Finite and Infinite Sets

Q.

If $z$ is a complex number such that the imaginary part of $z$ is non-zero and $a=z^2+z+1$ is real. Then $a$ cannot take the value:

1. $-1$

2. $\frac{1}{3}$

3. $\frac{1}{2}$

4. $\frac{3}{4}$

Q.

If $\alpha$ and $\beta$are the roots of the equation $x^2+3x-4=0$, then$1/\alpha +1/\beta$is equal to

1. $-3/4$

2. $3/4$

3. $-4/3$

4. $4/3$

5. $3/2$

Q.

The area of a rectangle will be maximum for the given perimeter when the rectangle is a

1. Parallelogram

2. Trapezium

3. Square

4. None of these

Q.

State which of the following sets are finite and which are infinite.

The set of leaves on a tree.

Q.

If A = (a, b, c), B = (x, y, z). Find B $\times$ A

1. None of these

2. {(a, x), (a, y), (a, z), (b, x), (b, y), (b, z), (c, x), (c, y), (c, z)}

3. {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}

4. {(a, a), (b, b), (c, c), (x, x), (y, y), (z, z)}

Q.

Question 29

Encircle the odd one of the following:

(a) $(-100)÷5$
(b) $(-81)÷9$
(c) $(-75)÷5$
(d) $(-32)÷9$

Q.

Let $f\left(x\right)=x,g\left(x\right)=\frac{1}{x}\text{and}h\left(x\right)=f\left(x\right)g\left(x\right).$ Then, $h\left(x\right)=1$ if and only if

1. $x$ is a real number

2. $x$ is a rational number

3. $x$ is an irrational number

4. $x$ is a non-zero real number

Q.

If R is a relation between A and B, then which of the following is correct?

1. R ⊆ A

2. R ⊆ B

3. R ⊆ (A × B)

4. R ⊆ (B ∩ A)

Q. The set of circles passing through the point (2, 3) is ______.

1. a finite set
2. an infinite set
3. a null set
4. None of the above

Q.

Question 30

Encircle the odd one of the following:

(a) $(-1)\times (-1)$
(b) $(-1)\times (-1)\times (-1)$
(c) $(-1)\times (-1)\times (-1)\times (-1)$
(d) $(-1)\times (-1)\times (-1)\times (-1)\times (-1)\times (-1)$

Q. The GCD of $15x^4{y}^3{z}^5,12x^2{y}^7{z}^2$ is:

1. $3x^4{y}^4{z}^2$
   
2. $3xy{z}^2$
3. $3x^2{y}^3{z}^2$
   
4. $3x^3{y}^3{z}^3$
   

Q.

The number of roots of $3^{\left|x\right|·\left|2-\left|x\right|\right|}=1$ is

1. $1$

2. $2$

3. $3$

4. $4$

Q.

The area of a rectangular field is $120sqm.$. If the perimeter is $46m,$, find the length and breadth of the rectangle.

Q.

When $7$ is subtracted from the square of a number, the result is $6$ times the number. Find a positive solution.

Q. Identify the infinite sets among the following.

1. {$x:x\in Z$, -60 < $x$ < 60}
2. {…., -5, -4, -3, -2, .....}
3. The set of letters in the English alphabet.
4. {$x:x\in W$, $x$ > 20}

Q. The set $A=\{x:x=\frac{n-1}{n},\text{where}nϵN\}$ is __________.

1. a finite set
2. a null set
3. an infinite set
4. singleton set

Q.

Approximate the root by using a linearization centered at an appropriate nearby number $\sqrt{101}$.

Q.

State which of the following are null or empty sets?

$\left\{x:xisapersonover100mtall\right\}$

Q.

State which of the following are null or empty set?

$\left\{Menover300yearsold\right\}$

Q.

State which of the following sets are finite and which are infinite.

The set of atoms on earth.

Q.

A set is said to be a/an ____ set if it has a limited number of elements.

1. equal

2. finite

3. infinite

4. equivalent

Q.

If A and A$\cap$B are void set (empty sets) and n(A$\cup$ B) = 50, find the value of n(B).

Q. If a set contains $n$ elements then number of elements in its power set is

1. $2^n-n$
2. $2^n-2$
3. $2^n$
4. $n^2$

Q.

Which is the least prime number?

Q.

Write the given set from Roster-form to set-builder form $G=\left\{a,e,i,o,u\right\}$

Q.

State whether the given set is finite or infinite.

$\text{C =}\left\{x:x\text{is a multiple of 20}\right\}$

Q.

If A $\subset$ B and U is the universal set, then find A $\cap$ B and A\B using Venn diagram

Q.

State which of the following sets are finite and which are infinite.

$\left\{0,1,2,3,........\right\}$

Q. State whether the following sets are finite or infinite
(i) $A=$ { $x:x$ is a multiple of 5, $x\in N$ }
(ii) $B=$ { $x:x$ is an even prime number }
(iii) The set of all positive integers greater than 50.

Q. State whether the following sets are finite or infinite.
I.{x:x ∈ N and x is even}
II.{x :x ∈ N and (2x-4) (x-5)=0}
III.The set of factors of 10