Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II ENGINEERING MATHEMATICS II Previous Question Paper (February - 2024 - R22)
Note: This question paper contains two parts A and B. Part-A for 10 marks, Part-B for 50 marks. Part-A is a compulsory question consisting of ten sub-questions. Part-B consists of ten questions (numbered 2 to 11) carrying 10 marks each. Answer five questions from Part-B, choosing one from each pair.
Part A
State addition theorem on probability of two events.
Answer
For any two events A and B, the addition theorem states that P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Is
Answer
Yes, it is a probability density function because f(x) ≥ 0 for all x, and the integral from -∞ to ∞ of f(x) dx = ∫₀∞ e-x dx = [-e-x]₀∞ = 0 - (-1) = 1.
Write the assumptions of Bernoulli process.
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Compute P(z ≥ -1.64), if z is normally distributed with mean 0 and variance 1.
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What is meant by biased estimator?
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Define statistic and parameter.
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Write at least one use of testing of hypothesis.
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Explain level of significance.
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Give the relations between the difference operators:
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Write Simpsons 1/3 formula.
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Part B
Of 10 girls in a class, 3 have blue eyes. If 2 of the girls are chosen at random, what is the probability that (i) both have blue eyes?, and (ii) at least one has blue eyes?
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A man alternatively tosses a coin and throws a die beginning with coin. What is the probability that he will get a head before he gets a 5 or 6 on the die?
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Suppose colored balls are distributed in three indistinguishable boxes as follows: Box I (Red: 2, White: 3, Blue: 5), Box II (Red: 4, White: 1, Blue: 3), Box III (Red: 3, White: 4, Blue: 3). A box is selected at random from which a ball is selected at a random. What is the probability that the ball is colored (a) red, (b) blue.
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In 256 sets of 12 tosses of a coin, in how many cases one can expect eight heads and four tails.
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Suppose that on the average one person in 1000 makes a numerical error in preparing income tax return. If 10,000 forms are selected at random and examined, compute the probability that 6, 7 or 8 of the forms will be in error.
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Assume that the average life span of computers produced by a company is 2040 hours with standard deviation of 60 hours. Estimate the expected number of computers whose life span is (a) more than 2150 hours, (b) less than 1950 hours, (c) more than 1920 hours and less than 2160 hours from a pool of 2000 computers assuming that the life span X is normally distributed.
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The efficiency expert of a computer company tested 40 engineers to estimate the average time it takes to assemble a certain computer component, getting a mean of 12.73 minutes and s.d. of 2.06 minutes.
If 12.73 is used as a point estimate, determine the maximum error with 99% confidence.
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Construct 98% confidence intervals for the true average time.
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With what confidence can we assert that the sample mean does not differ from the true mean by more than 30 seconds?
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Define sample and population. Give counter examples.
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If on the average, the test strips painted across heavily travelled roads in 15 different locations, disappeared after they had been crossed by 146692 cars with s.d. 14380 cars, calculate 99% confidence intervals for the true average number of cars it takes to wear off the paint, assuming normal population.
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An oceanographer wants to check whether the depth of the ocean in a certain region is 57.4 fathoms, as has previously been recorded. What can he conclude at the level of significance α = 0.05, if soundings taken at 40 random locations in the given region yielded a mean of 59.1 fathoms with a standard deviation of 5.2 fathoms? Also calculate 95% confidence interval.
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If 57 out of 150 patients suffering with certain disease are cured by allopathy and 33 out of 100 patients with same disease are cured by homeopathy, is there any reason to believe that allopathy is better than homeopathy at 0.05 level of significance.
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Apply Newton-Raphson method to derive the recurrence formula for finding the value of 1/N.
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Determine a real root of the equation by using Newton's method correct to three decimal places.
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Using modified Euler's method, find the values of y(0.1), y(0.2) and y(0.3) for the initial value problem
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