HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose the correct options from the given alternatives :

`int f x^x (1 + log x)*dx`

Choose the correct options from the given alternatives :

`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =

Choose the correct options from the given alternatives : 

`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =

`int logx/(log ex)^2*dx` = ______.

Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =

Choose the correct options from the given alternatives :

`int (e^(2x) + e^-2x)/e^x*dx` =

Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`

Integrate the following with respect to the respective variable:

`x^7/(x + 1)`

Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x

Determine the order and degree of the following differential equation:

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`

Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`

Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`

Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 0`

Determine the order and degree of the following differential equation:

(y''')² + 3y'' + 3xy' + 5y = 0

Determine the order and degree of the following differential equation:

`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`

Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`

Determine the order and degree of the following differential equation:

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`

Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`

Choose the correct option from the given alternatives:

The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.