HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions

Evaluate the following:

`intx^3e^(x^2)dx` 

Find `dy/dx` if, y = `x^(e^x)`

Evaluate the following.

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

Evaluate the following.

`intx^3 e^(x^2) dx`

Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`

Evaluate the following.

`intx^3e^(x^2) dx`

Evaluate `int (1 + x + x^2/(2!))dx`

Choose the correct pair:

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

Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  

Find `dy/(dx)` if, `y = x^(e^x)`

Find `dy/(dx)` if, `x = e^(3t),  y = e^sqrtt`.

Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`

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

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

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

Find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as E_c = (0.0003) I² + (0.075) I ; When I = 1000.

If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______