Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = x³ + 1

Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x³ − x

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = sin²x + cos²x

Classify the following function as injection, surjection or bijection :

f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`

Classify the following function as injection, surjection or bijection :

f : Q → Q, defined by f(x) = x³ + 1

Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 5x³ + 4

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 3 − 4x

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 1 + x²

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = `x/(x^2 +1)`

If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.

Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.

Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`

Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|  

Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x² 

Set of ordered pair of  a function? If so, examine whether the mapping is injective or surjective :{(x, y) : x is a person, y is the mother of x}

Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a} 

Let A = {1, 2, 3}. Write all one-one from A to itself.

If f : R → R be the function defined by f(x) = 4x³ + 7, show that f is a bijection.

Show that the exponential function f : R → R, given by f(x) = e^x, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?