Permutation & Combination

Cayley Hamilton Theorem

August 30, 2023

A metric space (X, d) is disconnected iff there exists a non-empty proper open & closed subset of X which is both open and closed

August 28, 2023

A bounded function \( f:[a, b]\to \mathbb{R} \) is Riemann integrable iff for every \( \epsilon>0 \) there exist a partition \( P_\epsilon \) of [a, b] such that \( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)

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FYBSCIT | Computational Logic and Discrete Structure: Set Theory 2023

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40 Maths General Knowledge Questions And Answers

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Introduction to Operations Research

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FYBSCIT | Computational Logic and Discrete Structure: Set Theory 2023

40 Maths General Knowledge Questions And Answers

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

The product of 2 numbers is 1575 and their quotient is $ \frac{9}{7} $. Then the sum of the numbers is

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Cayley Hamilton Theorem

FYBSCIT | Computational Logic and Discrete Structure: Set Theory 2023

First and Second fundamental theorem of calculus

Every continuous function f defined on \([a, b]\) is Riemann integrable

Every monotonic function on [a, b] is Riemann integrable

A bounded function \( f:[a, b]\to \mathbb{R} \) is Riemann integrable iff for every \( \epsilon>0 \) there exist a partition \( P_\epsilon \) of [a, b] such that \( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)

A metric space (X, d) is disconnected iff there exists a non-empty proper open & closed subset of X which is both open and closed

Any two closed subset of metric space are connected iff they are disjoint

A metric space (X, d) is connected iff every continuous function \( f:X\to {\lbrace 0, 1\rbrace} \) is constant.

Continuous image of connected set is connected

Introduction to Operations Research

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

The probability that a ticketless traveler is caught during a trip is 0.1. If the traveler makes 4 trips , the probability that he/she will be caught during at least one of the trips...

There are 8 steps to the top of the stairs. In how many ways can we get to the top if we can climb one step or two steps?

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Find the value of k, for which $f(x)=\begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, \text{if} \ -1\le x<0 \\ \frac{2x+1}{x-1}, \text{if} \ 0\le x<1 \end{cases}$ is continuous at x=0.

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Cayley Hamilton Theorem

A metric space (X, d) is disconnected iff there exists a non-empty proper open & closed subset of X which is both open and closed

A bounded function \( f:[a, b]\to \mathbb{R} \) is Riemann integrable iff for every \( \epsilon>0 \) there exist a partition \( P_\epsilon \) of [a, b] such that \( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)

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