Show that the equations x + 2y = 3, y - z = 2, x + y + z = 1 are consistent and have infinite sets of solution.

If f' (x) = 3x² - \(\frac { 2 }{ { x }^{ 3 } } \) and f(1) = 0, find f(x)

Find the area bounded by one arc of the curve y = sin ax and the x-axis.

Form the differential equation for \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \)=1 where a & b are arbitrary constants.

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^x-x-1).

Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

Wages (x)	20 - 30	30 - 40	40 - 50	50 - 60
No. of men (y)	9	30	35	42

A random variable. X has following distribution

X	-1	0	1	2
P(X=x)	\(\frac{1}{3}\)	\(\frac{1}{6}\)	\(\frac{1}{6}\)	\(\frac{1}{3}\)

Find E(2X+3)²

The probability that an event A happens in one treat of an experiment is 0.4. Three independent treats of the experiment are performed. Find the p!probability that the event A happens at least once.

A random sample of marks in mathematics secured by 50 students out of 200 students showed a mean of 75 and a standard deviation of 10. Find the 95% confidence limits for the estimate of their mean marks.

Find a trend line to the following data by the method of sami-averages.

Years	1980	1981	1982	1983	1984	1985	1986
Sales	102	105	114	110	108	116	112

From the data given below, construct a cost of living index number by family budget method for 1986 with 1976 as the base year.

Commodity	P	Q	R	S	T	U
Quantity in 1976	50	25	10	20	30	40
Price in 1976 (Rs)	10	5	8	7	9	6
Price in 1986 (Rs)	6	4	3	8	10	12

 

Find the initial basic feasible solution for the following transportation problem by Vogel's approximation method.