Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

$(x, y)$ and $(p, q)$ are two ordered pairs. Find the values of $x$ and $p$, if $(3x - 1, 9) = (11, p + 2)$

  1. $x = 4, p = 9$
  2. $x = 6, p = 7$
  3. $x = 4, p = 5$
  4. $x = 4, p = 7$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given$(x,y)=(p,q)$
$(3x - 1, 9) = (11, p + 2)$
By equating 
$3x - 1 = 11$
$3x = 12$
$x = 4$
$9 = p + 2$
$p = 7$
So, the value of $x = 4, p = 7.$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

 $(x, y)$ and $(p, q)$ are two ordered pairs. Find the values of $p$ and $y$, if $(4y + 5, 3p - 1) = (25, p + 1)$

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

Given $(x,y)=(p,q)$
$(4y + 5, 3p - 1) = (25, p + 1)$
On equating we get
$4y + 5 = 25$
$4y = 25 - 5$
$4y = 20$
$y = 5$
$3p - 1 = p + 1$
$3p - p = 1 + 1$
$2p = 2$
$p = 1$
So, the value of$ p = 1, y = 5$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

If A and B are two non-empty sets having n elements in common, then what is the number of common elements in the sets $A\times B$ and $B\times A$?

  1. $n$
  2. $n^2$
  3. $2n$

  4. Zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Say A has x elements and B has y elements in total. 


Their cartesian product $A\times B$ will have $x\times y$ elements.

Hence if they have n elements in common. $n^2$ common elements are present in the products $A\times B$ and $B\times A$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

Let $A=\left{ x\in W,the\quad set\quad of\quad whole\quad numbers\quad and\quad x<3 \right} $

$B=\left{ x\in N,the\quad set\quad of\quad natural\quad numbers\quad and\quad 2\le x<4 \right} $ and $C=\left{ 3,4 \right} $, then how many elements will $\left( A\cup B \right) \times C$ conatin?

  1. $6$
  2. $8$
  3. $10$
  4. $12$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$A={0,1,2}, B={2,3}$ and $C={3,4}$
$A \cup B={0,1,2,3}$
No. of elements in $(A\cup B)\times C$ $=$ No. of elements in $(A \cup B)\times $ No. of elements in $C$$=4\times 2=8$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

Let $A = \left{ a,b,c,d \right}$ and $ B=\left{ x,y,z \right}$. What is the number of elements in $ A\times B$?

  1. $6$
  2. $7$
  3. $12$
  4. $64$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given sets are $A={a,b,c,d}$ and ${x,y,z}$ 

So $A\times B={(a,x),(a,y),(a,z),(b,x),(b,y),(b,z),(c,x),(c,y),(c,z),(d,x),(d,y),(d,z)}$
No. of elements in $A\times B$ is $3\times 4=12$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

If $A = \left{ 1,2 \right}$, $B = \left{ 2,3 \right}$ and $ C = \left{ 3,4 \right}$, then what is the cardinality of $ \left( A\times B \right) \cap \left( A\times C \right) $

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

Now, $A\times B=\{ (1,2),(1,3),(2,2),(2,3)\}$ 

$A\times C=\{ (1,3),(1,4),(2,3),(2,4)\} $ And

$ (A\times B)\cap (A\times C)=\{ (1,3),(2,3)\} $

So cardinality is $2$.

Hence, option C is correct.