Home
Class 12
MATHS
The number of integral points (x,y) (i.e...

The number of integral points (x,y) (i.e, x and y both are integers) which lie in the first quadrant but not on the coordinate axes and also on the straight line `3x + 5y = 2007` is equal to

A

133

B

135

C

138

D

140

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`3x+5y=2007 or x+(5y)/(3)=669`
Clearly, 3 must divide 5y and so `y=3k`, for some `kinN`. Thus,
`x+5k=669`
or `5kle668`
`kle(668)/(5)or kle133`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Comprehension)|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The number of integral points (x,y) ( i.e,x and y both are integers) which lie in the first quadrant but not on the coordinate axes and also on the straight line 3x+5y=2007is equal to

The number of lattice points in the 1 st quadrant,lying on the straight line 3x+5y=283 is

The circle that can be drawn to touch the coordinate axes and the line 4x + 3y =12 cannot lie in

The radius of the larger circle lying in the first quadrant and touching the line 4x+3y-12=0 and the coordinate axes, is

The lines x+y=|a| and ax-y=1 intersect each other in the first quadrant. Then the set ofpossible values of a is the interval

A point on the straight line, 3x+5y=15 which is equidistant from the coordinate axes will lie only in

Find the greatest value of x^(2)y^(3), where x and y lie in the first quadrant on the line 3x+4y=5.

The lines x+y=|a| and ax-y=1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval:

CENGAGE-COORDINATE SYSYEM -Exercise (Single)
  1. Point A and B are in the first quadrant,point O is the origin. If the ...

    Text Solution

    |

  2. Let a,b,c be in A.P and x,y,z be in G.P.. Then the points (a,x),(b,y) ...

    Text Solution

    |

  3. if Sigma(i=1)^(4)(x(i)^(2)+y(i)^(2))le 2x1x3+2x2x4+2y2y3+2y1y4, the po...

    Text Solution

    |

  4. The vertices A and D of square A B C D lie on the positive sides of x-...

    Text Solution

    |

  5. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

    Text Solution

    |

  6. The locus of the moving point whose coordinates are given by (e^t+e^(-...

    Text Solution

    |

  7. The locus of a point represent by x=(a)/(2)((t+1)/(t)),y=(a)/(2)((t-...

    Text Solution

    |

  8. The maximum area of the triangle whose sides a ,b and 5sintheta), and ...

    Text Solution

    |

  9. Vertices of a variable triangle are (3,4); (5costheta, 5sintheta) and ...

    Text Solution

    |

  10. From a point, P perpendicular PM and PN are drawn to x and y axes, res...

    Text Solution

    |

  11. The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) ...

    Text Solution

    |

  12. If the roots of the equation (x(1)^(2)-a^2)m^2-2x1y1m+y(1)^(2)+b^2=0...

    Text Solution

    |

  13. Through point P(-1,4), two perpendicular lines are drawn which interse...

    Text Solution

    |

  14. The number of integral points (x,y) (i.e, x and y both are integers) w...

    Text Solution

    |

  15. The foot of the perpendicular on the line 3x+y=lambda drawn from the o...

    Text Solution

    |

  16. The image of P(a,b) in the line y=−x is Q and the image of Q in the li...

    Text Solution

    |

  17. If the equation of the locus of a point equidistant from the points (a...

    Text Solution

    |

  18. Consider three lines as follows. L1:5x-y+4=0 L2:3x-y+5=0 L3: x+y+8=0...

    Text Solution

    |

  19. Consider a point A(m,n) , where m and n are positve intergers. B is th...

    Text Solution

    |

  20. In the given figure, OABC is a rectangle. Slope of OB is

    Text Solution

    |