Definition of Sets

Q.

The collective noun for card is

Q.

In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both.

The probability that a student selected at random from the class has passed in only one subject is

1. $\frac{13}{25}$

2. $\frac{3}{25}$

3. $\frac{17}{25}$

4. $\frac{8}{25}$

Q.

Letters of the word RANDOM are arranged in all possible ways and those words are arranged as in the dictionary. What is the position of the word RANDOM in this list?

Q.

Which of the following collections are sets ? Justify your answer :

(i) A collection of all natural numbers less than 50.

(ii) The collection of good hockey players in India.

(iii) The collection of all girls in your class.

(iv) The collection of most talented writers of India.

(v) The collection of difficult topics in Mathematics.

(vi) The collection of all months of a year beginning with the letter J.

(vii) A collection of novels written by Munshi Prem Chand.

(viii) The collection of all questions in this chapter.

(ix) A collection of most dangerous animals of the world.

(x) The collection of prime integers.

Q.

If $\tan \left(A\right)$ and $\tan \left(B\right)$ are the roots of $x^2-ax+b=0$ then the value of ${\sin }^2\left(A+B\right)$ is

1. $\frac{a^2}{a^2+{\left(1-b\right)}^2}$

2. $\frac{a^2}{a^2+b^2}$

3. $\frac{a^2}{{\left(a+b\right)}^2}$

4. $\frac{b^2}{a^2+{\left(a-b\right)}^2}$

Q.

If a matrix has 6 elements, the number of possible orders it can have are

1. 3

2. 4

3. 6

4. 2

Q. Which of the following is not a set?

1. The collection of great people of the world
2. The collection of all boys of age greater than $10$ years
3. The collection of all letters of the word 'LEARNING'
4. The collection of questions of the topic 'SET THEORY'

Q.

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
(A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.

Q.

Let A={1, 2, 3}. Then, the number of relation containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
(a)1
(b)2
(c)3
(d)4

Q. Determine whether the following relations are reflexive, symmetric and transitive.
$a)A=\{2,3,4\}R=\{(2,2),(3,3),(4,4),(2,3),(3,4)\}$

$b)R=\{(x,y):y=x+5\&x<4;x,y\in R\}$

Q.

What is the difference between a collection and a set ? GIve reasona to support your answer ?

Q.

Which of the following collections are sets?

Rich people in your city

Q.

If $n\left(A\right)=4$, $n\left(B\right)=3$ and$n(A\times B\times C)=24$, then $n\left(C\right)$is equal to

1. $288$

2. $1$

3. $17$

4. $12$

5. $2$

Q. The number of binary operations on the set $\{1,2,3\}$ is ______

1. $3!$
2. $9^3$
3. $27$
4. $3^9$

Q.

The smallest set $A$ such that $A\cup \left\{1,2\right\}=\left\{1,2,3,5,9\right\}$ is

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

2. $\left\{3,5,9\right\}$

3. $\left\{1,2,5,9\right\}$

4. None of these

Q.

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is

1. $23$

2. $26$

3. $29$

4. $32$

Q.

If A ={1, 2, 3, 4}, define relations on A which have properties of being
(i) Reflexive, transitive but not symmetric.

(ii) symmetric but neither reflexive nor transitive.

(iii) reflexive, symmetric and transitive.

Q.

List all the elements of the following sets :

(i) A = {$x:x^2\underset{–}{<}10,xϵZ$}

(ii) B = { $x:x=\frac{1}{2n-1},1\underset{–}{<}n\underset{–}{<}5$}

(iii) {$C=x:x\text{is an integer},-\frac{1}{2}<x<\frac{9}{2}$ }

(iv) D = {x : x is a vowel in the word "EQUATION"}

(v) E = {x : x is a month of a year not having 31 days}

(vi) F = {x : x is a letter of the word "MISSISSIPPI" }

Q. Let $f:A\to B,g:B\to A$ be two functions such that $fog=I_B$, then which among the following is/are true

1. $f$ is a surjective function
2. $g$ is an injective function.
3. $g$ is many-one function
4. $f$ is an into function.

Q. The collection of pet animals is

1. a null set
2. a finite set
3. an infinite set
4. not a set

Q. Which of the following is/are a set?

1. $\{x:x$ is a natural number and is biggest number $\}$
2. The collection of students in Bangalore
3. The collection of all small flowers
4. $\{x:x$ is the tallest member of parliament $\}$

Q.

Write the following set in set builder form.

The set of all prime numbers less than $100$.

Q. A collection of all natural numbers less than 50 is

1. a set.
2. not a set.

Q.

Find the value of $\underset{x\to \infty }{lim}\frac{\left[x\right]+\left[2x\right]+\left[3x\right]+....\left[nx\right]}{n^2}$ where [.] is an greatest integer function.

1. x

2. 

3. 2x

4. 0

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. Six students are to be selected for a quiz competition from $10$ aspirants. The probability that two particular students are excluded is

1. $\frac{2}{15}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{1}{5}$

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. If $a,b,c,d$ are four distinct numbers chosen from the set $\{1,2,3....,9\},$ then the minimum value of $\frac{a}{b}+\frac{c}{d}$ is

1. $\frac{3}{8}$
2. $\frac{1}{3}$
3. $\frac{13}{36}$
4. $\frac{25}{72}$

Q.

Every set is a collection of object but every collection of object is not a set examples

Q. In the figure given below, two dots are placed that represent some common regions to circle, square, rectangle and triangle.
Choose the correct alternative figure that contains the similar common region to that represented by dots in the given figure.

1. 
   
2. 
   
3. 
   
4.