Cube of even positive integer is —

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Chandan Asked Sep 15, 2023

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Cube of positive integer is —

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Cube of odd positive integer is —

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Cube of negative integer is —

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LEELADHAR YADAV Asked Aug 13, 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

LEELADHAR YADAV Asked Aug 13, 2023

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LEELADHAR YADAV Asked Sep 5, 2023

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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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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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ALOK_RAJ Asked Aug 3, 2023

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If A is the set of the divisors of the number 15, B is set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9 , then $(A \cup C) \cap B$ is the set

ALOK_RAJ Asked Aug 3, 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:

LEELADHAR YADAV Asked Sep 2, 2023

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LEELADHAR YADAV Asked Aug 19, 2023

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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.

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 19, 2023

52 views

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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Aayush Asked Feb 22

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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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Ankit Asked Sep 14, 2023

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An edge of a variable cube is increasing at the rate of 10cm. How fast the volume of the cube will increase when the edge is 5cm long?

Ankit Asked Sep 14, 2023

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AnjaliYadav Asked May 17, 2022

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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

AnjaliYadav Asked May 17, 2022

by AnjaliYadav

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3 Votes

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XYZ Asked Aug 8, 2021

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The total surface area of a cube is 486 cm^2. Find its lateral surface area and diagonal of the cube.

XYZ Asked Aug 8, 2021

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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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Find the smallest number when it is multiplied by 392, then the product is perfect cube.

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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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LEELADHAR YADAV Asked Aug 28, 2023

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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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by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 24, 2023

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

LEELADHAR YADAV Asked Aug 24, 2023

by LEELADHAR YADAV

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Aayush Asked Apr 18

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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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What is the significance of the Aarogya Maitri Cube in disaster response?

Dev Yaduvanshi Asked Dec 5, 2023

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Chandan Asked Sep 15, 2023

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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?

Chandan Asked Sep 15, 2023

by Chandan

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Chandan Asked Aug 13, 2023

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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)

Chandan Asked Aug 13, 2023

by Chandan

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Sanjeev Yadav ji Asked Aug 11, 2023

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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.

Sanjeev Yadav ji Asked Aug 11, 2023

by Sanjeev Yadav ji

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ANAND_YADAV Asked Jul 29, 2023

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

ANAND_YADAV Asked Jul 29, 2023

by ANAND_YADAV

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ALOK_RAJ Asked May 7, 2022

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

ALOK_RAJ Asked May 7, 2022

by ALOK_RAJ

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1 Vote

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Cube of even positive integer is —

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