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Class 9 · Mathematics · 10 Aug 2026

Max marks: 40
Grade Class 9 · Mathematics · 19 questions
Name Class Date
Q.1 MCQ [4 marks]
(a)
Which of the following represents an empty set (null set) in standard mathematical notation?
[1 mark]
(a)  A = {0}
(b)  B = {x : x is a real number and x^2 = -1}
(c)  C = {x : x is a prime number and x = 1}
(d)  D = {x : x is an integer and 0 < x < 1}
(b)
In a standard two-set Venn diagram representing sets A and B within a universal set U, which region represents the symmetric difference $A \triangle B$?
[1 mark]
(a)  The intersection of A and B
(b)  The union of A and B excluding their intersection
(c)  The complement of the union of A and B
(d)  Only the elements belonging strictly to set B
(c)
If set $A$ is a proper subset of set $B$ ($A \subset B$), how should their Venn diagram be drawn?
[2 marks]
(a)  Two completely separate circles
(b)  Two intersecting circles with a non-empty overlap
(c)  Circle $A$ drawn entirely inside circle $B$
(d)  Circle $B$ drawn entirely inside circle $A$
Q.2 Match the Pairs [6 marks]
(a)
Match each set operation with its correct description in terms of standard Venn diagram shaded regions.
[2 marks]
Column AColumn B
1. Intersection ($A \cap B$) a. Common region shared by both circles $A$ and $B$
2. Union ($A \cup B$) b. Entire combined area covered by both circles $A$ and $B$
3. Complement ($A'$) c. Everything inside the universal box except circle $A$
4. Difference ($A \setminus B$) d. Part of circle $A$ that does not overlap with circle $B$
Answer
(b)
Match each set operation with its corresponding shaded region description in a two-set Venn diagram:
[2 marks]
Column AColumn B
1. A \cup B a. Entire region covered by circles A and B
2. A \cap B b. Only the overlapping region common to both circles
3. A' c. Everything inside the universal set outside circle A
4. A - B d. Part of circle A that does not overlap with circle B
Answer
(c)
Match the set operation property with its correct algebraic identity for any sets A, B, and Universal set U.
[2 marks]
Column AColumn B
1. A ∪ A' a. U
2. A ∩ A' b. ∅
3. A ∪ ∅ c. A
4. A ∩ U d. A
Answer
Q.3 Fill in the Blanks [4 marks]
(a)
In a Venn diagram, a rectangle is conventionally used to represent the universal set $U$, while closed curves or circles inside it represent its _____.
[1 mark]
(b)
For any two finite sets $A$ and $B$, the cardinality of their union is given by the formula $|A \cup B| = |A| + |B| - |$_____$|$.
[1 mark]
(c)
According to the distributive law of union over intersection, A ∪ (B ∩ C) is equal to _____.
[2 marks]
Q.4 One Sentence [3 marks]
(a)
Define a singleton set with a suitable mathematical example.
[2 marks]
(b)
State what the region outside the circle of set $A$ but inside the universal set rectangle $U$ represents.
[1 mark]
Q.5 Short Answer [9 marks]
(a)
State whether the set of all circles passing through the origin (0, 0) is a finite or infinite set. Justify your answer in one sentence.
[2 marks]
(b)
Classify the following sets as empty, singleton, finite, or infinite: (i) P = {x : x ∈ ℕ and 2x = 3}, (ii) Q = {x : x ∈ ℤ and x^2 < 10}. Justify your classification for each.
[3 marks]
(c)
Prove or disprove the following statement: "If A ⊂ B and B ⊂ C, then the power set of A is a subset of the power set of C, i.e., P(A) ⊆ P(C)."
[4 marks]
Q.6 Word Problem [11 marks]
(a)
In a survey of 100 students at a school in Jaipur, let U be the universal set of all students surveyed. Let A be the set of students who speak Hindi and B be the set of students who speak English. If n(A) = 60, n(B) = 40, and n(A ∩ B) = 20, classify and find the number of students who belong to the complement set (A ∪ B)'.
[3 marks]
(b)
At a cultural fest in Delhi, 120 students participated in events. 65 students participated in classical dance (D), 50 students participated in classical music (M), and 30 students participated in both events. Find the number of students who participated in: (i) Either classical dance or classical music. (ii) Neither classical dance nor classical music.
[4 marks]
(c)
A market survey in Mumbai showed that 500 consumers liked product X, 400 liked product Y, and 200 liked both products. Prove using set cardinality that the total number of consumers who liked at least one of the two products is 700, and determine how many liked product X only.
[4 marks]
Q.7 Diagram Labeling [3 marks]
(a)
Reference — Diagram: AI visual
UAB
Identify the shaded region in the provided Venn diagram reference.
[1 mark]
Label the following: 1 2 3 4
(b)
Identify the standard regions in a three-set Venn diagram representing sets P, Q, and R. Label the region corresponding to elements belonging to set P and Q but NOT to set R.
[2 marks]
Label the following: 1 2 3 4
Generated by Lumai — 10 September 2026
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Class 9 · Mathematics · 10 Aug 2026 — 40 Marks