Download PTU M-Sc -Chemistry 1st Semester May 2019 72262 MATHEMATICS IN CHEMISTRY Question Paper

MATHEMATICS IN CHEMISTRY

1. Write briefly:
   1. Give the drawback of Gauss elimination method.
   2. Give Newton's backward difference formula.

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   3. Evaluate the first approximation from (The equation is missing)
   4. Using Euler's method, find an approximate value of y(0.2) from (The equation is missing)
   5. Classify the following PDE (PDE missing).
   6. Give regression line x on y and y on x.
   7. Give four properties of normal distribution.

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   8. Define null hypothesis by giving a suitable example.
   9. Give four properties of F distribution.
   10. Give four properties of x² distribution.

UNIT-I

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2. 1. Solve using Gauss elimination method:
      2x + 2y + z = 12
      3x + 2y + 2z = 8,
      5x + 10y - 8z = 10.
   2. Solve by Jacobi's method 20x + y - 2z = 17, 3x + 20y – z = – 18, 2x – 3y + 20z = 25.

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3. 1. Find dy/dx at x = 1.6 and d²y/dx² at x = 1.1 from the following data:
      

      X	1.0	1.1	1.2	1.3	1.4	1.5	1.6
      y	7.989	8.403	8.781	9.129	9.451	9.750	10.031

   2. Evaluate ? (function missing) dx using Simpson's 1/3 rule from 0 to 1 (Limits missing).

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UNIT-II

4. 1. Using Taylor's series method, find the value of y(0.2) from (The equation is missing).
   2. Using modified Euler's method, find the value of y(0.3) from (The equation is missing).
5. Using Runge-Kutta method, find the value of y(0.2) and y(0.4) from (The equation is missing).

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UNIT-III

6. 1. Calculate the coefficient of correlation from the following data:
      

      X	105	104	102	101	100	99	98	96	93	92
      y	101	103	100	98	95	96	104	92	97	94

   2. A has one share in a lottery in which there is 1 prize and 2 blanks; B has three shares in a lottery in which there are 3 prizes and 6 blanks. Compare the probability of A's success to that of B's success.

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7. 1. In sampling a large number of parts manufactured by a machine, the mean number of defective in a sample of 20 is 2. Out of 1000 such samples, how many would be expected to contain at least 3 defective parts.
   2. Fit a Poisson distribution to the data:
      

      X	0	1	2	3	4
      f	122	60	15	2	1

UNIT – IV

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8. 1. A die was thrown 9000 times and a throw of 5 or 6 was obtained 3240 times. On the assumption of random throwing, do the data indicate an unbiased die? (take z_0.05 = 1.96)
   2. A sample height of 6400 soldiers has a mean of 67.85 inches and a standard deviation of 2.56 inches while a simple sample of heights of 1600 sailors has a mean of 68.55 inches and a standard deviation of 2.52 inches. Do the data indicate that the sailors are on the average taller than soldiers? (take z = 1.96)
9. 1. The nine items of a sample have the following values 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean of these differ significantly from the assumed mean of 47.5? (for v = 8, t_0.05 = 2.31)
   2. A set of five similar coins is tossed 320 times and the result is:
      

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      No. of heads	0	1	2	3	4	5
      Frequency	6	27	72	112	71	32

      
      Test the hypothesis that the data follows a Binomial distribution. (for v = 5, ?²_0.05 = 11.07)

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