BCA Semester 1 – Mathematics I () Questions & Answers | Past TU Exam Papers

Question 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 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

Question 2

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 +

Question 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:\ $\quad$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

Question 4

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

Question 5

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

Question 6

$ \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

Question 7

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

Question 8

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 -

Question 9

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

Question 10

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)(