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

Find the differential equation of the following:

y = c(x – c)²

Find the differential equation of the following:

xy = c² 

Find the differential equation of the following:

x² + y² = a² 

Form the differential equation by eliminating α and β from (x – α)² + (y – β)² = r²

Find the differential equation of the family of all straight lines passing through the origin

Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis

Find the differential equation of all circles passing through the origin and having their centers on the y axis

Find the differential equation of the family of a parabola with foci at the origin and axis along the x-axis

Choose the correct alternative:

The degree of the differential equation `("d"^4y)/("d"x^4) - (("d"^2y)/("d"x^2))^4 + ("d"y)/("d"x) = 3`

Choose the correct alternative:

The order and degree of the differential equation `sqrt(("d"^2y)/("d"x^2)) = sqrt(("d"y)/("d"x) + 5)` are respectively

Choose the correct alternative:

The order and degree of the differential equation `(("d"^2y)/("d"x^2))^(3/2) - sqrt((("d"y)/("d"x))) - 4 = 0` are respectively

Choose the correct alternative:

Th e differential equation `(("d"x)/("d"y))^3 + 2y^(1/2) = x` is

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The differential equation formed by eliminating a and b from y = ae^x + be^-x is

Choose the correct alternative:

The differential equation formed by eliminating A and B from y = e^-2x (A cos x + B sin x) is

Solve yx²dx + e^–x dy = 0

Evaluate Δ(log ax)

If y = x³ – x² + x – 1 calculate the values of y for x = 0, 1, 2, 3, 4, 5 and form the forward differences table

If h = 1 then prove that (E^–1Δ)x³ = 3x² – 3x + 1

If f(x) = x² + 3x than show that Δf(x) = 2x + 4

Evaluate Δ`[1/((x + 1)(x + 2))]` by taking ‘1’ as the interval of differencing