HSC Commerce कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Show that the function f(x) = 2x - |x| is continuous at x = 0

Verify the continuity and differentiability of f(x) = `{(1 - x if  x < 1),((1 - x)(2 - x) if 1 <= x <= 2),(3 - x if x > 2):}` at x = 1 and x = 2.

If f(x) = `{(x^2 - 4x if  x >= 2),(x+2 if x < 2):}`, then f(0) is

`lim_(theta->0) (tan theta)/theta` = 

\[\lim_{x->0} \frac{e^x - 1}{x}\]=

For what value of x, f(x) = `(x+2)/(x-1)`  is not continuous?

A function f(x) is continuous at x = a `lim_(x->"a")`f(x) is equal to:

`"d"/"dx" (1/x)` is equal to:

`"d"/"dx"` (5e^x – 2 log x) is equal to:

If y = x and z = `1/x` then `"dy"/"dx"` =

If y = e^2x then `("d"^2"y")/"dx"^2` at x = 0 is:

If y = log x then y₂ =

`"d"/"dx" ("a"^x)` = 

The technology matrix of an economic system of two industries is `|(0.50,0.30),(0.41,0.33)|` Test whether the system is viable as per Hawkins Simon conditions.

The technology matrix of an economic system of two industries is `|(0.6,0.9),(0.20,0.80)|`.
Test whether the system is viable as per Hawkins-Simon conditions.

The technology matrix of an economic system of two industries is `|(0.50,0.25),(0.40,0.67)|`. Test whether the system is viable as per Hawkins-Simon conditions.

Two commodities A and B are produced such that 0.4 tonne of A and 0.7 tonne of B are required to produce a tonne of A. Similarly 0.1 tonne of A and 0.7 tonne of B are needed to produce a tonne of B. Write down the technology matrix. If 68 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them.

Suppose the inter-industry flow of the product of two industries are given as under.

Determine the technology matrix and test Hawkin’s -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.

You are given the following transaction matrix for a two-sector economy.

1. Write the technology matrix
2. Determine the output when the final demand for the output sector 1 alone increases to 23 units.

Suppose the inter-industry flow of the product of two sectors X and Y are given as under.

Find the gross output when the domestic demand changes to 12 for X and 18 for Y.