Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

Given $A={a,b,c,d,e,f,g,h}$ and $B={a,e,i,o,u}$ then $A\cap B$ is equal to

  1. $\{a,e\}$
  2. $\{f,g\}$
  3. $\{g,h\}$
  4. $\{i,u\}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $A=\{a,b,c,d,e,f,g,h\}$ and $B=\{a,e,i,o,u\}$

$ A$ intersection $B $, which means a new set can be constructed by determining which members are common among the two sets.

So as per the question:-
$A\cap B=\left\{ a,e \right\}$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

If X=(multiples of $2$ ), Y = ( multiples of $5$) , Z= (multiples of $10$), then $ \displaystyle X \cap(Y\cap Z)    $ is equal to 

  1. Multiples of $10$
  2. Multiples of $5$
  3. Multiples of $2$
  4. Multiples of $7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$x= (multiples\ of\ 2\ is\ 2, 4, 6, 8, 10.............)$
$y=(multiples\ of\ 5\ is\ 5, 10,15,20,25.........)$
$z=(multiples\ of\ 10\ is\ 10,20,30,40...........)$
Then, $ X\cap(Y\cap Z)$

Apply the value
$=(2, 4, 6, 8, 10,.......)\cap[ (5, 10, 15, 20, 25,........)\cap (10, 20, 30, 40,.......)]$
$=(2, 4, 6, 8, 10,.......)\cap (10, 20, 30,........)$
$=(10, 20, 30,........)$

Hence, this is multiple of $10$.


Hence, this is the answer.

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

There are $19$ hockey players in a club. On a particular day $14$ were wearing the prescribed hockey shirts, while $11$ were wearing the prescribed hockey pants. None of them was without hockey pant or hockey shirt. How many of them were in complete hockey uniform?

  1. $8$
  2. $6$
  3. $9$
  4. $7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$n(S\cup P) = 19$

$n(S)=14 $
$ n(P)= 11 $
$n(S\cup P)= n(S)+n(P)-n(S\cap P)$
$19=14+11-n(S\cap P)$
$n(S\cap P)= 25-19 = 6$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

Out of $450$ students in a school, $193$ students read Science Today, $200$ students read Junior Statesman, while $80$ students read neither. How many students read both the magazines?

  1. $137$
  2. $80$
  3. $57$
  4. $23$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$n(U)=450$

n(Students read Science Today) $=193 =n(S) $

n(Students read Junior Statesman) $=200=n(J) $

n(students read neither) $=80$

$n(S \cup J) $= n(U)-n(students read neither) $= 450-80=370$

Also, $n(S \cup J) = n(S) + n(J)-n(S\cap J) $

$370 = 193+200-n(S\cap J) $

$n(S\cap J)=393-370 =23 $

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

In a community of $175$ persons, $40$ read the Times, $50$ reads the Samachar and $100$ do not read any. How many persons read both the papers?

  1. $10$
  2. $15$
  3. $20$
  4. $25$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$n(U)=175$

n(read Times) $=40 =n(T) $

n(read the samachar) $=50 = n(S) $

n(do not read any) $= 100$

$n(T\cup S)=  n(U)-$ n(do not read any) $= 175-100 =75$

$\therefore n(T \cup S)= n(T)+ n(S)- n(T\cap S) $

$n(T\cap S) =90-75 =15$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

In a group of $15, 7$ have studied, German, $8$ have studied French, and $3$ have not studied either. How many of these have studied both German and French?

  1. $0$
  2. $3$
  3. $4$
  4. $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$n(U)=15$

$n(German) =7 =n(G) $

$n(French) =8 =n(F) $

n(students who have studied neither) $=3$

$n(G \cup F) = n(U)-$ n(students who studied neither) $= 15-3=12 $

$n(G \cup F) = n(G) + n(F)-n(G\cap F) $

$12 = 7+8-n(G\cap F) $

$n(G\cap F)=15-12=3 $

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

In a class consisting of $100$ students, $20$ know English and $20$ do not know Hindi and $10$ know neither English nor Hindi. The number of students knowing both Hindi and English is

  1. $5$
  2. $10$
  3. $15$
  4. $20$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$n(U)=100$

$n(English) =20 =n(E) $

$n(Hindi) =100- 20= 80 =n(H) $

n(students who have studied neither Hindi nor English) $=10$

$n(E \cup H) = n(U)-$ n(students who studied neither) $= 100-10 =90 $

$n(E \cup H) = n(E) + n(H)-n(E\cap H) $

$90 = 20+80-n(E\cap H) $

$n(E\cap H)= 10$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

If $A = \left {1, 2, 3, 4, 5, 6, 7, 8\right }$ and $B \left {1, 3, 5, 7\right }$, then find $A - B$ and $A \cap B$

  1. $\left \{3, 5\right \}$ and $\left \{2, 4, 6\right \}$
  2. $\left \{2, 4, 6\right \}$ and $\left \{1, 5\right \}$
  3. $\left \{2, 4, 6, 8\right \}$ and $\left \{1, 3, 5, 7\right \}$
  4. $\left \{1, 3, 5, 8\right \}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$A=\{1,2,3,4,5,6,7,8\}$

$B=\{1,3,5,7\}$

$A-B=\{1,2,3,4,5,6,7,8\} - \{1,3,5,7\} = \{2,4,6,8\}$

$A \cap B = \{1,2,3,4,5,6,7,8\} \cap \{1,3,5,7\} =\{1,3,5,7\}$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

In a certain group of $36$ people, $18$ are wearing hats and $24$ are wearing sweaters. If six people are wearing neither a hat nor a sweater, then how many people are wearing both a hat and a sweater?

  1. $30$
  2. $22$
  3. $12$
  4. $8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$n(U)=36$

$n(Hats) =18 =n(H) $

$n(Sweaters) =24 =n(S) $

n(Wearing neither hat nor Sweater) =6

$n(S \cup H) = n(U)-$ n(Wearing neither hat nor sweater) $= 36-6 = 30 $

$n(S \cup H) = n(S) + n(H)-n(S\cap H) $

$30 = 24+18-n(S\cap H) $

$n(S\cap H)=42-30 = 12 $