Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech I MATHEMATICS - III Previous Question Paper (September - 2023 - R16)
Note: i) Question paper consists of Part A, Part B.
ii) Part A is compulsory, which carries 25 marks. In Part A, answer all questions.
iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
The probability density function is f(x) = K(3x-x^2), 1 ≤ x ≤ 2; 0, elsewhere. Find K.
Answer
The total probability must equal 1. Integrating the function from 1 to 2:
K [3(x2/2) - (x3/3)] from 1 to 2 = 1
K [(6 - 8/3) - (3/2 - 1/3)] = 1
K [10/3 - 7/6] = 1 => K [13/6] = 1, so K = 6/13.
If for a poisson variate P(X=2) = P(X=3). Find mean.
Answer
For a Poisson distribution, P(X=k) = (e-λ λk) / k!. Given P(X=2) = P(X=3):
λ2 / 2 = λ3 / 6
λ = 6 / 2 = 3. The mean is 3.
Write the formula to calculate F to test the difference the between variances.
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In a random sample of 200 packages shipped by air freight 52 had some damage. Find the maximum error with 95% confidence of proportions.
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Write the formula to find the maximum error for: i) single proportions ii) difference between the proportions
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In a random sample of 100 packages shipped by air freight 13 had some damage. Find the standard error of proportions.
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If first approximation of a root of x^2-x-4=0 is x0 = 2 then find x1 by Newton Raphson method.
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Find the two points a and b such that x sin x + cos x = 0 has a root in between a and b.
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Write a formula to find the approximate value of integral from a to b f(x) dx, when (xi, f(xi)) are known and a=x0 < x1 < x2 < ... < xn=b.
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If y' = x-y, y(1)=3 find the solution, up to third degree term, using Picard’s method.
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Part B
Find the mean and the variance of uniform probability distribution given by f(x) = 1/n for x= 1, 2, 3, 4…….. n
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Ten coins are thrown simultaneously. Find the probability of getting: i) At least 1 head ii) At least seven heads
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Assume that 50% of the Engineers are good in Mathematics. Find the probability that among 9 engineers: i) Exactly 5 ii) At least 2 are good in Mathematics.
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Given that the mean heights of students in a class is 158 cms with a standard deviation of 20 cms. Find how many students heights lie: i) Between 150 cms and 170 cms. ii) Above 180 cms.
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Five unbiased dice were thrown 276 times and the number of times 4 or 5 or 6 was obtained is given below. Fit a suitable distribution and test whether the die is unbiased.
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The gain in weight of two random samples of rats fed on two different diets A and B are given below. Examine whether the difference in mean weight increases is significant or not.
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A large group of athletes is found to have a mean weight of 140 lbs with a standard deviation of 5 lbs. One student from a college was found to weight 120 lbs. Can it be reasonably concluded that he was not an athlete?
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Among the items produced by a factory out of 500, 15 were defective, in another sample out of 400, 20 were defective. Test the significance between the difference of two proportions at 5% level.
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The mean height of 40 male students is 68 inches with a standard deviation of 3 where as the mean height of 50 female students is 66 inches with a standard deviation of 2.5 inches. Test the significance between the difference of two means at 5% level.
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Random samplers of 300 men and 500 women are asked whether they would like to have a fly over near their residence 150 and 200 women were in favour of the proposal. Find 95% confidence interval for the difference of proportions.
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Find a real root of cos x - x^2 = 0 using Newton Raphson method.
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Fit a parabola of the form y = a + bx + cx^2 for the given data.
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Solve the system of equations using Gauss Seidal method: 8x - 3y + 2z = 20; 6x + 3y + 12z = 35; 4x + 11y - z = 33
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Find the first two derivatives of f(x) at x= 1.2 from the given table.
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Evaluate integral 0 to 1 of 1/(1+x^2) dx by taking h=1/6 using Simpson’s 1/3 rule.
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Find y(0.1) and y(0.2) using Runge Kutta method given that y' = x^2 - y, y(0)=1.
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