Tag: set language

Quizzes (7) Questions (71)

Questions Related to set language

Multiple choice maths set concepts finite and infinite sets types of sets set language

Which of the following sets is not a finite set ?

  1. $\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in R\} $
  2. $\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in Z\} $
  3. $\{ (x,y):{ x }^{ 2 }\le y\le |x|,\ \ x,y\in Z\} $
  4. $\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }=1,\ \ x,y\in Z\} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in R} $ consists of all the points in the first quadrant which lie inside the circle ${ x }^{ 2 }+{ y }^{ 2 }=1$ and above the line $x+y=1$ .So, it is not a finite set.
Option $A$ is correct.

Multiple choice maths set concepts finite and infinite sets types of sets set language

Which of the following is incorrect.

  1. The power set of an infinite set is infinite.

  2. The union of two infinite set is infinite.

  3. The intersection of two infinite set is infinite.

  4. The cardinality of an infinite set is infinite.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The intersection of an infinite set may be finite.
Example:
$A={x:x\in N; x>2}$
$B={x:x\in I; x<5}$
Here, Both $A$ and $B$ are infinite but its intersection are finite.

Multiple choice maths set concepts finite and infinite sets types of sets set language

Define infinite set .
Is ${x:x\in R:1\le x\le 3}$ a infinite set?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Definition: A set having infinite number of elements is known as infinite set.
 ${x:x\in R:1\le x\le 3}$ is a infinite set because since $x\in R$, there are infinte number of real numbers lie in between two numbers.

Multiple choice maths set concepts finite and infinite sets types of sets set language

Let S be the set of all values of x such that $log _{2x}(x^{2}+5x+6)<1$ then the sum of all integral value of x in the set S, is

  1. 0

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$ log _{2x}(x^{2}+5x+6)< 1 $

$ \Rightarrow x^{2}+5x+6< 2x^1 $

$ \Rightarrow x^{2}+3x+6< 0 $

But $ x^{2}+3x+6 = 0 $ has no real roots 

$ \therefore S$  is an empty set 

$ \therefore $ sum of all integral values of $ x = 0 $ 
Multiple choice maths set concepts finite and infinite sets types of sets set language

If $A=\left{1, 2, 3\right}$, then the numbers of subsets of set $A$ containing element $3$, is 

  1. $24$
  2. $28$
  3. $8$
  4. $16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The set $\left\{1, 2, 3\right\}$ has $8$ subsets. The first subset would be the null or empty subset, which contains none of the numbers: $\left\{\right\}$.
 The null set is a subset of every set. The other subsets would include some of the numbers in the set, but not all of them: $\left\{1\right\}$,$\left\{2\right\}$,$\left\{3\right\}$,$\left\{1,2\right\}$,$\left\{1,3\right\}$,$\left\{2,3\right\},\{1,2,3\}$
Multiple choice maths set concepts finite and infinite sets types of sets set language

Let ${ a } _{ 1 },{ a } _{ 2 },{ a } _{ 3 },............{ a } _{ 10 }$ be in G.P. with ${ a } _{ i }>0$ for $i=1,2,....,10$ and $S$ be the set of pairs $(r,k),r\quad k\in N$ ( the set of natural numbers) for which
$\left| { log } _{ e }{ a } _{ 1 }^{ r }{ a } _{ 2 }^{ k }\quad { log } _{ e }{ a } _{ 2 }^{ r }{ a } _{ 3 }^{ k }\quad { log } _{ e }{ a } _{ 3 }^{ r }{ a } _{ 4 }^{ k }\ { log } _{ e }{ a } _{ 4 }^{ r }{ a } _{ 5 }^{ k }\quad { log } _{ e }{ a } _{ 5 }^{ r }{ a } _{ 6 }^{ k }\quad { log } _{ e }{ a } _{ 6 }^{ r }{ a } _{ 7 }^{ k }\ { log } _{ e }{ a } _{ 7 }^{ r }a _{ 8 }^{ k }\quad { log } _{ e }{ a } _{ 8 }^{ r }{ a } _{ 9 }^{ k }\quad { log } _{ e }{ a } _{ 9 }^{ r }{ a } _{ 10 }^{ k } \right| =0$
Then the number of elements in S, is :

  1. Infinitely many

  2. 4

  3. 10

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The determinant of the matrix involves logarithmic terms of a geometric progression. Since the rows/columns are linearly dependent based on the properties of logarithms and geometric sequences, the determinant is zero for any r and k in N, leading to infinitely many solutions.