Home
Class 12
MATHS
The number of integral values of m for w...

The number of integral values of `m` for which the x-coordinate of the point of intersection of the lines `3x+4y=9` and `y=m x+1` is also an integer is 2 (b) 0 (c) 4 (d) 1

A

2

B

0

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`"Solving "3x+4y=9, y=mx+1, "we get" `
`x=(5)/(3+4m)`
Here, x is an integer if 3+4m=1,-1,5,-5. Hence m=-2/4, -4/4, 2/4,-8/4. So, m has two integral values.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (LINKED COMPREHENSION TYPE)|27 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

The number of integral values of 'm' for which the x coordinate of the point of intersection of the lines 3x+4y=9 and y = mx+1 is also an integer is

The number of integer values of m. for which the x - coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an interger is

The number of interger values of m, for which the x coordinate of the point of intersection of the lines y = mx +1 and 3x+4 y =9 is also in integer, is-

Find the integer values of m for which x-coordinate of the point of intersection of the striaght lines 3x+4y=9 and y=mx+1 is also integer.

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0 .

Find the value of a if the points (1, 2) and (3, 4) are of opposite side of the line 3x - 4y + a = 0

The number of integral coordinates of the points (x, y) which are lying inside the circle x^(2) + y^(2) = 25 is n, then the integer value of (n)/(9) will be -

If a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

Find the equation of the straight line which passes through the point of intercestion of the straight lines 3x-4y+1=0 and 5x+y=0 and makes equal intercepts upon the coordinate axes .

CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
  1. The line L1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , resp...

    Text Solution

    |

  2. A beam of light is sent along the line x-y=1 , which after refracting ...

    Text Solution

    |

  3. The number of integral values of m for which the x-coordinate of the p...

    Text Solution

    |

  4. If the sum of the distances of a point from two perpendicular lines in...

    Text Solution

    |

  5. The equation of set of lines which are at a constant distance 2 units...

    Text Solution

    |

  6. The lines y=m1x ,y=m2xa n dy=m3x make equal intercepts on the line x+y...

    Text Solution

    |

  7. Find the condition in a,b such that the portion of the line ax+by=1, i...

    Text Solution

    |

  8. The area of the triangle formed by the lines y= ax, x+y-a=0, and y-axi...

    Text Solution

    |

  9. The line x/a+y/b=1 meets the x-axis at A , the y-axis at B , and the l...

    Text Solution

    |

  10. The line x/3+y/4=1 meets the y-axis and x-axis at A and B respectively...

    Text Solution

    |

  11. The area of a parallelogram formed by the lines a x+-b y+-c=0 is

    Text Solution

    |

  12. One diagonal of a square is 3x-4y+8=0 and one vertex is (-1,1), then t...

    Text Solution

    |

  13. In an isoceles triangle OAB , O is the origin and OA=OB=6 . The equati...

    Text Solution

    |

  14. Find the sum of the series 1^2-2^2+3^2-4^2+\ldots-{2008}^2+{2009}^2

    Text Solution

    |

  15. The coordinates of the foot of the perpendicular from the point (2,3) ...

    Text Solution

    |

  16. The straight lines 7x-2y+10=0 and 7x+2y-10=0form an isosceles triangle...

    Text Solution

    |

  17. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

    Text Solution

    |

  18. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

    Text Solution

    |

  19. The range of values of theta in the interval (0, pi) such that the poi...

    Text Solution

    |

  20. Distance of origin from the line (1+sqrt3)y+(1-sqrt3)x=10 along the li...

    Text Solution

    |