What are Real Numbers?

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Chandan Asked Aug 5, 2023

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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 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;

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 11, 2023

66 views

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

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 22, 2023

101 views

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

by LEELADHAR YADAV

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101 Views

LEELADHAR YADAV Asked Aug 19, 2023

97 views

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 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

118 views

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

by LEELADHAR YADAV

1 Answer

1 Vote

118 Views

Chandan Asked Aug 5, 2023

129 views

What are Composite Numbers?

Chandan Asked Aug 5, 2023

by Chandan

1 Answer

1 Vote

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Chandan Asked Aug 5, 2023

73 views

What are Perfect Numbers?

Chandan Asked Aug 5, 2023

by Chandan

2 Answers

2 Votes

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Chandan Asked Aug 5, 2023

160 views

What are Consecutive Numbers?

Chandan Asked Aug 5, 2023

by Chandan

1 Answer

1 Vote

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Chandan Asked Aug 5, 2023

132 views

What are Imaginary Numbers?

Chandan Asked Aug 5, 2023

by Chandan

1 Answer

0 Votes

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Chandan Asked Aug 5, 2023

127 views

What are Odd Numbers?

Chandan Asked Aug 5, 2023

by Chandan

1 Answer

0 Votes

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ALOK_RAJ Asked Aug 5, 2023

61 views

What are Twin Prime Numbers?

ALOK_RAJ Asked Aug 5, 2023

by ALOK_RAJ

1 Answer

0 Votes

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ALOK_RAJ Asked Aug 4, 2023

160 views

What are Co-prime Numbers?

ALOK_RAJ Asked Aug 4, 2023

by ALOK_RAJ

2 Answers

1 Vote

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ALOK_RAJ Asked Aug 4, 2023

93 views

What are Natural numbers?

ALOK_RAJ Asked Aug 4, 2023

by ALOK_RAJ

2 Answers

1 Vote

93 Views

LEELADHAR YADAV Asked Sep 5, 2023

66 views

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.

LEELADHAR YADAV Asked Sep 5, 2023

by LEELADHAR YADAV

1 Answer

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66 Views

Aayush Asked Apr 18

52 views

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

Aayush Asked Apr 18

by Aayush

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Aayush Asked Mar 29

40 views

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.

Aayush Asked Mar 29

by Aayush

1 Answer

0 Votes

40 Views

Chandan Asked Sep 15, 2023

89 views

All natural numbers, whole numbers and integers are —

Chandan Asked Sep 15, 2023

by Chandan

1 Answer

0 Votes

89 Views

Aayush Asked Jan 2

50 views

What is Divisible Numbers?

Aayush Asked Jan 2

by Aayush

1 Answer

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50 Views

ALOK_RAJ Asked Aug 5, 2023

67 views

What is a Prime Triplet Numbers?

ALOK_RAJ Asked Aug 5, 2023

by ALOK_RAJ

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Chandan Asked Aug 26, 2023

72 views

The values of $P_{C}$ and $T_{C}$ for two real gases X and Y (both gases have same molar mass) are given below.

Chandan Asked Aug 26, 2023

by Chandan

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Chandan Asked Sep 22, 2023

96 views

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.

Chandan Asked Sep 22, 2023

by Chandan

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Chandan Asked Aug 26, 2023

49 views

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

Chandan Asked Aug 26, 2023

by Chandan

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ANAND_YADAV Asked Jul 30, 2023

67 views

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

ANAND_YADAV Asked Jul 30, 2023

by ANAND_YADAV

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Aayush Asked Apr 15

48 views

What is the Definition of Real Image?

Aayush Asked Apr 15

by Aayush

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LEELADHAR YADAV Asked Sep 5, 2023

113 views

Find the set of all real values of $x$ satisfying the inequality $\sec ^{-1} x>\tan ^{-1} x$.

LEELADHAR YADAV Asked Sep 5, 2023

by LEELADHAR YADAV

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113 Views

LEELADHAR YADAV Asked Aug 19, 2023

141 views

Consider the following relation R on the set of real square matrices of order 3 . $R=\left\{(A, B) \mid A=P^{-1} B P\right.$ for some invertible matrix $\left.P\right\}$.

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

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141 Views

LEELADHAR YADAV Asked Aug 19, 2023

53 views

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

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

53 Views

Aayush Asked Feb 22

55 views

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

1 Answer

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55 Views

Aayush Asked Jan 2

48 views

Define Numbers.

Aayush Asked Jan 2

by Aayush

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LEELADHAR YADAV Asked Aug 22, 2023

65 views

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

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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ALOK_RAJ Asked Aug 3, 2023

103 views

Rule to find the HCF of two or more numbers?

ALOK_RAJ Asked Aug 3, 2023

by ALOK_RAJ

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ALOK_RAJ Asked Aug 3, 2023

160 views

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

by ALOK_RAJ

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160 Views

XYZ Asked Apr 14, 2021

117 views

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

XYZ Asked Apr 14, 2021

by XYZ

1 Answer

7 Votes

117 Views

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What are Real Numbers?

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