Cube of odd positive integer is —

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Chandan Asked Sep 15, 2023

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Let n be a fixed positive integer. Define a relation R on the set of integers Z, $a R b \Leftrightarrow n \mid(a-b)$. Then prove that R is equivalence relation

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The range of the function $f(x)=\sin ^{-1}\left[x^2+\frac{1}{2}\right]+\cos ^{-1}\left[x^2-\frac{1}{2}\right]$, where [ ] is the greatest integer function, is:

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Let R be the set of real numbers. Statement-1 : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$. Statement-2 : $B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on R.

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If $\alpha$ and $\beta$ are imaginary cube roots of unity, then $\alpha^4+\beta^4+\frac{1}{\alpha \beta}$ is equal to

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Let $f(x)=A x^2+B x+C$, where $A, B, C$ are real numbers. Prove that if $f(x)$ is an integer whenever $x$ is integer, then the numbers $2 A, A+B$ and $C$ are all integers.

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A cell is containing two H electrodes. The negative electrode is in contact with a solution of 10^{-6} M H+ ions. The emf of the cell is 0.118 V at $25^{\circ} {C}$. What is the $\left[{H}^{+}\right]$at positive electrode?

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The equivalent conductance of NaCl at concentration C and at infinite dilution are $\lambda_C$ and $\lambda_{\infty}$, respectively. The correct relationship between $\lambda_C$ and $\lambda_{\infty}$ is given as (where, the constant B is positive)

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In response to the speaker's question." What singed thy wings?" The Koel replies, "The fire of love has charred my wings." What does the Koel's answer suggest? Can love burn like fire? Is this burning a positive thing on a negative one. Explain.

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The edge of a cube is $a=1.2 \times 10^{-2} m$. Then its volume will be recorded as :

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The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is —

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Cube of odd positive integer is —

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