HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Show that f(x) = x – cos x is increasing for all x.

Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.

Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`

Choose the correct option from the given alternatives :

Let f(x) = x³ – 6x² + 9x + 18, then f(x) is strictly decreasing in ______.

Solve the following : Find the intervals on which the function y = x^x, (x > 0) is increasing and decreasing.

Solve the following:

Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.

Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =

Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =

Choose the correct options from the given alternatives :

`int (e^x(x - 1))/x^2*dx` =

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)`