Phrases Sets and Relations Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases Sets And Relations PYQ

Qus : 1Phrases PYQ 2020

If A is a subset of B and B is a subset of C, then cardinality of A ∪ B ∪ C is equal to

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 2Phrases PYQ 2023

Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

Qus : 3Phrases PYQ 2019

Number of real solutions of the equation

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

Solution

Qus : 4Phrases PYQ 2022

Inverse of the function

$f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}}$ is

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

Let

$f(x)=y$ , then

⇒

$\frac{10^x-10^-x}{10^x+10^-x}=y$

⇒

$\frac{10^{2x}-1}{10^{2x}+1}=y$

⇒

$10^{2x}=\frac{1+y}{1-y}$ By Componendo Dividendo Rule

⇒

$x=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}$

⇒

${f}^{-1}(y)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}$

⇒

${f}^{-1}(x)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+x}{1-x}\Bigg{)}$

Qus : 5Phrases PYQ 2019

Suppose A₁ , A₂ , A₃ , …..A₃₀ are thirty sets each having 5 elements with no common elements across the sets and B₁ , B₂ , B₃ , ..... , B_n are

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

Solution

Qus : 6Phrases PYQ 2024

Find the cardinality of the set C which is defined as

$C={\{x|\, \sin 4x=\frac{1}{2}\, forx\in(-9\pi,3\pi)}\}$ .

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

We are given:

$\sin(4x) = \frac{1}{2}, \quad x \in (-9\pi,\ 3\pi)$

Step 1: General solutions for $\sin(θ) = \frac{1}{2}$

$θ = \frac{\pi}{6} + 2n\pi \quad \text{or} \quad θ = \frac{5\pi}{6} + 2n\pi$

Let $θ = 4x$ , so we get:

$x = \frac{\pi}{24} + \frac{n\pi}{2}$
$x = \frac{5\pi}{24} + \frac{n\pi}{2}$

✅ Step 2: Count how many such $x$ fall in the interval $(-9\pi, 3\pi)$

By checking all possible $n$ values, we find:

For $x = \frac{\pi}{24} + \frac{n\pi}{2}$ : 24 valid values
For $x = \frac{5\pi}{24} + \frac{n\pi}{2}$ : 24 valid values

? Total distinct values = 24 + 24 = 48

✅ Final Answer: $\boxed{48}$

Qus : 7Phrases PYQ 2022

A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation like tea and 72% of the population like coffee. Let

$x$ be the number of people who like both tea & coffee. Let

$m{\leq x\leq n}$ , then choose the correct option.

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

Qus : 8Phrases PYQ 2024

Let Z be the set of all integers, and consider the sets

$X=\{(x,y)\colon{x}^2+2{y}^2=3,\, x,y\in Z\}$ and

$Y=\{(x,y)\colon x{\gt}y,\, x,y\in Z\}$ . Then the number of elements in

$X\cap Y$ is:

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Given: $x^2 + 2y^2 = 3 \text{ and } x > y \text{ with } x, y \in \mathbb{Z}$

Solutions to the equation are: $\{(1,1), (1,-1), (-1,1), (-1,-1)\}$

Among them, only $(1, -1)$ satisfies $x > y$ .

Answer: $\boxed{1}$

Qus : 9Phrases PYQ 2024

Out of a group of 50 students taking examinations in Mathematics, Physics, and Chemistry, 37 students passed Mathematics, 24 passed Physics, and 43 passed Chemistry. Additionally, no more than 19 students passed both Mathematics and Physics, no more than 29 passed both Mathematics and Chemistry, and no more than 20 passed both Physics and Chemistry. What is the maximum number of students who could have passed all three examinations?

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

? Maximum Students Passing All Three Exams

Given:

Total students = 50
$|M| = 37$ , $|P| = 24$ , $|C| = 43$
$|M \cap P| \leq 19$ , $|M \cap C| \leq 29$ , $|P \cap C| \leq 20$

We use the inclusion-exclusion principle:

$|M \cup P \cup C| = |M| + |P| + |C| - |M \cap P| - |M \cap C| - |P \cap C| + |M \cap P \cap C|$

Let $x = |M \cap P \cap C|$ . Then:

$50 \geq 37 + 24 + 43 - 19 - 29 - 20 + x \Rightarrow 50 \geq 36 + x \Rightarrow x \leq 14$

✅ Final Answer: $\boxed{14}$

Qus : 10Phrases PYQ 2022

There are two sets A and B with |A| = m and |B| = n. If |P(A)| − |P(B)| = 112 then choose the wrong option (where |A| denotes the cardinality of A, and P(A) denotes the power set of A)

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

Qus : 11Phrases PYQ 2018

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 12Phrases PYQ 2018

In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business. 8 students like both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 13Phrases PYQ 2021

If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

Solution

Qus : 14Phrases PYQ 2021

Suppose

$A_1,A_2,\ldots,A_{30}$ are 30 sets each with five elements and

$B_1,B_2,B_3,\ldots,B_n$ are n sets (each with three elements) such that

$\bigcup ^{30}_{i=1}{{A}}_i={{\bigcup }}^n_{j=1}{{B}}_i=S\,$ and each element of S belongs to exactly ten of the

$A_i$ 's and exactly 9 of the

$B^{\prime}_j$ 's. Then

$n=$

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

Solution

Qus : 15Phrases PYQ 2017

The number of elements in the power set P(S) of the set S = [2, (1, 4)] is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Qus : 16Phrases PYQ 2021

If X and Y are two sets, then X∩Y ' ∩ (X∪Y) ' is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

Solution

Qus : 17Phrases PYQ 2020

In a class of 50 students, it was found that 30 students read "Hitava", 35 students read "Hindustan" and 10 read neither. How many students read both: "Hitavad" and "Hindustan" newspapers?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

P(x)=50,

P(A ∩ B)' = 10

So P(A ∪ B) = 50 - 10 = 40.

So P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

= 30 + 35 - 40 = 25

Solution Contribution by Priyanka Soni

Qus : 18Phrases PYQ 2020

If A = {4^x - 3x - 1 : x ∈ N} and B = {9(x - 1) : x ∈ N}, where N is the set of natural numbers, then

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

A = {0,9,54...}

B = {0,9,18,27...}

So, A ⊂ B

Qus : 19Phrases PYQ 2020

If A = { x, y, z }, then the number of subsets in powerset of A is

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 20Phrases PYQ 2014

If the sets A and B are defined as A = {(x, y) | y = 1 / x, 0 ≠ x ∈ R}, B = {(x, y)|y = -x ∈ R} then

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Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

Solution

Qus : 21Phrases PYQ 2015

Let

$\bar{P}$ and

$\bar{Q}$ denote the complements of two sets P and Q. Then the set

$(P-Q)\cup (Q-P) \cup (P \cap Q)$ is

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Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution

Qus : 22Phrases PYQ 2015

A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics:

$n(P) = 8, n(Q) = 13, n(R) = 13, n(P \cap R) = 3, n(P \cap R) = 3, n(Q \cap R) = 3, n(Q \cap R) = 6, n(P \cap Q \cap R) = 2$ where

$n(x)$ is the cardinality of the set

$x$ . Then the number of text books that have no material on compilers is

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Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution

Qus : 23Phrases PYQ 2023

Let A and B be sets.

$A\cap X=B\cap X=\phi$ and

$A\cup X=B\cup X$ for some set X, relation between A & B

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

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Phrases Previous Year Questions (PYQs)

Phrases Sets And Relations PYQ

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We are given:

✅ Step 2: Count how many such x x fall in the interval (-9\pi, 3\pi) (-9\pi, 3\pi)

? Total distinct values = 24 + 24 = 48

Solution

Solution

Solution

? Maximum Students Passing All Three Exams

✅ Final Answer: \boxed{14}\boxed{14}

Solution

Solution

Solution

Solution

Solution

Solution

Solution

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✅ Step 2: Count how many such $x$ fall in the interval $(-9\pi, 3\pi)$

✅ Final Answer: $\boxed{14}$