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

Calculate the correlation coefficient from the following data:

∑X = 125, ∑Y = 100, ∑X² = 650, ∑Y² = 436, ∑XY = 520, N = 25

Determine whether the following function is odd or even?

f(x) = `((a^x - 1)/(a^x + 1))`

Determine whether the following function is odd or even?

f(x) = `log (x^2 + sqrt(x^2 + 1))`

Determine whether the following function is odd or even?

f(x) = sin x + cos x

Determine whether the following function is odd or even?

f(x) = x² – |x|

Determine whether the following function is odd or even?

f(x) = x + x²

Let f be defined by f(x) = x³ – kx² + 2x, x ∈ R. Find k, if ‘f’ is an odd function.

If f(x) = `x^3 - 1/x^3`, then show that `"f"(x) + "f"(1/x)` = 0

If f(x) = `((x + 1)/(x - 1))`, then prove that f(f(x)) = x.

For f(x) = `(x - 1)/(3x + 1)`, write the expressions of `"f"(1/x) and 1/("f"(x))`

If f(x) = e^x and g(x) = log_e x then find (f + g)(1)

If f(x) = e^x and g(x) = log_e x then find (fg)(1).

If f(x) = e^x and g(x) = log_e x then find (3f) (1).

If f(x) = e^x and g(x) = log_e x then find (5g)(1).

Draw the graph of the following function:

f(x) = 16 – x²

Draw the graph of the following function:

f(x) = |x – 2|

A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are ₹ 5 and ₹ 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.

A company produces two types of products say type A and B. Profits on the two types of product are ₹ 30/- and ₹ 40/- per kg respectively. The data on resources required and availability of resources are given below.

Formulate this problem as a linear programming problem to maximize the profit.

Draw the graph of the following function:

f(x) = x |x|

A company manufactures two models of voltage stabilizers viz., ordinary and auto-cut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at the company’s own works. The assembly and testing time required for the two models are 0.8 hours each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests a maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at ₹ 100 and ₹ 150 respectively. Formulate the linear programming problem.