HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Evaluate the following integrals as the limit of the sum:

`int_0^1 (x + 4)  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_1^3 x  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_1^3 (2x + 3)  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_0^1 x^2  "d"x`

Choose the correct alternative:

`int_0^1 (2x + 1)  "d"x` is

Choose the correct alternative:

`int_0^oo "e"^(-2x)  "d"x` is

Choose the correct alternative:

`int_(-1)^1 x^3 "e"^(x^4)  "d"x` is

Choose the correct alternative:

If f(x) is a continuous function and a < c < b, then `int_"a"^"c" f(x)  "d"x + int_"c"^"b" f(x)  "d"x` is

Choose the correct alternative:

The value of `int_(- pi/2)^(pi/2) cos  x  "d"x` is

Choose the correct alternative:

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is

Choose the correct alternative:

Γ(n) is

Choose the correct alternative:

Γ(1) is

Choose the correct alternative:

If n > 0, then Γ(n) is

Choose the correct alternative:

`Γ(3/2)`

Choose the correct alternative:

`int_0^oo x^4"e"^-x  "d"x` is

The cost of an overhaul of an engine is ₹ 10,000 The operating cost per hour is at the rate of 2x – 240 where the engine has run x km. Find out the total cost if the engine runs for 300 hours after overhaul

Elasticity of a function `("E"y)/("E"x)` is given by `("E"y)/("E"x) = (-7x)/((1 - 2x)(2 + 3x))`. Find the function when x = 2, y = `3/8`

The elasticity of demand with respect to price for a commodity is given by `((4 - x))/x`, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2. Also, find the revenue function

A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x², the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days

An account fetches interest at the rate of 5% per annum compounded continuously. An individual deposits ₹ 1,000 each year in his account. How much will be in the account after 5 years. (e^0.25 = 1.284)