HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Find y₂ for the following function:

y = log x + a^x

Find y₂ for the following function:

x = a cosθ, y = a sinθ

If y = 500e^7x + 600e^-7x, then show that y₂ – 49y = 0.

If y = 2 + log x, then show that xy₂ + y₁ = 0.

If = a cos mx + b sin mx, then show that y₂ + m²y = 0.

If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x²) y₂ + xy₁ – m²y = 0

If y = sin(log x), then show that x²y₂ + xy₁ + y = 0.

If x^y . y^x , then prove that `"dy"/"dx" = y/x((x log y - y)/(y log x - x))` 

If xy² = 1, then prove that `2 "dy"/"dx" + y^3`= 0

If y = tan x, then prove that y₂ - 2yy₁ = 0.

If y = 2 sin x + 3 cos x, then show that y₂ + y = 0.

The following table gives the annual demand and unit price of 3 items.

Ordering cost is ₹ 5 per order and holding cost is 10% of unit price. Determine the following:

1. EOQ in units
2. Minimum average cost
3. EOQ in rupees
4. EOQ in years of supply
5. Number of orders per year

A dealer has to supply his customer with 400 units of a product per week. The dealer gets the product from the manufacturer at a cost of ₹ 50 per unit. The cost of ordering from the manufacturers in ₹ 75 per order. The cost of holding inventory is 7.5 % per year of the product cost. Find

1. EOQ
2. Total optimum cost.

A certain manufacturing concern has total cost function C = 15 + 9x - 6x² + x³. Find x, when the total cost is minimum.

By the principle of mathematical induction, prove the following:

1³ + 2³ + 3³ + ….. + n³ = `("n"^2("n + 1")^2)/4` for all x ∈ N.

By the principle of mathematical induction, prove the following:

1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` for all n ∈ N.

By the principle of mathematical induction, prove the following:

4 + 8 + 12 + ……. + 4n = 2n(n + 1), for all n ∈ N.

By the principle of mathematical induction, prove the following:

1 + 4 + 7 + ……. + (3n – 2) = `("n"(3"n" - 1))/2`  for all n ∈ N.

By the principle of mathematical induction, prove the following:

3²ⁿ – 1 is divisible by 8, for all n ∈ N.

By the principle of mathematical induction, prove the following:

aⁿ – bⁿ is divisible by a – b, for all n ∈ N.