Home
Class 12
MATHS
Let a,b,c,d be real numbers such that |a...

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

A

`9`

B

`18`

C

`24`

D

`30`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `|a-b|=2impliesa-b=+2`
`|b-c|=3impliesb-c=+-3`
`|c-d|=4impliesc-d=+-4`
Possible values of `a-d` are `+-9`, `+-5`, `+-3`, `+-1`
`:. |a-d|=9,5,3,1`
Sum `=18`
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

If a,b,c and d are integers such that a+b+c+d=30, then the minimum possible value of (a-b)^(2)+(a+c)^(2)+(a+d)^(2) is

Let a,b,c,d,e, be real numbers such that a+b lt c+d , b+c lt d+e, c+d lt e+a, d+e lt a+b . Then

If a,b,a and d are natural numbers such that a^(5)=b^(6),c^(3)=d^(4), and d-a=61, then the smallest value of c-b is :

If a,b,c,d are distinct complex number and |a|=|b|=|c|=|d|=3,|a-b|=|b-c|=|c-d|=sqrt(3) then the value of |a-d| is equals to

If a,b,and c are nonzero rational numbers, then find the sum of all the possible values of (|a|)/(a)+(|b|)/(b)+(|c|)/(c)

Let a,b,c , d ar positive real number such that a/b ne c/d, then the roots of the equation: (a^(2) +b^(2)) x ^(2) +2x (ac+ bd) + (c^(2) +d^(2))=0 are :

Let a, b, c, d be distinct real numbers such that a, b are roots of x^2-5cx-6d=0 and c, d are roots of x^2-5ax-6b=0 . Then b+d is

Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 and e=18 , then the sum of all possible value of c is ________.

If a,b and c are non-zero rational numbers, then the sum of all the possible values of (|a|)/(a)+(|b|)/(b)+(|c|)/(c) 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

    |