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40 Maths General Knowledge Questions And Answers

1. Who discovered Zero (0)? Answer: Aryabhatta, AD 458 Explanation: Aryabhatta invented zero but he didn’t give any symbol for zero, Brahmagupta was the first to give symbol for zero and rules to compute with zero.

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

Given that, ​\( f(x)=\begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, \text{if} \ -1\le x<0 \\ \frac{2x+1}{x-1}, \text{if} \ 0\le x<1 \end{cases} \)​ 

First and Second fundamental theorem of calculus

If ​\( F'(x)=f(x) \)​ then F is called primitive or antiderivative of f. e.g.\( F(x)=x^2sin(\frac{1}{x}) \) ​\( \therefore F'(x)=2xsin(\frac{1}{x})+x^2.cos(\frac{1}{x}).(\frac{-1}{x^2}) \)​

GENERAL APTITUDE

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

Let (X, d) be a metric space and suppose that it is disconnected. Claim: ​\( \exists \)​ a non-empty proper subset of X which is both open & closed.

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SET NET

Compititive

Linear Functionals, Annihilator and Double Dual

If V is a vector space over the field F and S be a subset of V, the annihilator of S is ​\( S^0 \)​ and ​\( S^0 \)​ is the set of linear functionals f on V such that ​\( f(\alpha)=0 \)​ for each ​\( \alpha \in S \)

The Matrix of Linear Transformation and Linear Functionals

Let V be n-dimensional vector space over the field F and W be an m-dimensional vector space over the same field F.

Linear Transformation Part II – Inverse Linear Transformation and Isomorphism

A function T from V into W is called invertible if there exists a function S from W to V such that TS is an identity on W and ST is an identity on V.  i.e. ​\( TS=I_w, ST=I_v \)

Linear Transformation Part I – Algebra of Linear Transformation

Let ​\( \alpha, \beta \in V \)​ and c \in F and S & T are linear transformation from V to W.  ​\( (S+T)(c\alpha+\beta) \) \( =S(c\alpha+\beta)+T(c\alpha+\beta) \)

Cayley Hamilton Theorem

Let K be the commutative ring with identity consisting of all polynomials in T. Choose an ordered basis ​\( \{\alpha_1, \alpha_2, ... ,\alpha_n\} \)​ for V. Let A be the matrix of T in the basis ​\( \{\alpha_1, \alpha_2, ... ,\alpha_n\} \)
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Matrices

Let V be n-dimensional vector space over the field F and W be an m-dimensional vector space over the same field F.
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Statistics

Probability

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