Cube of negative integer is —

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Chandan Asked Sep 15, 2023

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LEELADHAR YADAV Asked Sep 2, 2023

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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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Let R be the real line. Consider the following subsets of the plane R×R $S=\{(x, y): y=x+1 \text { and } 0<x<2\} \\ T=\{(x, y): x-y \text { is an integer }\}$

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by LEELADHAR YADAV

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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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If ω is a cube root of unity, then $\left|\begin{array}{ccc}x+1 & \omega & a^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega\end{array}\right|$ equal to

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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 A={1,2,3,4,5,6} and * be an operation A defined by $a{ }^* b=r$, where r is the least non-negative remainder when the product a b is divided by k. Operation * is binary operation if k=

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An vehicle is to be stopped with a negative acceleration of 1.7 m s s-²?

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245 views

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?

Chandan Asked Sep 15, 2023

by Chandan

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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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LEELADHAR YADAV Asked Sep 3, 2023

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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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(i) Find all positive integral solutions of the equation, $\tan ^{-1} x+\cot ^{-1} y=\tan ^{-1} 3$. (ii) If ' $k$ ' be a positive integer, then show that the equation: $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} k$ has no non-zero integral solution.

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Solve $\left\{\cos ^{-1} x\right\}+\left[\tan ^{-1} x\right]=0$ for real values of $x$. Where $\{$.$\} and [$. ] are fractional part and greatest integer functions respectively.

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If $\mathrm{f}$ be a greatest integer function and $\mathrm{g}$ be an absolute value function. Find the value of $\text { (log) }\left(\frac{-3}{2}\right)+(\text { gof })\left(\frac{4}{3}\right) \text {. }$

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Find the range of the following functions : where (.) and (.) represent fractional part and greatest integer part functions respectively)

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There are three glass cubes of edges 20 cm, 16 cm and 12 cm respectively. These are melted to form a new cube. Find the edge of the new cube.

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An unknown gas SO _x diffuses slowly than O2 but faster than SF2. Considering that x is a positive integer, find ratio of rate of diffusion of He w.r.t. SO _x.

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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 negative integer is —

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