Home
Class 12
MATHS
Let g(x) be a continous and differentiab...

Let `g(x)` be a continous and differentiable function such that
`int_(0)^(2) {int_(sqrt2)^(sqrt(5//2))[2x^(2)-3]dx} g(x)dx=0, "then" g(x)=0`
when `x in (0,2)` has (where,`[.]` denotes the greatest integer function )

A

Exactly one real root

B

Atleast one real root

C

No real root

D

Two real roots

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (More than one answer)|32 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Linked Comprehension Type Questions|11 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Let g(x) be a continuous and differentiable function such that int_0^2{int_(sqrt2)^(sqrt5/2)[2x^2-3]dx}.g(x)dx=0, then g(x) = 0 when x in (0, 2) has (where [ *] denote greatest integer function)

the value of int_(0)^([x]) dx (where , [.] denotes the greatest integer function)

int_(0)^(2) sqrt(2-x)dx .

Evaluate int_(-2)^(4)x[x]dx where [.] denotes the greatest integer function.

int_(0)^(sqrt(2)) [x^(2)]dx , is

The value of int_(0)^(2)[x+[x+[x]]] dx (where, [.] denotes the greatest integer function )is equal to

If [sin x]+[sqrt(2) cos x]=-3 , x in [0,2pi] , (where ,[.] denotes th greatest integer function ), then

The value of int_(0)^(2)[x^(2)-x+1] dx (where , [.] denotes the greatest integer function ) is equal to

int_(-1)^(41//2)e^(2x-[2x])dx , where [*] denotes the greatest integer function.

The range of the function y=[x^2]-[x]^2 x in [0,2] (where [] denotes the greatest integer function), is

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  2. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  3. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

    Text Solution

    |

  4. If f:RrarrR defined by f(x)=sinx+x, then find the value of int0^pi(f^-...

    Text Solution

    |

  5. The value of int0^100 [tan^-1 x]dx is, (where [*] denotes greatest in...

    Text Solution

    |

  6. Iff(x)={0,w h e r ex=n/(n+1),n=1,2,31,e l s e w h e r e t h e nt h ev...

    Text Solution

    |

  7. Let g(x) be a continous and differentiable function such that int(0...

    Text Solution

    |

  8. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  9. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

    Text Solution

    |

  10. int(-pi//4) ^(pi//4) x^(3) sin^(4) xdx=

    Text Solution

    |

  11. The value of int(-10)^(10)[{f(f(x)}+{f(f((1)/(x))}]dx, where f(x)=(1-x...

    Text Solution

    |

  12. The value of int(-2)^(2)(ax^(2011)+bx^(2001)+c)dx, where a, b, c are c...

    Text Solution

    |

  13. If for non zero x, 3f(x)+4f((1)/(x))=(1)/(x)-10, then the value of int...

    Text Solution

    |

  14. The value of int(2010pi+(pi)/(6))^(2010pi+(pi)/(3))(sinx+cosx)dx is

    Text Solution

    |

  15. Let int(a)^(b)f(x)dx=int(a+c)^(b+c)f(x-c)dx. Then the value of int(0)^...

    Text Solution

    |

  16. If x^(f(x))=e^(x-f(x)), then the value of integral int(1)^(2)f'(x){(1+...

    Text Solution

    |

  17. If overset(x)underset(e )int t f(t)dt=sin x-x cos x-(x^(2))/(2) for al...

    Text Solution

    |

  18. The value of the integral int(-2012pi)^(2012pi) {d/dx(int0^(x^2) cost^...

    Text Solution

    |

  19. The value of int(-2010pi)^(2010pi) {x^2011(1+tan(pi/3-x)(1+tan(x-pi/1...

    Text Solution

    |

  20. Let f(x)=min{|x+2|,|x|,|x-2|} then the value of the integral int-2^2 ...

    Text Solution

    |