HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  

Evaluate the following.

`int x^3 e^(x^2) dx` 

Evaluate the following.

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

Evaluate the following.

`intx^2e^(4x)dx`

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

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

Find `dy/(dx)  "if", y = x^(e^(x))` 

Evaluate the following.

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

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

Evaluate the following.

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

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.

Find `dy/dx if x^3 + y^2 + xy = 7`

Find `"dy"/"dx"` ; if x = sin³θ , y = cos³θ

Find `"dy"/"dx"` ; if y = cos^-1 `("2x" sqrt (1 - "x"^2))`

Differentiate e^{4x + 5} w.r..t.e^3x

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

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.