Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.

Let f: R → R be defined by f(x) = 3x – 4. Then f^–1(x) is given by ______.

Let f: R → R be defined by f(x) = x² + 1. Then, pre-images of 17 and – 3, respectively, are ______.

The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______

Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______

Let A be a finite set. Then, each injective function from A into itself is not surjective.

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.

Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D

Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f^–1 

If f: R → R is defined by f(x) = x² – 3x + 2, write f(f (x))

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(x, y): x is a person, y is the mother of x}

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(a, b): a is a person, b is an ancestor of a}

Let C be the set of complex numbers. Prove that the mapping f: C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.

Let the function f: R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto

Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

f = {(1, 4), (1, 5), (2, 4), (3, 5)}

Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

g = {(1, 4), (2, 4), (3, 4)}

Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

h = {(1,4), (2, 5), (3, 5)}

Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

k = {(1,4), (2, 5)}