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

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`

Integrate the following w.r.t.x:

`x^2/((x - 1)(3x - 1)(3x - 2)`

Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`

Integrate the following w.r.t.x :  `sec^2x sqrt(7 + 2 tan x - tan^2 x)`

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

The demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.

The total cost function for production of x articles is given as C = 100 + 600x – 3x² . Find the values of x for which total cost is decreasing.

The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing

The total cost of manufacturing x articles C = 47x + 300x² – x⁴ . Find x, for which average cost is decreasing

Find the price, if the marginal revenue is 28 and elasticity of demand is 3.

If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.

Find the price for the demand function D = `((2"p" + 3)/(3"p" - 1))`, when elasticity of demand is `11/14`.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 5 comment on the result.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 2 comment on the result

For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.

For the demand function D = 100 – `"p"^2/2`. Find the elasticity of demand at p = 6 and comment on the results.

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which profit is increasing.