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

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`

Solve the following:

`x ("d"y)/("d"x) + 2y = x^4`

Solve the following:

`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`

Solve the following:

`("d"y)/("d"x) + y/x = x'e"^x`

Solve the following:

`("d"y)/("d"x) + y tan x = cos^3x`

Solve the following:

If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x

Solve the following:

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

Solve the following:

A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e^0.8 = 2.2255)

Choose the correct alternative:

If y = ex + c – c³ then its differential equation is

Choose the correct alternative:

The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is

Choose the correct alternative:

The differential equation of y = mx + c is (m and c are arbitrary constants)