5.a) Explain the principle of working of a precision rotary phase shifter, with neat ... and (ii) a simple ideal dielectric phase shifter in a rectangular guide.
1.a) Mercury thermometer is a first order system â Say âTrueâ or âFalseâ. b) Prove your answer by deriving the transfer function of this system. c) How will this ...
A 2 pole-50 Hz Turbo alternator has a rating of 50 MVA. Its rotor has a moment · of inertia 9000 Kg-m · 2 . Calculate its inertia constant in MJ/MVA and its.
4.a) Explain the working of pressure lubrication used in automobile engines. b) Explain the effect of super charging on diesel engine performance. 5.a) Write a ...