Home
Class 12
MATHS
The natural numbers ware not sufficient ...

The natural numbers ware not sufficient to deal with various equations that mathematicians encountered so some new sets of numbers were defined
Ehole numbers (W) = `{0,1,2,3,4,……….}`
Integers (Z or I) `= (……, -3,-2,-1,1,0,2,3,4,……}`
Even integers :- Intigers divisible by 2, they are expressed as `2n n in Z.`
odd Integers :- Integers not divisible by 2, they are expressed as `2n+1or 2n-1,ninZ.`
If `m^(2)-n^(2)=7,` where m, `n in Z,` then number of ordered pairs (m,n) is

A

42

B

56

C

50

D

none of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

The natural numbers ware not sufficient to deal with various equations that mathematicians encountered so some new sets of numbers were defined Ehole numbers (W) = {0,1,2,3,4,……….} Integers (Z or I) = (……, -3,-2,-1,1,0,2,3,4,……} Even integers :- Intigers divisible by 2, they are expressed as 2n n in Z. odd Integers :- Integers not divisible by 2, they are expressed as 2n+1or 2n-1,ninZ. Difference of squarees of two odd integeers is always divisible by

Show that n^2-1 is divisible by 8, if n is an odd positive integer.

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

Prove by induction that if n is a positive integer not divisible by 3 , then 3^(2n)+3^(n)+1 is divisible by 13 .

Prove that n^2-n divisible by 2 for every positive integer n.

Prove that if xa n dy are odd positive integers, then x^2+y^2 is even but not divisible by 4.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If A={n:(n^(3)+5n^(2)+2)/(n)"is an integer"}, then the number of elements in the set A, is

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

RESONANCE ENGLISH-DPP-QUESTION
  1. The natural numbers ware not sufficient to deal with various equations...

    Text Solution

    |

  2. The natural numbers ware not sufficient to deal with various equations...

    Text Solution

    |

  3. The natural numbers ware not sufficient to deal with various equations...

    Text Solution

    |

  4. Number of ordered pairs of intergers {n,m} for which n^(2)-m^(2)=14 is

    Text Solution

    |

  5. Identify the correct statement (1) If a, b, c are odd itergers a + b...

    Text Solution

    |

  6. If n^(2)+2n -8 is a prime number where n in N then n is

    Text Solution

    |

  7. If n^(2)-11n+24=0 is satisfied by n(1)&n(2) where n(2)gtn(1) then (A)...

    Text Solution

    |

  8. Which of the following numbers is irrational?

    Text Solution

    |

  9. If p,q in N and 0.1bar2=p/q where p and q are relatively prime then wh...

    Text Solution

    |

  10. Consider the following statements (i) The sum of a rational number w...

    Text Solution

    |

  11. The equation 7x^(2)-(7pi+22)x+22pi=0has (A) equal roots (B) a root wh...

    Text Solution

    |

  12. Theere are four prime numbers written in ascending order. The product ...

    Text Solution

    |

  13. Find out (A+B+C+D) such that ABxxCB=DDD, where AB and CB are two-digit...

    Text Solution

    |

  14. Let a,b inQ"such that"(39sqrt2-5)/(3-sqrt2)=a+bsqrt2, then (A) sqrt((...

    Text Solution

    |

  15. Text Solution

    |

  16. If xx=sqrt(3)+sqrt(2), then find xx+1/x,x^(2)+(1)/(x^(2)),x^(3)+(1)/(x...

    Text Solution

    |

  17. Find the sum (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4...

    Text Solution

    |

  18. If a statement is true for all the values of the variable, such statem...

    Text Solution

    |

  19. If a statement is true for all the values of the variable, such statem...

    Text Solution

    |

  20. If a statement is true for all the values of the variable, such statem...

    Text Solution

    |