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

Solve the following linear programming problem graphically.

Maximize Z = 60x₁ + 15x₂ subject to the constraints: x₁ + x₂ ≤ 50; 3x₁ + x₂ ≤ 90 and x₁, x₂ ≥ 0.

If f(x) = `1/(2x + 1)`, x > `-1/2`, then show that f(f(x)) = `(2x + 1)/(2x + 3)`

Draw the graph of y = 9 - x².

If f(x) = x² – x + 1 then f(x + 1) is:

If f(x) = `{(x^2 - 4x if  x >= 2),(x+2 if x < 2):}`, then f(5) is

If f(x) = `(1 - x)/(1 + x)` then f(-x) is equal to:

The graph of the line y = 3 is

The graph of y = 2x² is passing through:

The graph of y = e^x intersect the y-axis at:

The minimum value of the function f(x) = |x| is:

Which one of the following functions has the property f(x) = `"f"(1/x)`?

If f(x) = 2^x and g(x) = `1/2^x` then (fg)(x) is:

Which of the following function is neither even nor odd?

f(x) = -5, for all x ∈ R is a:

The range of f(x) = |x|, for all x ∈ R is:

The graph of f(x) = e^x is identical to that of:

If f(x) = x² and g(x) = 2x + 1 then (fg)(0) is:

A firm produces x tonnes of output at a total cost of C(x) = `1/10x^3 - 4x^2 - 20x + 7` find the

1. average cost
2. average variable cost
3. average fixed cost
4. marginal cost and
5. marginal average cost.

The total cost of x units of output of a firm is given by C = `2/3x + 35/2`. Find the

1. cost when output is 4 units
2. average cost when output is 10 units
3. marginal cost when output is 3 units

Revenue function ‘R’ and cost function ‘C’ are R = 14x – x² and C = x(x² – 2). Find the

1. average cost
2. marginal cost
3. average revenue and
4. marginal revenue.