हिंदी

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 ______. - Mathematics

Advertisements
Advertisements

प्रश्न

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 ______.

विकल्प

  • 144

  • 12

  • 24

  • 64

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

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 24.

Explanation:

The total number of injective mappings from the set containing 3 elements into the set containing 4 elements is 4P3 = 4! = 24.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ ८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 20 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Check the injectivity and surjectivity of the following function:

f : Z → Z given by f(x) = x2


Check the injectivity and surjectivity of the following function:

f : R → R given by f(x) = x2


Let A = R − {3} and B = R − {1}. Consider the function f : A → B defined by f(x) = `((x- 2)/(x -3))`. Is f one-one and onto? Justify your answer.


Give examples of two functions fN → Z and gZ → Z such that g o f is injective but gis not injective.

(Hint: Consider f(x) = x and g(x) =|x|)


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 : R → R, defined by f(x) = x3 + 1


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 → Q, defined by f(x) = x3 + 1


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 3 − 4x


Find  fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → Rg(x) = 3x3 + 1.


Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.


Let  f  be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.


Let f be a real function given by f (x)=`sqrt (x-2)`
Find each of the following:

(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f2

Also, show that fof ≠ `f^2` .


Consider f : R → R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with inverse f−1 of f given by f−1 `(x)= sqrt (x-4)` where R+ is the set of all non-negative real numbers.


If f : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.


If A = {1, 2, 3} and B = {ab}, write the total number of functions from A to B.


Let f be an invertible real function. Write ( f-1  of ) (1) + ( f-1  of ) (2) +..... +( f-1 of ) (100 )


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.


If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]


If f(x) = 4 −( x - 7)3 then write f-1 (x).


If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =

 

 


The  function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is

 


\[f : R \to R\] is defined by

\[f\left( x \right) = \frac{e^{x^2} - e^{- x^2}}{e^{x^2 + e^{- x^2}}} is\]

 


\[f : Z \to Z\]  be given by

 ` f (x) = {(x/2, ", if  x is even" ) ,(0 , ", if  x  is  odd "):}`

Then,  f is


Let  \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation

\[fog \left( x \right) = gof \left( x \right)\] is 



Let [x] denote the greatest integer less than or equal to x. If \[f\left( x \right) = \sin^{- 1} x, g\left( x \right) = \left[ x^2 \right]\text{  and } h\left( x \right) = 2x, \frac{1}{2} \leq x \leq \frac{1}{\sqrt{2}}\]

 


If  \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to


Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is


Write about strcmp() function.


Let f, g: R → R be two functions defined as f(x) = |x| + x and g(x) = x – x ∀ x ∈ R. Then, find f o g and g o f


Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto


Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.


Let f : R → R be defind by f(x) = `1/"x"  AA  "x" in "R".` Then f is ____________.


Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • The function f: R → R defined by f(x) = x − 4 is ____________.

A function f: x → y is said to be one – one (or injective) if:


Let f: R→R be defined as f(x) = 2x – 1 and g: R – {1}→R be defined as g(x) = `(x - 1/2)/(x - 1)`. Then the composition function f (g(x)) is ______.


Consider a set containing function A= {cos–1cosx, sin(sin–1x), sinx((sinx)2 – 1), etan{x}, `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}. B, C, D, are subsets of A, such that B contains periodic functions, C contains even functions, D contains odd functions then the value of n(B ∩ C) + n(B ∩ D) is ______ where {.} denotes the fractional part of functions)


Let a function `f: N rightarrow N` be defined by

f(n) = `{:[(2n",", n = 2","  4","  6","  8","......),(n - 1",", n = 3","  7","  11","  15","......),((n + 1)/2",", n = 1","  5","  9","  13","......):}`

then f is ______.


Let f(x) be a polynomial function of degree 6 such that `d/dx (f(x))` = (x – 1)3 (x – 3)2, then

Assertion (A): f(x) has a minimum at x = 1.

Reason (R): When `d/dx (f(x)) < 0, ∀  x ∈ (a - h, a)` and `d/dx (f(x)) > 0, ∀  x ∈ (a, a + h)`; where 'h' is an infinitesimally small positive quantity, then f(x) has a minimum at x = a, provided f(x) is continuous at x = a.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×