Home
Class 12
MATHS
Let S={(a,b): a,binZ,0lea,ble18} . The n...

Let `S={(a,b): a,binZ,0lea,ble18}` . The number of elements (x ,y) in Such that 3x+4y+5 is divisible by 19 is

A

38

B

19

C

18

D

1

Text Solution

Verified by Experts

The correct Answer is:
B

3x+4y+5=19 I
`5le(3x+4y+5)le131`
`5le191le131`

Total Solution =19
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-II MATHEMATICS|10 Videos
  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part A - Mathematics|20 Videos
  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2(MATHEMATICS)|10 Videos
  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

The number of common solutions for 3x+2y=18 and 5x+4y=3 is

Let S be the set of the first 21 natural numbers, then the probability of choosing {x, y}inS , such that x^3+y^3 is divisible by 3, is

Let S be the set of first 18 natural numbers. Then attempt the following. The probability of choosing {x,y} sube S such that x^(3)+y^(3) is divisible by 3

The number of common solutions for 3x + 2y = 18 and 5x+4y =3 is ______.

The number of solution for the simultaneous equations 3x + 4y = 12 and 4x +3y = 18 is ____

If x and y are two digits of the number 653xy such that the number is divisible by 80, then x + y is equal to 3 (b) 4 (c) 5 (d) 6

Show that the relation S on the set : A={x inZ:0lexle12} given by: S = { (a,b):a,binZ,|a-b| is divisible by 3} is an equivalence relation.

KVPY PREVIOUS YEAR-KVPY-PART -I MATHEMATICS
  1. Let C(0) be circle of radius 1. For nge1, let C(n) be a circle whose ...

    Text Solution

    |

  2. For a real number r we denote by [r] the largest integer less than or ...

    Text Solution

    |

  3. For each positive integer n, let An=max{(C(n,r) 0 le r le n} then the ...

    Text Solution

    |

  4. Let b,dgt0 . The locus of all points P(r,theta) for which the line OP ...

    Text Solution

    |

  5. Let C be the circle x^(2)+y^(2)=1 in the xy-plane . For each tge0, let...

    Text Solution

    |

  6. In an ellipse, its foci and the ends of its major axis are equally spa...

    Text Solution

    |

  7. Let ABC be a triangle such that AB=BC. Let F be midpoint of AB and X...

    Text Solution

    |

  8. The number of solutions to the equations cos^(4)x+(1)/(cos^(2)x)=sin^...

    Text Solution

    |

  9. Consider the function f(x)= {{:((x+5)/(x-2),"if " xne 2),(" 1", "if "...

    Text Solution

    |

  10. For a real number x let [x] denote the largest number less than or equ...

    Text Solution

    |

  11. Let :[0,pi]rarrR be defined as f(x) ={{:(sinx,"if x is irrational a...

    Text Solution

    |

  12. Let f: [0,1]rarr[0,oo] be a continuous function such that int(0)^(1) f...

    Text Solution

    |

  13. A continuous function f: R rarrR satisfies the equation f(x)=x+int(0)^...

    Text Solution

    |

  14. For a real number x let [x] denote the largest integer les than or eq...

    Text Solution

    |

  15. Two persons A and B throw a (fair) die (six faced cube faces numbered ...

    Text Solution

    |

  16. Let nge3. A list of numbers x(1),x(2),....,x(n) has mean mu and standa...

    Text Solution

    |

  17. What is the angle substended by an edge of regular tetrahedron at its ...

    Text Solution

    |

  18. Let S={(a,b): a,binZ,0lea,ble18} . The number of elements (x ,y) in Su...

    Text Solution

    |

  19. For a real number r let [r] denote the largest integer less than or eq...

    Text Solution

    |

  20. Let X be a set of 5 elements. The number d of ordered pairs (A,B) of s...

    Text Solution

    |