Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.

Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)

Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.

Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0

Find the missing term from the following data.

x	20	30	40
y	51	-	34

Determine whether the following is a probability distribution of a random variable X.

X	0	1	2
P(X)	0.6	0.1	0.2

If the mean of the binomial distribution is 20 and standard deviation is 4, then find the number of events.

Out of 1000 T.V. viewers, 320 watched a particular programme. Calculate the standard error.

Calculate the 3-yearlymoving averages of the production figures (in tonnes) for the following data.

Year	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987
Production	15	21	30	36	42	46	50	56	63	70	74	82	90	95	102

Determine an initial basic feasible solution to the following transportation problem using feast cost method.