Home
Class 11
MATHS
Statement 1 : If 27a+9b+3c+d=0, then the...

Statement 1 `:` If `27a+9b+3c+d=0`, then the equation f(x) `=4ax^(3) + 3b^(2) +2cx + d=0` . Has at least one real root lying between (0,3).
Statement 2 `:` If f(x) is continuous in [a,b], derivable in (a,b) such that f(a) =f(b) , then at least one point `c in (a,b)` such that f(c ) = 0.

A

If both the statement are TRUE and STATEMENT 2 is the correct explanation of STATMEMENT -1

B

If both the statement are TRUE and STATEMENT2 is NOT the correct explanation of STATEMENT-1

C

If STATEMENT -1 is TRUE and STATEMENT 2 is FALSE

D

If STATEMENT-1 is FALSE and STATEMENT 2 is TRUE

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise LECTURE SHEET(EXERCISE-I (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS)|1 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (PRACTICE SHEET )(ADVANCED)) (INTEGER TYPE QUESTIONS)|3 Videos

  • MULTIPLE & SUBMULTIPLE

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE - II) (LEVEL - II) (Linked Comprehension Type Questions)|5 Videos

Similar Questions

Explore conceptually related problems

If 27a+9b+3c+d=0 , then the equation 4ax^(3)+3bx^(2)+2cx+d =0 has atleast one real root lying between

If f is continuous on [a,b] and differentiable in (a,b) (ab gt 0 ) , then there exists c in (a,b) such that (f(b)-f(a))/((1)/(b) - ( 1)/(a))=

If 2a+3b+6c =0 then the equation ax ^2 + bx +c=0 has atlest one root in

If the equation x^(2) + 12 + 3 sin (a + bx) + 6x = 0 has at least one real solution, when a, b in [0, 2 pi] , then the value of a = 3b is (n in Z)

If 1,2,3 and 4 are the roots of the eqaution x^(4) + ax^(3) + b x^(2) + cx + d = 0, then a + 2b + c =

If 1,2,3 and 4 are the roots of the equation x^4 + ax^3 + bx^2 +cx +d=0 then a+ 2b +c=

Let f(x)=(x-1)(x-2)(x-3) then prove that there is more than one 'c' in (1,3) such that f'(c )=0

If a+b+c=0 then the quadratic equation 3ax^2+2bx+c=0 has at least one root in

AAKASH SERIES-MEAN VALUE THEOREMS-PRACTICE SHEET (EXERCISE-I (LEVEL-I))
  1. The value of 'c' prescribed by Lagrange's mean value theorem , when f(...

    Text Solution

    |

  2. The value of C in the lagrange's mean value theroem for f(x) = sqrt( x...

    Text Solution

    |

  3. The value of 'theta' of the Lagrange's mean value theorem for f(x) = x...

    Text Solution

    |

  4. The chord joining the points where x=p and x=q on the curve y =a x^(2)...

    Text Solution

    |

  5. Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2) i...

    Text Solution

    |

  6. If a lt c lt b , and if 1-k(1) lt ln ((b)/(a)) lt k(2) -1 , then ( ...

    Text Solution

    |

  7. If a(1) lt ( 257)^(1//4) -4 lt b (1), then (a(1) , b(1) ) ( a(1) , b(...

    Text Solution

    |

  8. For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in ...

    Text Solution

    |

  9. Let f be a function which is continuous and differentiable for all rea...

    Text Solution

    |

  10. The value of c in Lagrange's Mean Value theorem for the function f(x) ...

    Text Solution

    |

  11. The value of 'c' of Lagrange's mean value theorem for f(x) = x^(3) - 5...

    Text Solution

    |

  12. In the mean value theorem, f(b) - f(a) = (b-a) f(c ) , if a= 4, b = 9 ...

    Text Solution

    |

  13. The constant c of Lagrange's mean value theorem for f(x) =2 sin x+ sin...

    Text Solution

    |

  14. If f(x) = x^(n) for 0 lt a lt b and na^(n-1) le (b^(n) - a^(n))/( b-a...

    Text Solution

    |

  15. Let f(x) and g(x) be differentiable functions in (a,b) continuous in [...

    Text Solution

    |

  16. Lagrange's mean value theorem cannot be applied for

    Text Solution

    |

  17. Let f(x) and g(x) be two differentiable functions in R such that f(2) ...

    Text Solution

    |

  18. If the function f(x) and phi (x) are continuous in [a,b] and different...

    Text Solution

    |

  19. Statement 1 : If 27a+9b+3c+d=0, then the equation f(x) =4ax^(3) + 3b^(...

    Text Solution

    |

  20. Assertion (A) : Suppose f is differentiable on R such that 1le f'(x ) ...

    Text Solution

    |