HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Answer the following:

Find f(x) if g(x) = x² + x – 2 and (g ° f) (x) = 4x² – 10x + 4

Answer the following:

Find f(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`

Answer the following:

Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^2)`

Answer the following:

Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`

Evaluate the following limit:

`lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`

Evaluate the following limit :

`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`

Evaluate the following limit :

`lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`

Evaluate the following limit :

`lim_(x -> -2) [(-2x - 4)/(x^3 + 2x^2)]`

Evaluate the following limit :

`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`

Evaluate the following limit :

`lim_(u -> 1) [(u^4 - 1)/(u^3 - 1)]`

Evaluate the following limit :

`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`

Evaluate the following limit :

`lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`

Evaluate the following limit :

`lim_(Deltax -> 0) [((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)]`

Evaluate the following limit :

`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`

Evaluate the following limit :

`lim_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`

Evaluate the following limit :

`lim_(y -> 1/2) [(1 - 8y^3)/(y - 4y^3)]`

Evaluate the following limit :

`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`

Evaluate the following limit:

`lim_(x -> 1) [(x^4 - 3x^2 + 2)/(x^3 - 5x^2 + 3x + 1)]`

Evaluate the following limit :

`lim_(x -> 1) [(x + 2)/(x^2 - 5x + 4) + (x - 4)/(3(x^2 - 3x + 2))]`

Evaluate the following limit :

`lim_(x -> "a")[1/(x^2 - 3"a"x + 2"a"^2) + 1/(2x^2 - 3"a"x + "a"^2)]`