Riemann Integration

Dimension theorem of a quotient space: If W be a subspace of a finite dimensional vector space V over \( \mathbb{R} \) then \( dim\frac{V}{W}=\dim V – \dim W \)

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Continuous image of connected set is connected

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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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FYBSCIT | Computational Logic and Discrete Structure: Set Theory 2023

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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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Dimension theorem of a quotient space: If W be a subspace of a finite dimensional vector space V over \( \mathbb{R} \) then \( dim\frac{V}{W}=\dim V – \dim W \)

Continuous image of connected set is connected

Female rabbits are either juvenile or adult. Each month, each juvenile grows to adulthood and each adult female gives birth (on average) to one juvenile female. Starting with one juvenile female rabbit, how many...

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