MCQ

MCQ 11 Mark

In a town of $840$ persons, $450$ persons read Hindi, $300$ read English and $200$ read both. Then the number of person who read neither is

A
$180$
B
$210$
C
$260$
✓
$290$

Answer

Correct option: D.

$290$

Total number of person $= 840$
Person who read Hindi $= 450$
$\Rightarrow n(A) = 450$
Person who read English $= 300$
$\Rightarrow n(B) = 300$
Person who read both $= 200$
$\Rightarrow n(A ∩ B) = 200$
Now, $n(A ∪ B) = n(A) + n(B) – n(A ∩ B)$
$= 450 + 300 – 200$
$= 750 – 200 = 550$
$\therefore$ Person who read neither $= 840 – 550 = 290$

View full question & answer→

MCQ 21 Mark

If $A$ and $B$ are two sets such that $n(A) = 22, n(B) = 18$ and $n(A ∪ B) = 35$, then $n(A ∩ B)$

A
$4$
✓
$5$
C
$15$
D
$75$

Answer

Correct option: B.

$5$

$n(A) = 22, n(B) = 18$
$n(A ∪ B) = 35$
$n( A ∪ B) = n(A) + n( B) – n(A ∩ B)$
$35 = 22 + 18 – n(A ∩ B)$
$n(A ∩ B) = 40 – 35 = 5 $

View full question & answer→

MCQ 31 Mark

If $ξ = ($all digits in our number system$), A = \{x | x$ is prime$\}$ and $B = \{x | x$ is even$\}$, then $B – A$ is

A
$\{4, 6, 8\}$
✓
$\{0, 4, 6, 8\}$
C
$\{3, 5, 7\}$
D
$\{2\}$

Answer

Correct option: B.

$\{0, 4, 6, 8\}$

$ξ = \{$all digits in our number system$\}$
$= \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$
$A = \{x | x$ is prime$\}$
$= \{2, 3, 5, 7\}$
$B = \{x | x$ is even$\}$
$= \{0, 2, 4, 6, 8\}$
$B – A = \{0, 4, 6, 8\}$

View full question & answer→

MCQ 41 Mark

If $ξ= \{x | x \in W, x \leq 12\}, A – \{x | x$ is a multiple of $3\}$ and $B = \{x | x$ is a multiple of $4\},$ then $A ∩ B$ is

A
$ϕ$
B
$\{0\}$
C
$\{12\}$
✓
$\{0, 12\}$

Answer

Correct option: D.

$\{0, 12\}$

$A = \{x | x$ is a multiple of$ 3\}$
$= \{0, 3, 6, 9, 12\}$
$B = \{x | x$ is a multiple of $4\}$
$= \{0, 4, 8, 12\}$
$\therefore A ∩ B = \{0, 12\}$

View full question & answer→

MCQ 51 Mark

If $ξ = W$ and $A = \{x | x \in W$ and $x \leq 10\}$, then $A\ ’$ is

A
$ϕ$
B
$\{x | x \in W$ and $0 ≤ x ≤ 10\}$
C
$\{x | x\ ϵ\ W$ and $x ≤ 10\}$
✓
$\{x | x\ ϵ\ W$ and $x ≥ 11\}$

Answer

Correct option: D.

$\{x | x\ ϵ\ W$ and $x ≥ 11\}$

$ξ = W, A = \{x | x \in W$ and $x \leq 10\}$
$= \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$
$\therefore A’ = \{x | x \in W$, and $x \geq 11\}$

View full question & answer→

MCQ 61 Mark

$A ∩ ξ$ is same as

A
$A$
B
$ϕ$
C
$A\ ’$
D
$ξ$

Answer

$A ∩ ξ = A (a)$

View full question & answer→

MCQ 71 Mark

If $A$ is any set, then $A ∪ ϕ$ is

✓
$A$
B
$ϕ$
C
$2,$
D
none of these

Answer

Correct option: A.

$A$

$A ∪ ϕ = A$
Where $A$ is any set.

View full question & answer→

MCQ 81 Mark

If $A$ and $B$ are two sets, then $A – B$ is defined as

A
$\{x |x\ \epsilon \ A$ or $x\ \epsilon \ B\}$
B
$\{x | x\ \epsilon \ A$ and $x\ \epsilon \ B\}$
✓
$\{x | x\ \epsilon \ A$ and $x\ ∉\ B\}$
D
$\{x | x\ \epsilon \ B$ and $x\ ∉\ A\}$

Answer

Correct option: C.

$\{x | x\ \epsilon \ A$ and $x\ ∉\ B\}$

$A$ and $B$ are two sets
$\therefore A – B = \{x |x \in A$ and $x ∉ B\}$

View full question & answer→

MCQ 91 Mark

If $P = \{-1, 0, 1, 2, 5\}$ and $Q = \{3, 5, 7\}$, then $P ∪ Q$ is

A
$\{5\}$
B
$\{-1, 0, 1, 2, 3, 7\}$
✓
$\{-1, 0, 1, 2, 3, 5, 7\}$
D
none of these

Answer

Correct option: C.

$\{-1, 0, 1, 2, 3, 5, 7\}$

$P = \{-1, 0, 1, 2, 5\}$
$Q = \{3, 5, 7\}$
$\therefore P ∪ Q = \{0, 1, 2, 3, 5, 7\}$

View full question & answer→

MCQ 101 Mark

If $A = \{x | x$ is a colour of rainbow$\}$ and $B = \{$white, red, green$\}$, then $A ∩ B$ is

A
$B$
B
$\{$green$\}$
C
$\{$red$\}$
✓
$\{$green, red$\}$

Answer

Correct option: D.

$\{$green, red$\}$

$A = \{x | x$ is a colour of rainbow$\}$
$= \{$red, green, blue, voilet, yellow, Indigo, orange$\}$
$B = \{$white, red, green$\}$
$A ∩ B = \{$red, green$\}$

View full question & answer→

MATHS MCQ

Test yourself on this topic