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Questions Related to maths

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

For any three sets A, B and C, $A \cap (B \cup C)$ is

  1. $(A\cup B)\cup (B\cap C)$
  2. $(A\cap B)\cup (A\cap C)$
  3. $A\cup (B\cap C)$
  4. $(A\cup B)\cap (B\cup C)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the problem statement we are taking union of $B$ and $C$ and then taking its intersection with $A$.

This means $A\cap (B\cup C)$will contain elements that are in $A$ and are in either $B$ or $C$.
$\therefore A\cap (B\cup C) $ is equivalent to taking intersection of $A,B$ and $A,C$ and then taking there union i.e. $(A\cap B)\cup(A\cap C)$
Hence, option B is correct.

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

Define finite set.
Is $A=$set of animals on the earth a finite set.

  1. True

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

Definition: A finite set is a set which has fixed or finite number of elements.
$A=$ Set of animals on the earth is a finite set because number of animals on the earth is large in number, but it is finite/fixed.

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

State which of the following are finite sets.
$(i){x:x\in N }$ and $(x-1)(x-2)=0.$
$(ii){x:x\in N }$ and $x$ is prime.
$(ii){x:x\in N }$ and $x$ is odd.

  1. $(i)$ only
  2. $(i),(ii)$ and $(iii)$
  3. $(i)$ and $(ii)$
  4. $(ii)$ and $(iii)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$(i)(x-1)(x-2)=0$

$\Rightarrow x-1=0$ or $x-2=0$
$\Rightarrow x=1$ or $x=2$, Number of solutions of equation are finite.
$(ii){2,3,5,7,11,...}$, This set contains infinte number of elements.
$(iii){..,1,3,5,7,...}$, This set contains infinite number of elements. 

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 $