Empty Set

Q.

$A=\{x:x\in R,x^2=16\text{and}2x=6\}$ can be represented in the roster form as _________ .

1. A = { 14, 3, 4 }

2. A = { 3 }

3. A = { 4 }

4. A = {}

Q.

Find, which of the following sets are empty:

(i)The set of points of intersection of two parallel lines.

(ii) $A=\{x:x\in Nand5<x\le 6\}$

(iii) $B=\{x:x^2+4=0,x\in N\}$

(iv)$C=\left\{evennumbersbetween6\&10\right\}$

(v) $D=\left\{primenumbersbetween7\&11\right\}$

Note : The set, which has no element in it, is called the empty or null set.

Q.

Concentric circles is a case of translation.

1. True

2. False

Q. Which of the following is not a null set?

1. A = { $x:x\in$ N, 2 < $x$ < 10 }
2. D = {$x:x$ is an odd natural number divisible by 2}
3. B = { $x:x$ is an even prime number greater than 2 }
4. C = { $x:x$ is a rational number, $x^2$ - 3 = 0 }

Q.

Can you divide the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 into two groups such that the product of numbers in one group divides the product of numbers in the other group and the quotient is minimum?

Q.

If A and B are two given sets, then $A\cap (A\cap B{)}^{\prime }$ is equal to

1. A

2. $(A\cap B^{\prime })$

3. ∅

4. B

Q.

One or more options are correct:

Which of the following is/are null sets?

1. A = {x: -10<x<2, x is a natural number}

2. B = {x:x is an even prime number greater than 2}

3. C = {x: x²- 3=0. X is rational number}

4. D = {x: x is an odd natural number divisible by 2}

Q. A prime number is squared and then added to a different prime number. The number thus obtained is:
I. An even number
II. An odd number
III. A positive number

1. II only
2. III only
3. I only
4. I and III only
5. I, II, and III

Q.

$A=\{x:x\in R,x^2=16\text{and}2x=6\}$ can be represented in the roster form as _________ .

1. $A=\{14,3,4\}$

2. $A=\left\{3\right\}$

3. $A=\left\{4\right\}$

4. $A=\left\{\right\}$

Q.

Which of the following is an empty set

1. {x:x is a real number and $x^2$ - 1 = 0}

2. {x:x is a real number and $x^2$ +1 = 0}

3. {x:x is a real number and $x^2$ - 9 = 0}

4. {x:x is a real number and $x^2$ = x + 2}

Q. Help Ross find the total number of triangles in the figure.

1. 14
2. 13
3. 18
4. 22

Q.

Which of the following sets are “empty sets”?

1. $A$ = {set of prime numbers, less than $2$}

2. $B=\left\{x\right|x+8=x\mathrm{and}\mathrm{x}\in \mathrm{N}\}$

3. $C=\left\{0\right\}$

4. $D=\left\{x\right|x$ is a point common to any two parallel lines$\}$

Q.

Which of the following is not a null set?

1. A = {x: -10<x<2, x is a natural number}

2. B = {x:x is an even prime number greater than 2}

3. C = {x: x²- 3=0, x is rational number}

4. D = {x: x is an odd natural number divisible by 2}