Definition of Sets

Q. 10. How to find the rank of the Word INDIA

Q. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces: (i) 5…A (ii ) 8…A (iii) 0…A (iv) 4…A (v) 2…A (vi) 10…A

Q. The number of equivalence relations that can be defined on set \{a, b, c\} is

Q. Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = { x : x is solution of x 2 + 5 x + 6 = 0} (ii) A = { x : x is a letter in the word FOLLOW}; B = { y : y is a letter in the word WOLF}

Q. How many elements has P(A), if A = Φ?

Q. 5. Find the sum of all natural numbers less than 1000 and which are divisible by neither 5 nor 2. (1) a proton and a neutron (2) a proton and deuterium (3) deuterium and an alpha particle (4) an electron and gamma rays

Q. the number of divisors of the form 4k+2, k≥0 of the integer 240 is

Q. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

Q. 4. Let A={a, b, c, d}. B and C are two sets such that B and C subset of A and B intersection c = 0. Number of possible ordered pair (B, C) satisfying above condition is

Q. 43. The number if ways in which 10 letters can be posted in five letter boxes is

Q. Number of letters of the word Tiktok in which no two T and no two K are together.

Q.

Which of the following collections is not a set?

1. The vowels in the English alphabet

2. All natural numbers which divide 42

3. Names of 10 most renowned actors

4. Names of rivers in India

Q.

Check the given collection is set? If not a set, give reason

Interesting books in the library

Q. 15.The number of ways in which r letters can be posted in n letter boxes in a town is

Q. Choose the correct Set-builder representation of the interval $(4,12)$.

1. $\{p:p\in R,4\le p<12\}$
2. $\{p:p\in R,4\le p\le 12\}$
3. $\{p:p\in R,4<p<12\}$
4. $\{p:p\in R,4<p\le 12\}$

Q.

The relation "less than” in the set of natural numbers is

[UPSEAT 1994, 98, 99; AMU 1999]

1. Only symmetric

2. Only transitive

3. Only reflexive

4. Equivalence relation

Q. In the following, state whether A = B or not: (i) A = { a , b , c , d }; B = { d , c , b , a } (ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18} (iii) A = {2, 4, 6, 8, 10}; B = { x : x is positive even integer and x ≤ 10} (iv) A = { x : x is a multiple of 10}; B = {10, 15, 20, 25, 30 ...}

Q. From the sets given below, select equal sets: A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2} E = {–1, 1}, F = {0, a }, G = {1, –1}, H = {0, 1}

Q. 82.A dictionary is printed consisting of 7-lettered words that can be made with the letters of the word CRICKET. If tge words are printed in the alphabetic order, as in an ordinary dictionary, Find the position of the word CRICKET in the dictionary.

Q. 57.What is sector

Q. Which of the following are sets? Justify our answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection of all natural numbers less than 100. (vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers. (viii) The collection of questions in this Chapter. (ix) A collection of most dangerous animals of the world.

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

Q. 26. What is taylor series??describe it.

Q. Are the following sets equal?
A = {x : x is a letter in the word reap}:
B = {x : x is a letter in the word paper};
C = {x : x is a letter in the word rope}.

Q.
Q. What is the difference between a collection and a set? Give reasons to support your answer.
Q. Which of the following collections are sets? Justify your answer.

1. A collection of all natural numbers less than 50.
2. The collection of good hockey players in India.
3. The collection of all girls in your class.
4. The collection of most talented writers of India.
5. The collection of difficult topics in Mathematics.
6. The collection of all months of a year beginning with the letter J.
7. A collection of novels written by Munshi Prem Chand.
8. The collection of all questions in this chapter.
9. A collection of most dangerous animals of the world.
10. The collection of prime integers.

Q. In roster notation of a set

1. order of elements is important
2. elements represented in square brackets
3. Only finite sets can be represented in roster form
4. none of the above

Q. What are different between a collection and a set ??

Q.

What word should he have avoided in his request to see the manager?