Home
Class 12
MATHS
The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(...

The equation `|2ax-3|+|ax+1|+|5-ax|=(1)/(2)` possesses

A

Infinite number of real solutions for some `a in R`

B

finitely many real solutions for some `a in R''`

C

no real solutions for some `a in R`

D

no real solutions `a in R`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` We have `|2ax-3|+|ax+1|+|5-ax|=(1)/(2)`
Now
`|2ax-3|+|ax+1|+|5-ax| ge |2ax-3-(ax+1)+5-ax|=1`
So the given equation has no solution.
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|25 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise (Numerical) & JEE Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

The set of real values of a for which the quadratic equation ax^(2)+(2a-3)x+5=0 possesses roots of opposite signs is given by

If the equations x^(5) + ax + 1= 0 and x^(6) + ax^(2) + 1= 0 have a common root , then the value of ' -3a ' is equal to ______.

If 2a=b, the pair of equations ax+by=2a^(2)-3b^(2),x+2y=2a-6b possess

The value of a for which the equation x^3+2ax+2=0 and x^(4)+2ax^(2)+1=0 have a common root is "

The number of values of a for which equations x^(3)+ax+1=0 and x^(4)+ax^(2)+1=- have a common root is a.0 b.1 c.2 d.Infinite

If the equation 2sin x+3cos ax=5 has a solution,then a is

If x = 1 is a common root of the equations ax^(2) + ax + 3 = 0 and x^(2) + x + b = 0 , then ab =

The quadratic equation ax^(2) - 4ax + 2a + 1 = 0 has repeated roots, if a =

If all roots of the equation x^(3)+ax^(2)-ax-1=0 are real and distinct,then the set of values of a is

CENGAGE-INEQUALITIES AND MODULUS-Single correct Answer
  1. The complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+...

    Text Solution

    |

  2. The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x...

    Text Solution

    |

  3. The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-...

    Text Solution

    |

  4. The solution set of inequality (1)/(2^(x)-1) gt (1)/(1-2^(x-1)) is

    Text Solution

    |

  5. Let A={x:x^(2)-4x+3 lt 0,x in R } B={x: 2^(1-x)+p le 0 , x^(2)-2(p+7)...

    Text Solution

    |

  6. Let a, b gt 0 satisfies a^(3)+b^(3)=a-b. Then

    Text Solution

    |

  7. The number of integers satisfying |2x-3|+|x+5| le |x-8| is

    Text Solution

    |

  8. Which of the following is not the solution of |2x+5|-|x-3| ge |x+8| ...

    Text Solution

    |

  9. The number of integral values of x satisfying the equation |x-|x-4||=4...

    Text Solution

    |

  10. The solution of |2x-3| lt |x+2| is

    Text Solution

    |

  11. The solution set of the inequation |(1)/(x)-2| lt 4, is

    Text Solution

    |

  12. The solution of |x+(1)/(x)| gt 2 is

    Text Solution

    |

  13. The solution of the inequality (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0 is

    Text Solution

    |

  14. If |(12x)/(4x^(2)+9)| le 1, then

    Text Solution

    |

  15. Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then t...

    Text Solution

    |

  16. The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+...

    Text Solution

    |

  17. If |x^2- 2x- 8| + |x^2+ x -2|= 3|x +2|, then the set of all real valu...

    Text Solution

    |

  18. The number of integers satisfying the equation |x|+|(4-x^(2))/(x)|=|(4...

    Text Solution

    |

  19. The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses

    Text Solution

    |

  20. The set of values of x satisfying |(x^(2)-5x+4)/(x^(2)-4)| le 1 is

    Text Solution

    |