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

If X – P(m) with P(X = 1) = P(X = 2), then find the mean and P(X = 2) given that e^–2 = 0.1353

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

`(e^-mm^1)/(1!) = square`

∴ m = `square`

∴ mean = `square` = `square`

Then P(X = 2) = `square` = `square`

Find the equation of tangent and normal to the curve y = x² + 5 where the tangent is parallel to the line 4x – y + 1 = 0.

If y = 2x² + a² + 2² then `dy/dx` = ______.

Laspeyre’s Price Index Number uses current year’s quantities as weights.

An agent places insurance for ₹ 4,00,000 on life of a person. The premium is to be paid annually at the rate of ₹ 35 per thousand per annum. Find the agent’s commission at 15% on the premium.

An agent was paid ₹ 88,000 as a commission on the sales of computers at the rate of 12.5%. If the price of each computer was ₹ 32,000, how many computers did he sell?

Calculate Marshall – Edgeworth’s price index number for the following data:

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

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

Solve the following:

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

Solve the following:

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

Evaluate `int1/(x(x-1)) dx`

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

Evaluate `int(5x^2 - 6x+3)/(2x- 3 )dx`

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

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

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

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`