6551262052

Con. 6058-MP-4468-11.

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5. (a) An rnsulated rod of length / has its ends A and B maintained at 0°C and 100°C    8

respectively, until steady State conditions prevail. If B is suddenly reduced to 0°C and maintained at 0°C, find the temperaturę at a distance x from A at time t.

(b) Ten individuals are chosen at random from a population and their hights are found 6 to be 63, 63, 64, 65, 66, 69, 69, 70, 70, 71 inches. Discuss the suggestion that the mean hight of the universe is 65 inches.

(c) Express the function f(x) =

⁶ . kx*^{0r X <} ^ as Fourier integral and hence prove that e for x > 0

J

CC

wsinwx    _y

—5—-r-dw = % e"^KX, x > 0 , k > 0. w + k    ' ^d-

6. (a) Find the half rangę sine series for x sin x in (0, n)

n

1

1

1

1

(b)

deduce that—

8

8/2 1² 3² 5² 7² Obtain the rank correlation coefficient from the following data—

■

(c)

7. (a)

(b)

(c)

x    :    10    12    18    18    15    40

y 12 18 25 25 50 25 K    |l

State and prove the one dimensional wave equation.

Fit a second degree parabolic curve to the following data. x    :    1    2    3    V    5    6    7    8    9

y    :    2    6    7    8    10    11    11    10    09

Explain in brief what is method of Least Squares.

It is known that the probability of an item produced by a certain machinę will be defective is 0 05. If the produced items are sent to the market in packets of 20, find the number of packets containing (1) at least (2) exactly and (3) at most 2 detective items in a consignment of 1000 packets using Poisson approximation to the Binomial distribution.

Explain following terms :—

(i)    Errors in hypothesis testing.

(ii)    Test statistic and degrees of freedom.

(iii)    Level of significance and critical regiop.

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