List of top Mathematics Questions asked in CBSE Class XI

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A - B
(ii) A - C
(iii) A - D
(iv) B - A
(v) C - A
(vi) D - A
(vii) B - C
(viii) B - D
(ix) C - B
(x) D - B
(xi) C - D
(xii) D - C

Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x: x is a natural number and \(4 ≤ x ≤ 6\)}
(ii) {a, e, i, o, u} and {c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}

If A = {x: x is a natural number}, B ={x: x is an even natural number}
C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(i) \(A ∩ B\)
(ii) \(A ∩ C\)
(iii) \(A ∩ D\)
(iv) \(B ∩ C\)
(v) \(B ∩ D\)
(vi) \(C ∩ D\)

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) \(A ∩B\)
(ii) \(B ∩C\)
(iii) \(A ∩C ∩D\)
(iv) \(A ∩C\)
(v) \(B ∩D\)
(vi) \(A ∩(B ∪ C)\)
(vii) \(A ∩D\)
(viii) \(A ∩(B ∪ D)\)
(ix) \((A ∩B) ∩(B ∪ C)\)
(x) \((A ∪ D) ∩(B ∪ C)\)

Find the intersection of each pair of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}
B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and \(1 < x ≤ 6\)}
B = {x: x is a natural number and \(6 < x < 10\)}
(v) A = {1, 2, 3}, B = \(\phi\)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
(i) \(A∪ B\)
(ii) \(A ∪ C\)
(iii) \(B ∪ C\)
(iv) \(B ∪ D\)
(v) \(A ∪ B ∪ C\)
(vi) \(A∪ B ∪ D\)
(vii) \(B ∪ C ∪ D\)

If A and B are two sets such that \(A \subset B\), then what is \(A \cup B\)?

Let A = {a, b}, B = {a, b, c}. Is \(\subset\) B? What is \(A ∪ B\)?

Find the union of each of the following pairs of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}
B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and \(1 <x ≤ 6\)}
B = {x: x is a natural number and \(6 <x< 10\)}
(v) A = {1, 2, 3}, B = \(\phi\)

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) \(\phi\)
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}

What universal set (s) would you propose for each of the following:
(i) The set of right triangles
(ii) The set of isosceles triangles

Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)

Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} \(⊂\) A
(ii) {3, 4}}\(∈\) A
(iii) {{3, 4}}\(⊂\) A
(iv) 1\(∈\) A
(v) 1\(⊂\) A
(vi) {1, 2, 5} \(⊂\) A
(vii) {1, 2, 5}\(∈\) A
(viii) {1, 2, 3} \(⊂\) A
(ix) \( \phi ∈A\)
(x) \( \phi⊂ A\)
(xi)  {\(\phi\)}\( ⊂ A\)

Examine whether the following statements are true or false:
(i) {a, b} \(⊄\) {b, c, a}
(ii) {a, e} \(⊂\) {x: x is a vowel in the English alphabet}
(iii) {1, 2, 3} \(⊂\) {1, 3, 5}
(iv) {a} \(⊂ \) {a. b, c}
(v) {a} \(∈\) (a, b, c)
(vi) {x: x is an even natural number less than 6} \(⊂\) {x: x is a natural number which divides 36}

Make correct statements by filling in the symbols \( ⊂ \) or \(⊄\) in the blank spaces:
(i) {2, 3, 4} … {1, 2, 3, 4, 5}
(ii) {a, b, c} … {b, c, d}
(iii) {x: x is a student of Class XI of your school} … {x: x student of your school}
(iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}
(v) {x: x is a triangle in a plane}…{x: x is a rectangle in the plane}
(vi) {x: x is an equilateral triangle in a plane}… {x: x is a triangle in the same plane} 
(vii) {x: x is an even natural number} … {x: x is an integer}

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}

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

State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)

Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7 }
(iv) {y: y is a point common to any two parallel lines}

Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) {1, 2, 3 ...}
(iii) {1, 2, 3 ... 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99

List all the elements of the following sets: 
(i) A = {x: x is an odd natural number} 
(ii) B = {x: x is an \(\frac{-1}{2} < x <\frac{ 9}{2}\)  integer,} 
(iii) C = {x: x is an \(x^2 ≤ 4 \) integer, 
(iv) D = {x: x is a letter in the word “LOYAL“} 
(v) E = {x: x is a month of a year not having 31 days} 
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)  (ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}  (iv) {2, 4, 6 …}
(v) {1, 4, 9 … 100}

Write the following sets in roster form: 
(i) A = {x: x is an integer and \(-3 < x < 7\)}. 
(ii) B = {x: x is a natural number less than 6}. 
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8} 
(iv) D = {x: x is a prime number which is divisor of 60}. 
(v) E = The set of all letters in the word TRIGONOMETRY. 
(vi) F = The set of all letters in the word BETTER

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

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.