MCQ

MCQ 11 Mark

The domain of the relation, $R=\{(x, y): x, y \in Z$, $z x y=4\}$ is

✓
$\{-4,-2,-1,1,2,4\}$
B
$\{-2,-1,1,2,4\}$
C
$\{-2,-1,1,2\}$
D
$\{1,2,4\}$

Answer

Correct option: A.

$\{-4,-2,-1,1,2,4\}$

(A) $\{-4,-2,-1,1,2,4\}$
Explanation : Given,
$ \begin{aligned}
R & =\{(x, y): x, y \in Z, z x y=4\} \\
& =\{(-4,-1),(-2,-2), \\
& (-1,-4),(1,4),(2,2),(4,1)\}
\end{aligned}
$
Therefore, domain of $R=\{-4,-2,-1,1,2,4\}$

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MCQ 21 Mark

If $A \times B=\{(a, x),(a, y),(b, x),(b, y)\}$, then set $A$ and $B$ are given as

A
$A=\{a\}, B=\{x, y\}$
✓
$A=\{a, b\}, B=\{x, y\}$
C
$A=\{a, b\}, B=\{x\}$
D
none of these

Answer

Correct option: B.

$A=\{a, b\}, B=\{x, y\}$

(B) $A=\{a, b\}, B=\{x, y\}$
Explanation: If $A=\{a, b\}$ and $B\{x, y\}$, then $A \times B=$
$\{(a, x),(a, y),(b, x),(b, y)\}$.

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MCQ 31 Mark

If $(x-2, y+5)=\left(-2, \frac{1}{3}\right)$ are two equal ordered pairs, then values of $x$ and $y$ are :

✓
$x=0, y=\frac{-14}{3}$
B
$x=4, y=\frac{-14}{3}$
C
$x=0, y=\frac{-4}{3}$
D
$x=4, y=\frac{-4}{3}$

Answer

Correct option: A.

$x=0, y=\frac{-14}{3}$

(A) $x=0, y=\frac{-14}{3}$
Explanation : Given that: $(x-2, y+5)=(-2,13)$
$\Rightarrow x-2=-2 \Rightarrow x=0$ and $y+5=\frac{1}{3} \Rightarrow y=\frac{1}{3}-5=$ $\frac{-14}{3}$

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MCQ 41 Mark

Let $n(A)=m$, and $n(B)=n$. Then the total number of possible relations that can be defined from $A$ to $B$ is

A
$m^n$
B
$n^m-1$
C
$m n-1$
✓
$2^{m n}$

Answer

Correct option: D.

$2^{m n}$

(D) $2^{m n}$
Explanation : Given, $n(A)=m$, and $n(B)=n$
$
\therefore n(A \times B)=n(A) \cdot n(B)=m n
$
So, the total number of non-empty relations from $A$ to $B : 2^{m n}$.

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MCQ 51 Mark

The set $\{x: x \in R,-3 \leq x<7\}$ as an interval can be written as

A
$[-3,-7]$
B
$[3,7]$
C
$(-3,7)$
✓
$[-3,7)$

Answer

Correct option: D.

$[-3,7)$

(D) $[-3,7)$
Explanation : Because the set of all real numbers lying between $a$ and $b$ and including the number $a$ is said to form a closed open interval, denoted by $[a, b)$. It is written as $[a, b)=\{x: x \in R, a \leq x<b\}$.

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MCQ 61 Mark

If $A=\{0,\{0,1\}\}$, then cardinal number set of $P(A)$ is

A
2
B
3
✓
4
D
1

Answer

Correct option: C.

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MCQ 71 Mark

The power set of $A=\phi$ is

✓
$\{\phi\}$
B
$\{0\}$
C
$\{\phi,\{0\}\}$
D
none of these

Answer

Correct option: A.

$\{\phi\}$

(A) $\{\phi\}$
Explanation : As only subset of $\phi$ is $\phi$, thus $P(A)=\{\phi\}$

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MCQ 81 Mark

If $P=\left\{x: \frac{x-8}{2}=4\right\}$, the $P$ is a

A
empty set
✓
singleton set
C
infinite set
D
none of these

Answer

Correct option: B.

singleton set

(B) singleton set
Explanation : Given, $P=\left\{x: \frac{x-8}{2}=4\right\}$, therefore,
$\frac{x-8}{2}=4 \Rightarrow x-8=8 \Rightarrow x=16$
$\begin{array}{l}\Rightarrow \text { Set } P \text { will have one element i.e., } P=\{16\} \\ \Rightarrow \text { Set } P \text { is not a empty set, it is a singleton set. }\end{array}$

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