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ProgramsBCASemester 1Mathematics IUnit 1: Set Theory and Real & Complex Number
Chapter Study

BCA Semester 1 – Mathematics I – Unit 1: Set Theory and Real & Complex Number

Comprehensive questions and detailed answers for Unit 1: Set Theory and Real & Complex Number. Perfect for exam preparation and concept clarity.

10
Questions
60
Marks
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1

In a class of 100 students, 40 failed in mathematics, 70 in English, and 20 in both subjects. Find:
\quad a) How many students passed in both subjects?
\quad b) How many passed in Mathematics only?
\quad c) How many failed in mathematics only?

MediumTHEORY5 marks2019(TU FOHSS Final)
2

If X+iy=1+i1−i,X+iy=1+i1−i,X+iy=1+i1−i, show that x2+y2=1.x2+y2=1.x2+y2=1.

MediumTHEORY5 marks2019(TU FOHSS Final)
3

Out of 500 people, 285 like tea, 195 like coffee, 115 like lemon juice, 45 like tea and coffee, 70 like tea and juice, 50 like juice and coffee. If 50 do not like any drinks:
\quadi) How many people like all three drinks?
\quadii) How many people like only one drink?

MediumTHEORY5 marks2020(TU FOHSS Final)
4

If x−iy=3−2i3+2ix - i y = \frac{3-2i}{3+2i}x−iy=3+2i3−2i​, prove that x2+y2=1.x^2 + y^2 = 1.x2+y2=1.

MediumTHEORY5 marks2020(TU FOHSS Final)
5

In a certain village in Nepal, all the people speak Nepali or Tharu or both languages.
If 90%90\%90% speak Nepali and 20%20\%20% speak Tharu, find how many people speak:
\quadi) Nepali language only
\quadii) Tharu language only
\quadiii) Both languages

MediumNumerical5 marks2022(TU FOHSS Final)
6

If x−ty=5−6i5+6i,\text{If}\space x - ty = \frac{5 - 6i}{5 + 6i},If x−ty=5+6i5−6i​, prove that x2+y2=1.x^2 + y^2 = 1.x2+y2=1.

MediumNumerical5 marks2022(TU FOHSS Final)
7

Solve the inequality: 6+5x−x2≥06 + 5x - x^2 \ge 06+5x−x2≥0

MediumNumerical5 marks2023(TU FOHSS Final)
8

a) If AAA and BBB are two subsets of universal set UUU such thatn(U)=350,n(A)=100,n(B)=150,andn(A∩B)=50,n(U) = 350, \quad n(A) = 100, \quad n(B) = 150, \quad \text{and} \quad n(A \cap B) = 50,n(U)=350,n(A)=100,n(B)=150,andn(A∩B)=50, then find n(A′∩B′)n(A' \cap B')n(A′∩B′).
b) If a,b,ca,b,ca,b,c are in A.P.,b,c,dA.P., b,c,dA.P.,b,c,d are in G.P.,G.P.,G.P., and c,d,ec,d,ec,d,e are in H.P.,H.P.,H.P., then prove that a,c,ea,c,ea,c,e are in G.P.G.P.G.P.

HardNumerical10 marks2023(TU FOHSS Final)
9

Solve the inequality: 3+2x−x2≥03 + 2x - x^2 \ge 03+2x−x2≥0

MediumNumerical5 marks2024(TU FOHSS Final)
10

Prove that

3+4i1−i+3−4i1+i\quad\quad\quad\quad\quad\frac{3 + 4i}{1 - i} + \frac{3 - 4i}{1 + i}1−i3+4i​+1+i3−4i​ is a real number.
b) If x2+y2=11xyx^2 + y^2 = 11xyx2+y2=11xy, prove that

log⁡(x−y3)2=12(log⁡x+log⁡y)\quad\quad\quad\quad\quad\log \left( \frac{x - y}{3} \right)^2 = \frac{1}{2} (\log x + \log y)log(3x−y​)2=21​(logx+logy)

HardNumerical10 marks2024(TU FOHSS Final)
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Exam Years

Past question papers

2024
TU FOHSS Final•2 questions
2023
TU FOHSS Final•2 questions
2022
TU FOHSS Final•2 questions
2020
TU FOHSS Final•2 questions
2019
TU FOHSS Final•2 questions

Questions in Unit 1: Set Theory and Real & Complex Number

In a class of 100 students, 40 failed in mathematics, 70 in English, and 20 in both subjects. Find:\ \(\quad \)a) How many students passed in both subjects?\ \(\quad \)b) How many passed in Mathematic

Marks: 5

Year: 2019 Final TU FOHSS

Given: Total students = \(100\)\ Failed in Mathematics = \(40\)\ Failed in English = \(70\)\ Failed in both subjects = \(20\) Failed in at least one subject \[= 40 + 70 − 20\\ = 90\] a) Students who p

If \(X+iy=1+i1−i,\) show that \(x2+y2=1.\)

Marks: 5

Year: 2019 Final TU FOHSS

Given: \( X + iy = \dfrac{1 + i}{1 - i} \) To show: \( x^{2} + y^{2} = 1 \) Solution: Rationalize the denominator by multiplying numerator and denominator by the conjugate of \( 1 - i \), i.e. \( 1 +

Out of 500 people, 285 like tea, 195 like coffee, 115 like lemon juice, 45 like tea and coffee, 70 like tea and juice, 50 like juice and coffee. If 50 do not like any drinks:\ \(\quad\)i) How many peo

Marks: 5

Year: 2020 Final TU FOHSS

Given: Total people = 500 Tea (T) = 285 Coffee (C) = 195 Lemon juice (J) = 115 Tea ∩ Coffee = 45 Tea ∩ Juice = 70 Coffee ∩ Juice = 50 People who like none = 50 Let the number of people

If \(x - i y = \frac{3-2i}{3+2i}\), prove that \(x^2 + y^2 = 1.\)

Marks: 5

Year: 2020 Final TU FOHSS

Given: \[ x - i y = \frac{3 - 2i}{3 + 2i} \] $\textbf{Solution:} $ Rationalize the denominator by multiplying numerator and denominator by the conjugate of $3 + 2i$, which is $3 - 2i$: \[ x - i y

In a certain village in Nepal, all the people speak Nepali or Tharu or both languages. If \(90\%\) speak Nepali and \(20\%\) speak Tharu, find how many people speak: \(\quad\)i) Nepali language on

Marks: 5

Year: 2022 Final TU FOHSS

$\textbf{Given:}$ $\text{Let total population = 100\%}$ $\text{Nepali speakers } = 90\%, \quad \text{Tharu speakers } = 20\%$ $\textbf{Step 1:}$ Use the principle of inclusion-exclusion: \[ \t

\( \text{If}\space x - ty = \frac{5 - 6i}{5 + 6i}, \) prove that \( x^2 + y^2 = 1. \)

Marks: 5

Year: 2022 Final TU FOHSS

$\textbf{Given:}$ \[ x - ty = \frac{5 - 6i}{5 + 6i} \] $\textbf{Step 1:}$ Rationalize the denominator: \[ \frac{5 - 6i}{5 + 6i} \cdot \frac{5 - 6i}{5 - 6i} = \frac{(5 - 6i)^2}{5^2 + 6^2} = \frac{2

Solve the inequality: \( 6 + 5x - x^2 \ge 0 \)

Marks: 5

Year: 2023 Final TU FOHSS

$\textbf{Given inequality:}$ \[ 6 + 5x - x^2 \ge 0 \] $\textbf{Step 1:}$ Rewrite in standard quadratic form: \[ -x^2 + 5x + 6 \ge 0 \implies x^2 - 5x - 6 \le 0 \] $\textbf{Step 2:}$ Factorize the

a) If \(A\) and \(B\) are two subsets of universal set \(U\) such that\(n(U) = 350, \quad n(A) = 100, \quad n(B) = 150, \quad \text{and} \quad n(A \cap B) = 50,\) then find \(n(A' \cap B')\).\ b) If \

Marks: 10

Year: 2023 Final TU FOHSS

$\textbf{Problem a:}$ Find $n(A' \cap B')$ $\textbf{Step 1:}$ Recall formula: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] $\textbf{Step 2:}$ Compute $n(A \cup B)$: \[ n(A \cup B) = 100 + 150 -

Solve the inequality: \( 3 + 2x - x^2 \ge 0 \)

Marks: 5

Year: 2024 Final TU FOHSS

$\textbf{Given inequality:}$ \[ 3 + 2x - x^2 \ge 0 \] $\textbf{Step 1:}$ Rewrite in standard quadratic form: \[ -x^2 + 2x + 3 \ge 0 \implies x^2 - 2x - 3 \le 0 \] $\textbf{Step 2:}$ Factorize the

Prove that \[ \quad\quad\quad\quad\quad\frac{3 + 4i}{1 - i} + \frac{3 - 4i}{1 + i} \) is a real number. b) If \(x^2 + y^2 = 11xy\), prove that \[ \quad\quad\quad\quad\quad\log \left( \frac{x - y

Marks: 10

Year: 2024 Final TU FOHSS

$\textbf{Problem a:}$ Prove that $\frac{3 + 4i}{1 - i} + \frac{3 - 4i}{1 + i}$ is real. $\textbf{Step 1:}$ Rationalize denominators: \[ \frac{3 + 4i}{1 - i} \cdot \frac{1 + i}{1 + i} = \frac{(3 + 4i)(

About Unit 1: Set Theory and Real & Complex Number Questions

This page contains comprehensive questions from the Unit 1: Set Theory and Real & Complex Number chapter of Mathematics I, part of the BCA Semester 1 curriculum. All questions include detailed model answers from past TU exam papers.

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Unit 1: Set Theory and Real & Complex Number chapter questions with answers for Mathematics I (BCA Semester 1). Prepare for TU exams with our comprehensive question bank and model answers.

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