What is Divisible Numbers?

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Show that the relation S in the set $A=\{x \in Z: 0 \leq x \leq 12\}$ given by $S=\{(a, b): a, b \in Z,|a-b|$ is divisible by 4$\}$ is an equivalence relation. Find the set of all elements related to 1 .

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LEELADHAR YADAV Asked Aug 22, 2023

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Show that the relation S in the set $A=\{x \in Z: 0 \leq x \leq 12\}$ given by $S=\{(a, b): a, b \in Z,|a-b|$ is divisible by 4$\}$ is an equivalence relation. Find the set of all elements related to 1 .

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 15, 2023

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The relation R defined in N as aRbb is divisible by a is

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LEELADHAR YADAV Asked Aug 22, 2023

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Let $Z$ be the set of all integers and R be the relation on Z defined as $R=\{(a, b): a, b \in Z$, and $(a-b)$ is divisible by 5} Prove that $R$ is an equivalence relation.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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Aayush Asked Feb 22

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The average of 8 numbers is 21.2. The average of first five numbers is 22.3 and last 4 numbers is 19.8. Find the fifth number.

Aayush Asked Feb 22

by Aayush

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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.

LEELADHAR YADAV Asked Sep 3, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 22, 2023

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Show that the relation S in the set R of real numbers, defined as $S=\left\{(a, b): a, b \in R\right.$ and $\left.a \leq b^2\right\}$ is neither reflexive, nor symmetric nor transitive.

LEELADHAR YADAV Asked Aug 22, 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

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LEELADHAR YADAV Asked Aug 16, 2023

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Let S be the set of all real numbers. Then the relation R $\{(a, b): 1+a b>0\}$ on S is

LEELADHAR YADAV Asked Aug 16, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 15, 2023

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For real numbers x and y, we write xRy $\Rightarrow$ $-y+\sqrt{2}$ is an irrational number. Then the relation R is :

LEELADHAR YADAV Asked Aug 15, 2023

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LEELADHAR YADAV Asked Aug 11, 2023

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Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R. of non zero real numbers.

LEELADHAR YADAV Asked Aug 11, 2023

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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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XYZ Asked Apr 14, 2021

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The sum of two numbers is 29 and the difference of their square is 145. Find their difference.

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Aayush Asked Apr 18

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The sum and the multiplication of two numbers are 11 and 18 gradually. Find the sum of their inverse.

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Parwez (V.P.) has some cocks and goats. If the total numbers of heads and feet are 76 and 212 respectively, then find the number of cocks he has.

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Define Numbers.

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Chandan Asked Sep 15, 2023

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All natural numbers, whole numbers and integers are —

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LEELADHAR YADAV Asked Aug 22, 2023

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Let " be a binary operation on set Q of rational numbers defined as $a$ * $b=\frac{a b}{5}$. Write the identity for ", if any

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LEELADHAR YADAV Asked Aug 19, 2023

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Consider the following relations : $R:\{(x, y) \mid x, y$ are real numbers and $x=$ wy for some rational number w;

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Rule to find the HCF of two or more numbers?

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Infinite numbers of flasks are connected to one another as shown above. The volumes and pressures in each flask vary as shown. The stopcocks are initially closed. The common pressure, when all the stopcocks are opened, is

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An element is found in nature in two isotopic forms with mass numbers (A-1) and (A+3).

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An electron in a hydrogen atom makes a transition from n1 to n2 where n1 and n2 are principal quantum numbers of the two states.

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The electrons identified by quantum numbers n and l

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ANAND_YADAV Asked Jul 30, 2023

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The respective number of significant figures for the numbers $23.023,0.0003$ and $2.1 \times 10^{-3}$ are

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