HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x²] − 5[x] + 6 = 0

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x − 2] + [x + 2] + {x} = 0

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

`[x/2] + [x/3] = (5x)/6`

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`

Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = e^x, g(x) = log x

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)]`