Definition of Sets

Q.

Pick out the noun in the following sentences and write in the blank space

Q. $A$ is set of letters of the word 'debit card'
$B$ is the set of letters of the word 'bad credit'.
Then which of the following options is/are correct ?

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are unequal sets
3. $A$ and $B$ are equal sets
4. $n\left(A\right)=n\left(B\right)$

Q.

Which of the following is a set?

1. The collection of 6 most talented dancers in India

2. Collection of all boys in your class

3. Collection of most tasty dishes in world

4. Team of 5 best basketball players

Q. The number of real roots of the equation ${\tan }^{-1}\sqrt{x(x+1)}+{\sin }^{-1}\sqrt{x^2+x+1}=\frac{\pi }{4}$ is

1. $2$
2. $0$
3. $1$
4. $4$

Q. Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is

1. $5^3$
2. $5^2$
3. $3^5$
4. $2^5$

Q. If $R=\{x:x^2=7\},S=\{x:x+4=4\}$ and $T=\{x:x^2+2=8\}$, then which of the following is correct?

1. $R$ and $T$ are equal sets.
2. $R$ and $S$ are equal sets.
3. $S$ and $T$ are equal sets.
4. None of them are equal sets.

Q. Which of the follwing is a set?

1. The collection of all strong boys in a class
2. The collection of all short people in a colony
3. The collection of letters of the word 'CORONA'
4. The collection of difficult topics in Maths