HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Find the rate of change of demand (x) of acommodity with respect to its price (y) if

`y = 12 + 10x + 25x^2`

The position vector of points A and B are `6bar(a) + 2bar(b) and bar(a) -3bar(b)` . If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is 3`bar(a)- bar(b)`.

Find `dy/dx` if, y = `e^(5x^2-2x+4)`

Solve the following:

If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`

If X ∼ P(m) with P(X = 1) = P(X = 2), then find the mean and P(X = 2).

Given e^–2 = 0.1353

Solution: Since P(X = 1) = P(X = 2)

∴ `("e"^square"m"^1)/(1!) = ("e"^"-m""m"^2)/square`

∴ m = `square`

∴ P(X = 2) = `("e"^-2. "m"^2)/(2!)` = `square`

Find `dy/dx` if, y = `e^(5x^2 -2x + 4)`

If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`. 

Evaluate `int 1 / (x (x - 1)) dx`

If f'(x) = 4x³ - 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`

Solve the following:

If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`

Find `dy/dx` if, y = `e^(5x^2-2x+4)`

If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`

Find `dy/dx` if, `y = e^(5x^2 - 2x +4)`

Solve the following:

If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`

Find `dy/dx` if, `y=e^(5x^2-2x+4)`

If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`

Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`

Solve the following:

If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"` 

Evaluate.

`intx^3/sqrt(1+x^4) dx`