The technology matrix of an economic system of two industries is \(\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\). Test whether the system is viable as per Hawkins-Simon conditions.

Find the rank of the word 'CHAT' in dictionary.

Find the equation of the circle having (4,7) and (-2,5) as the extremities of a diameter.

Convert the following degree measure into radian measure -320^o

Determine whether the following functions are odd or even?
 \(f(x)=log({ x }^{ 2 }+\sqrt { { x }^{ 2 } } +1)\)

A demand function is given by xpⁿ = k where n and k are constants. Prove that elasticity of demand is always constant.

A limited company wants to create a fund to help their employees in critical circumstances. The estimated expenses per month is Rs. 18,000. Find the amount to be deposited by the company if the rate of compound interest is 15%.

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

Calculate the coefficient of correlation between X and Y series from the following data.

Description	X	Y
Number of pairs of observation	15	15
Arithmetic mean	25	18
Standard deviation	3.01	3.03
Sum of squares of deviation from the arithmetic mean	136	138

Summation of product deviations of X and Y series from their respective arithmetic means is 122.

Draw the network for the project whose activities with their relationships are given below:
Activities A, D, E can start simultaneously; B, C > A; G, F > D, C; H > E, F.