HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following:

Find f ° g and g ° f: f(x) = 256x⁴, g(x) = `sqrt(x)`

Answer the following:

If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x

Answer the following:

If f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)` then show that (f ° g) (x) = x

Answer the following:

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

1 < |x − 1| < 4

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 − x − 6| = x + 2

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 − 9| + |x² − 4| = 5

Answer the following:

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

2[2x − 5] − 1 = 7

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)]`