Union

Q.

Question 70
In the following question, state whether the given statement is true (T) or false (F).
There is a natural number which when added to a natural number, gives the natural number itself.

Q.

(a) If A = {0, 2, 4, 6, 8} and B = {x : x is an even digit less than 5 and x ≥ 0}

Find (i) A ∪ B, (ii) B ∪ A, (iii) A ∩ B, (iv) B ∩ A

(b) If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}

Verify (i) A ∪ B = B ∪ A, (ii) A ∩ B = B ∩ A

Q. If three dice are rolled once, the number of ways of getting atleast one prime number on the dice is____

1. 189
2. 159
3. 169
4. 179

Q.

In a committee 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of persons speaking at least one of these two languages is

1. 60

2. 40

3. 38

4. 58

Q. The set of all possible real values of a such that the inequality (x−(a−1))(x−(a^2+2))<0 holds for all x∈(−1, 3) is

Q. Let $a$ and $b$ be co-prime, thus $a^2$ and $b^2$ are

1. co-prime
2. odd numbers
3. even numbers
4. not co-prime

Q.

(a) If A = {0, 2, 4, 6, 8} and B = {x : x is an even digit less than 5 and x ≥ 0}

Find (i) A ∪ B, (ii) B ∪ A, (iii) A ∩ B, (iv) B ∩ A

(b) If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}

Verify (i) A ∪ B = B ∪ A, (ii) A ∩ B = B ∩ A

Q. What is the least common multiple of $9$ and $15$?

Q. If $n\epsilon N$, the $n(n^2-1)$ is divisible by?

Q. $A=\{a,b\}$, $B=\left\{a\right\}$, $C=\left\{b\right\}$, and $D=\left\{\right\}$. In the table for the union of A, B, C, and D, how many times does A appear?

$\cup$	A	B	C	D
A
B
C
D

1. 6
2. 7
3. 8
4. 9

Q. When a train started from station $A$, there were certain number of passengers in it. On the next station $\frac{1}{11}$ of these passengers got down and $20\%$ of these got down passengers got into the train. Now if the number of passengers in the train is $510$, how many passengers were there at station $A$?

1. $600$
2. $580$
3. $560$
4. $550$

Q. Can the number $6^n$, $n$ being a natural number, end with the digit $5$4 ? Give reason.