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

Evaluate the following.

`int "x"^5/("x"^2 + 1)`dx

Evaluate the following.

`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx

Evaluate the following.

`int 1/(sqrt"x" + "x")` dx

Evaluate the following.

`int 1/(x(x^6 + 1))` dx 

State whether the following statement is true or false:

Order and degree of a differential equation are always positive integers.

State whether the following is True or False:

The order of highest derivative occurring in the differential equation is called degree of the differential equation.

Evaluate the following.

`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt

State whether the following is True or False:

The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called order of the differential equation.

State whether the following is True or False:

The degree of the differential equation `e^((dy)/(dx)) = dy/dx +c` is not defined.

Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx

Find the order and degree of the following differential equation:

`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`

Find the order and degree of the following differential equation:

`x+ dy/dx = 1 + (dy/dx)^2`

Evaluate the following.

`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx

Evaluate the following.

`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx

Evaluate the following.

`int 1/(4"x"^2 - 1)` dx

Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx

Evaluate the following.

`int 1/(4x^2 - 20x + 17)` dx

Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`

Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx

Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` dx