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CUET PG MCA Previous Year Questions (PYQs)

CUET PG MCA Sets And Relations PYQ

CUET PG MCA PYQ
Let A ={1,2,3} and consider the relation R= {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} then R is:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
Let $n$ be a positive integer and $R=\{(a,b) \in Z\times Z\, |\, a-b\, =nm\, for\, \, some\, \, m\ne0\in Z\}$ 
Then R is:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
Consider the diagram given below and the following two statements:


Statement I: Events A and B can be expressed as:
$\begin{array}{ll}{A=(A\cap\overline{B})\cup Y} \\ {B=(A\cap B)\cup Z}\, \end{array}$

Statement II: Events A and B can be expressed as:
$A= X-Y$
$B=Y+Z$

In the light of the above statements, choose the most appropriate answer from the options given below:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : In a class of 40 students. 22 drink Sprite, 10 drink Sprite but not Pepsi. Then the number of students who drink both Sprite and Pepsi is 15.

Reason R: For any two finite sets A and B, $n(A) = n(A - B) + n (A \cup B)$

In the light of the above statements, choose the most appropriate answer from the options given below:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
From the given sets, which is an infinite set:
1. $\{x:x\in N~and~(x-1)(x-2)=0\}$
2. $\{x: x \in N ~ and ~ x ~ is ~prime ~number~ and ~less ~than ~199\}$
3. $\{x:x\in N ~and~ x^{5}-1=0\}$ 
4. $\{x:x\in N~and~x~is~odd\}$





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2025 PYQ

Solution

Solution:

We check each option one by one: 1. \(\{x \in \mathbb{N} : (x-1)(x-2)=0\} = \{1,2\}\), which is a finite set.

2. \(\{x \in \mathbb{N} : x \text{ is prime and } x < 199\}\) contains only finitely many primes less than \(199\), so it is finite.

3. \(\{x \in \mathbb{N} : x^{5}-1=0\} \;\Rightarrow\; x^{5}=1 \;\Rightarrow\; x=1\). Thus the set is \(\{1\}\), which is finite.

4. \(\{x \in \mathbb{N} : x \text{ is odd}\} = \{1,3,5,7,\dots\}\), which is an infinite set.

Answer: Option (4).
CUET PG MCA PYQ
There are 200 students in a school out which 120 students play football, 50 students play cricket and 30 students play both football and cricket. The number of students who play one game only is:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2024 PYQ

Solution

Let total students be \( n(U) = 200 \). Football players: \( n(F) = 120 \) Cricket players: \( n(C) = 50 \) Both: \( n(F \cap C) = 30 \)

Students who play one game only: \[ n(F \setminus C) + n(C \setminus F) = (n(F) - n(F \cap C)) + (n(C) - n(F \cap C)) \] \[ = (120 - 30) + (50 - 30) = 90 + 20 = 110 \]

\(\therefore\) The number of students who play one game only = 110.

CUET PG MCA PYQ
Match List-I with List-II
List - I List - II
(A) If X and Y are two sets such that $n(X)=17$, $n(Y)=23$, $n(X \cup Y)=38$, then $n(X \cap Y)$ is I. 20
(B) If $n(X)=28$, $n(Y)=32$, $n(X \cap Y)=10$, then $n(X \cup Y)$ is II. 10
(C) If $n(X)=10$, then $n(7X)$ is III. 50
(D) If $n(Y)=20$, then $n\!\left(\tfrac{Y}{2}\right)$ is IV. 2
Choose the correct answer from the options given below:
1. (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

2. (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

3. (A) - (IV), (B) - (I), (C) - (II), (D) - (III)

4. (A) - (IV), (B) - (II), (C) - (I), (D) - (III)





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2025 PYQ

Solution

(A) Given: n(X)=17, n(Y)=23, n(X ∪ Y)=38
Formula: n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)
⇒ 38 = 17 + 23 – n(X ∩ Y)
⇒ 38 = 40 – n(X ∩ Y)
⇒ n(X ∩ Y) = 2 → Matches with IV.

(B) Given: n(X)=28, n(Y)=32, n(X ∩ Y)=10
Formula: n(X ∪ Y) = 28 + 32 – 10 = 50 → Matches with III.

(C) If n(X) = 10, then n(?(X)) (power set) = 210 = 1024.
But here notation looks like 7X (probably means ?(X)). If it was typo → correct is 210 = 1024. ? But given options map (C) with II = 10, so they mean **n(?(X)) = 2n(X)** was NOT intended. They likely meant n(X) itself. So (C) → II.

(D) If n(Y)=20, then n(Y/2) = 10 (halved set). But given mapping option says (D) → I = 20. → So answer considered: (D) = I.

Final Matching:
(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Answer: Option 1

CUET PG MCA PYQ
Consider the diagram given below and the following two statements: 

Statement I: Regions X, Y and Z can be expressed as $A\cap\overline{B},\, A\cap B$ and $\, \overline{A}\cap B$ respectively 

Statement II: P(Y) = P (A) - P (X) = P (B) - P (Z) 

In the light of the above statements, choose the correct answer from the options given below:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
In a class there are 400 students, the following table shows the number of students studying one or more of the subjects:
 SubjectNumber of Students 
 Mathematics 250
 Physics 150
 Chemistry 100
 Mathematics and Physics 100
Mathematics and Chemistry 60
Physics and Chemistry 40
Mathematics, Physics and chemistry 30
A. The number of students who study only Mathematics is 100. 
B. The number of students who study only Physics is 40. 
C. The number of students who study only Chemistry is 40. 
D. The number of students who do not study Mathematics, Physics and Chemistry is 70.
Choose the correct answer from the options given below:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution


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