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

Solve the following differential equation:

`("d"^2y)/("d"x^2) - 2"k" ("d"y)/("d"x) + "k"^2y = 0`

Solve the following differential equation:

(D² – 2D – 15)y = 0 given that `("d"y)/("d"x)` = 0 and `("d"^2y)/("d"x^2)` = 2 when x = 0

Solve the following differential equation:

(4D² + 4D – 3)y = e^2x

Solve the following differential equation:

`("d"^2y)/("d"x^2) + 16y = 0`

Solve the following differential equation:

(D² – 3D + 2)y = e^3x which shall vanish for x = 0 and for x = log 2

Solve the following differential equation:

(D² + D – 2)y = e^3x + e^–3x 

Solve the following differential equation:

(D² – 10D + 25) y = 4e^5x + 5

Solve the following differential equation:

`(4"D"^2 + 16"D" + 15)y = 4"e"^((-3)/2x)`

Solve the following differential equation:

(3D² + D – 14)y – 13e^2x

Solve the following differential equation:

Suppose that the quantity demanded Q_d = `13 - 6"p" + 2 "dp"/"dt" + ("d"^2"p")/("dt"^2)` and quantity supplied Q_s = `- 3 + 2"p"` where p is the price. Find the equilibrium price for market clearance

Choose the correct alternative:

The complementary function of (D² + 4) y = e^2x is

Choose the correct alternative:

The particular intergral of the differential equation `("d"^2y)/("d"x^2) - 8 ("d"y)/("d"x) + 16y = 2"e"^(4x)`

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The integrating factor of `x ("d"y)/("d"x) - y = x^2` is

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The particular integral of the differential equation f(D) y = e^ax where f(D) = (D – a)² 

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The complementary function of `("d"^2y)/("d"x^2) - ("d"y)/("d"x) = 0` is

Choose the correct alternative:

The P.I of (3D² + D – 14)y = 13e^2x is

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The general solution of the differential equation `("d"y)/("d"x) = cos x` is

Suppose that Q_d = `30 - 5"P" + 2 "dP"/"dt" + ("d"^2"P")/("dt"^2)` and Q_s = 6 + 3P. Find the equilibrium price for market clearance

What is null hypothesis? Give an example

Define alternative hypothesis