HSC Commerce कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x^–0.4. Find out the number of hours required to produce additional 400 units. [(900)^0.6 = 59.22, (500)^0.6 = 41.63]

The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.

Solve: `("d"y)/("d"x) = "ae"^y`

Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`

Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0

Solve: ydx – xdy = 0 dy

Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`

Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0

Solve: (1 – x) dy – (1 + y) dx = 0

Solve: `log(("d"y)/("d"x))` = ax + by

Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin

Solve the following homogeneous differential equation:

`x ("d"y)/("d"x) = x + y`

Solve the following homogeneous differential equation:

`(x - y) ("d"y)/("d"x) = x + 3y`

Solve the following homogeneous differential equation:

`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`

Solve the following homogeneous differential equation:

`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`

Solve the following homogeneous differential equation:

(y² – 2xy) dx = (x² – 2xy) dy

Solve the following homogeneous differential equation:

The slope of the tangent to a curve at any point (x, y) on it is given by (y³ – 2yx²) dx + (2xy² – x³) dy = 0 and the curve passes through (1, 2). Find the equation of the curve

Solve the following homogeneous differential equation:

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x² + y²) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?

Solve the following:

`("d"y)/("d"x) - y/x = x`

Solve the following:

`("d"y)/(""dx) + y cos x = sin x cos x`