PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

The point at which the maximum value of x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x ≥ 0, y ≥ 0 is obtained, is ______.

The value of objective function is maximum under linear constraints ______.

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Find `intsqrtx/sqrt(a^3-x^3)dx`

Integrate the functions:

`(1+ log x)^2/x`

Give an example of a function which is one-one but not onto ?

Give an example of a function which is not one-one but onto ?

Give an example of a function which is neither one-one nor onto ?

Which of the following functions from A to B are one-one and onto?
 f₁ = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}

Which of the following functions from A to B are one-one and onto?

 f₂ = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {a, b, c}

 Which of the following functions from A to B are one-one and onto ?  

f₃ = {(a, x), (b, x), (c, z), (d, z)} ; A = {a, b, c, d,}, B = {x, y, z}. 

Prove that the function f : N → N, defined by f(x) = x² + x + 1, is one-one but not onto

Let A = {−1, 0, 1} and f = {(x, x²) : x ∈ A}. Show that f : A → A is neither one-one nor onto.

Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x²

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x²

Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x³

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x³

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = |x|

Classify the following function as injection, surjection or bijection :

f : Z → Z, defined by f(x) = x² + x