Tag: finite and infinite sets

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Questions Related to finite and infinite sets

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

Which of the following are infinite set?
$(i)$The set of lines which are parallel to x-axis.
$(ii)$The set of animals living on the earth.
$(iii)$ The set of numbers which are multiple of $5.$
$(iv)$ The set of the circles passing through the origin $(0,0).$

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

$(i)$The set of lines which are parallel to x-axis is an infinite set because line parallel to x-axis are infinite in number.
$(ii)$The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (although it is quite a big number)
$(iii)$ The set of numbers which are multiple of $5$ is an infinite numbers multiples of $5$ are infinite in number.
$(iv)$ The set of the circles passing through the origin $(0,0)$ is an infinite set because infinite number of circles can pass through the origin.

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

Which of the following sets are finite sets.
$(i)$ The sets of months in a year.
$(ii){1,2,3,....}$
$(iii){1,2,3,...,99,100}$
$(iv)$ The set of positive integers greater than $100.$ 

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

$(i)$ The sets of months in a year is a finite set because it has $12$ elements.
$(ii){1,2,3,....}$ is an infinite set as it has infinite number of elements.
$(iii){1,2,3,...,99,100}$ is a finite set as it has number from $1$ to $100$ which is finite in number.
$(iv)$ The set of positive integers greater than $100$ is an infinite set because positive integers greater than $100$ are infinite in number. 

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

State which of the following are infinite sets.
$(i)A={x:x\in Z: x $ is odd$}$
$(ii)B={x:x\in R:<-10}$

  1. $(i)$ only
  2. $(ii)$ only
  3. $(i)$ and $(ii)$ both
  4. Neither $(i)$ nor $(ii)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$(i)A={x:x\in Z: x^2 $ is even $}$
$A={...,-3,-1-1,3,...}$ which is an infinite set.
$(ii)B={x:x\in R:-2<x<-4}$
$B={...,-14,-13,-12,-11}$ so it is an infinite set.

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

State whether the following statement is True or False
$A= { x| x\ is\ a\ negative\ integer\ ;x>-5 }$ is a finite set.

  1. True

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

We have to state whether the statement "$A={x|x:is:a:negative:integer:;x>-5} : is:a:finite : set$" is true or false.

Consider $A={x|x:is:a:negative:integer:;x>-5} $
                     $={-4,-3,-2,-1} $ which has finite number of elements.

So $A$ is a finite set.

Hence the given statement is true.

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

If the system of equation $x+2y-3z=1$, $(p+2)z=3$, $(2p+1)y+z=2$ has infinite number of solutions, then the value of p is not equal to.

  1. $-2$
  2. $-\displaystyle\frac{1}{2}$
  3. $0$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$x+2y-3z=1$
$(p+2)z=3$
$(2p+1)y+z=2$
let $p=5$, $s\in R/ \left\{ -2, 1/2\right\}$
$\therefore z=\dfrac{3}{s+2}$
$\Rightarrow y=\left(2-\dfrac{3}{s+2}\right)\dfrac{1}{(2s+1)}\Rightarrow \dfrac{2s+1}{(s+2)(2s+1)}-\dfrac{1}{s+2}$
$[As\ 2s+1\neq 0]$
$\therefore x=3z+1-2y$
$=\dfrac{9}{s+2}+1-\dfrac{2}{s+2}=\dfrac{7}{s+2}+1$
$\therefore$ solutions $(x, y, z)=\left(\dfrac{7}{s+2}+1, \dfrac{1}{s+2}, \dfrac{3}{s+2}\right)$
is an infinite set,
$\therefore p$ cannot be equal to $-2$ or $1/2$