Home
Class 12
MATHS
If f''(x) =- f(x) and g(x) = f'(x) and F...

If f''(x) =- f(x) and g(x) = f'(x) and `F(x)=(f((x)/(2)))^(2)+(g((x)/(2)))^(2)`
and given that F(5) =5, then F(10) is

A

5

B

10

C

0

D

15

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL -1|134 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 and given that F(5)=5, then F(10) is (a)5 (b) 10 (c) 0 (d) 15

If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 and given that F(5)=5, then F(10) is 5 (b) 10 (c) 0 (d) 15

If f(x)=|x-2| and g(x)=f(f(x)) then g'(x)=

If f (x) is a function such that f (x) + f''(x) =0 and g (x)= (f (x))^(2) +(f' (x))^(2) and g (3) =8, then g (8)=

If f(x) = x log x and g(x) = 10^(x) , then g(f(2)) =

If f(x)=4x-5 and g(x)=3^(x) , then f(g(2)) =

If f(x) =4x^2 and g(x) =f(sin x)+f(cos x), then g (23^(@)) is

If f(g(x))=4x^(2)-8x and f(x)=x^(2)-4, then g(x)=

If f(x)=sqrt(x^(2)-1) and g(x)=(10)/(x+2) , then g(f(3)) =

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL 2
  1. If f(x)=-1+|x-2|,0lexle4 g(x)=2-|x|,-1lexle3 Then find fog(x) and ...

    Text Solution

    |

  2. Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If f(...

    Text Solution

    |

  3. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  4. Let f(x) = sqrt(x - 1)+sqrt(x+ 24 - 10sqrt(x-1)), 1 lt x lt 26 be a re...

    Text Solution

    |

  5. If f(x)=(|x|)^(|sinx|), then f'(-pi//4) is equal to

    Text Solution

    |

  6. If f(x) = cos x cos 2x cos 4x cos 8x cos 16x then find f' (pi/4)

    Text Solution

    |

  7. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  8. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  9. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  10. underset(xto0)lim[(1-e^(x))(sinx)/(|x|)] is (where [.] represents the ...

    Text Solution

    |

  11. Indicate all correct alternatives: if f(x) = x/2-1, then on the interv...

    Text Solution

    |

  12. Let function f be defined as f:R^(+)toR^(+) and function g is defined ...

    Text Solution

    |

  13. If f(x)={(2cos x ,s in2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x...

    Text Solution

    |

  14. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  15. Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is different...

    Text Solution

    |

  16. {:(f(x) = cos x and H(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)...

    Text Solution

    |

  17. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |

  18. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  19. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

    Text Solution

    |

  20. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

    Text Solution

    |