Difference of Two Sets

Q. A person always prefers to eat 'parantha' and ’vegetable dish’ in his meal on Monday, Tuesday and Wednesday but on other days he adds salads to his meal.
How many ways can he make his platter in a marriage party if there are three types of paranthas, four types of ‘vegetable dish’, three types of ’salads’ and two types of ‘sauces’ ?

1. If the marriage party is on Monday, then he can make his platter in $3360$ ways
2. If the marriage party is on Sunday, then he can make his platter in $3360$ ways
3. If the marriage party is on Sunday, then he can make his platter in $2940$ ways
4. If the marriage party is on Monday, then he can make his platter in $3300$ ways

Q. In a group of $50$ people, $35$ speak Hindi and $25$ speak both English and Hindi. Then how many people speak only English ? (Assuming each person speaks at least one language)

1. $16$
2. $15$
3. $10$
4. $25$

Q. Let $A=\{1,2,3,4\},B=\{2,3,4,5,6\},$ then $A\Delta B=$

1. $\{2,3,4\}$
2. $\left\{1\right\}$
3. $\{5,6\}$
4. $\{1,5,6\}$

Q. If $n\left(A\right)=50,n\left(B\right)=20,n(A\cap B)=10,$ then $n\left(A\Delta B\right)=$

1. $50$
2. $60$
3. $70$
4. $40$

Q. If $A$ and $B$ are subsets of a set $X,$ then $(A\cap (X-B))\cup B$ is equal to

1. $A\cup B$
2. $A\cap B$
3. $A$
4. $B$

Q. The correct interval representation for the set $A=\{x:-4<x\le 4\}$ is given by

1. $(-4,4)$
2. $[-4,4)$
3. $(-4,4]$
4. $[-4,4]$

Q.

Let A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}. Find A - B and B - A.

1. {1, 3, 5}; {8}

2. {1, 5}; {8}

3. {1, 3, 5}; {2, 4, 6}

4. {2, 4, 6}; {2, 4, 6}

Q. If $n\left(A\right)=50,n(A\cup B)=80,n(A\cap B)=30$, then $n(B–A)=$

1. $20$
2. $30$
3. $40$
4. $23$

Q. For all the sets A, B and C,
(A – B) ∩ (C – B) =

1. $\left(A\cap C\right)\cap B\text{'}$
2. $\left(A\cap C\right)-B$
3. $\left(A\cap C\right)\cap B$
4. $\left(A-C\right)-B$

Q. If $A$ and $B$ are two sets, then $\frac{A}{\left(\frac{A}{B}\right)}$ is equal to
$(\frac{A}{B}$ represents the difference of the sets $A$ and $B$ in this order.$)$

1. $A$
2. $B^{\prime }$
3. $A\cap B$
4. $A\cup B$