Home
Class 12
MATHS
Consider the following statements (i) ...

Consider the following statements (i) The sum of a rational number with an irrational number is always irrationa. (ii) The product of two rational numbers is always rational. (iii) The product of two irrationals is always irrationals. (iv) The sum of two rational is always rational. (v) The sum of two irrationals is always irrational. The correct order of True/False of above statements is :

A

T F T F F

B

F F T T T

C

T T F T F

D

T T F F T

Text Solution

AI Generated Solution

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

sum of two rational numbers is

The product of any two irrational numbers is

The product of a non-zero rational number with an irrational number is always a/an

The sum of two irrational numbers is an irrational number (True/false).

Sum of two natural numbers is a rational number.

Which one of the following statement is true? (i) The sum of two irrational numbers is always an irrational number. (ii) The sum of two irrational numbers is always a rational number. (iii) The sum of two irrational numbers may be a rational number or irrational number. (iv) The sum of two irrational numbers is always an integer.

State whether the given statements are true or false : (i) The sum of two rationals is always rational. (ii) The sum of two irrationals is always irrational. (iii) The product of two rationals is always rational. (iv) The product of two irrationals is always irrational. (v) The sum of a rational and an irrational is always rational. (vi) The product of a rational and an irrational is always irrational.

The product of two irrational numbers is an irrational number (True/false).

The sum of two prime numbers is always prime

Prove the following statement by contradiction method p The sum of in irrational number and a rational number is irrational

RESONANCE ENGLISH-DPP-QUESTION
  1. Which of the following numbers is irrational?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Which of the following collections are sets ? (i) Collection of all ...

    Text Solution

    |

  16. Write the following sets in the tabular from : (i) A={x:x is a posit...

    Text Solution

    |

  17. Write the following sets in the set builder from : {:((i), 0={0),(i...

    Text Solution

    |

  18. How many positive integer x are there such that 3x has 3 digits and 4x...

    Text Solution

    |

  19. If a and b are positive integers such that a^(2)-b^(4)=2009, find a+b

    Text Solution

    |

  20. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

    Text Solution

    |