Home
Class 11
MATHS
The equation x log x = 3-x has, in the i...

The equation `x log x = 3-x` has, in the interval (1,3) :

A

exactly one root

B

at most one root

C

at least one root

D

no root

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|4 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|19 Videos

Similar Questions

Explore conceptually related problems

The equation x^(log_(3)x)=9 has

Verify Rolle's theorem for the function f(x) = {log (x^(2) +2) - log 3 } in the interval [-1,1] .

Let- 1<=p<1 show that the equation 4x^(3)-3x-p=0 has a unique root in the interval [(1)/(2),1]

If the function f(x)=2x^(2)+3x-m log x is monotonic decreasing in the interval (0,1) then the least value of the parameter m is

The function log (1+x) - (2x)/(x+2) is increasing in the interval:

The equation log_(2)(3-x)+log_(2)(1-x)=3 has

The equation log_(2)(3-x)+log_(2)(1-x)=3 has

If x satisfies log_(3)(2x+1) < log_(3)5 ,then the solution set contains the interval(s)

If f(x)=x ln x-2, then show that f(x)=0 has exactly one root in the interval (1,e).

Let f(x)=3sin^(3)x+4x-sin|x|+log(1+|x|) beidd euen adefined on the interval [0,1]. The even extensionof f(x) to the interval [-1,0] is

OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
  1. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  2. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  3. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  4. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

    Text Solution

    |

  5. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

    Text Solution

    |

  6. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

    Text Solution

    |

  7. The value of c in Largrange's theorem for the function f(x)= log(e) s...

    Text Solution

    |

  8. n is a positive integer. If the value of c presecribed in Rolle's th...

    Text Solution

    |

  9. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

    Text Solution

    |

  10. The number of real root of the equation e^(x-1)+x-2=0, is

    Text Solution

    |

  11. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  12. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

    Text Solution

    |

  13. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  14. If from Largrange's mean value theorem, we have f(x'(1))=(f'(b)-f(a))...

    Text Solution

    |

  15. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

    Text Solution

    |

  16. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

    Text Solution

    |

  17. When the tangent the curve y=x log (x) is parallel to the chord joinin...

    Text Solution

    |

  18. The value of c in Rolle's theorem for the function f (x) =(x(x+1))/e^x...

    Text Solution

    |

  19. The value of c in Largrange's mean value theorem for the function f(...

    Text Solution

    |

  20. The value of c in Rolle's theorem for the function f(x) = x^(3) - 3...

    Text Solution

    |