Home
Class 12
MATHS
f'(x) = g(x) and g'(x) =-f(x) for all re...

`f'(x) = g(x) and g'(x) =-f(x)` for all real x and `f(5)=2=f'(5) then f^2 (10) + g^2 (10)` is

A

2

B

4

C

8

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

f'(x)=g(x) and g'(x)=-f(x) for all real x and f(5)=2=f'(5)thenf^(2)(10)+g^(2)(10) is

If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f^(2)(4)+g^(2)(4) is

If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f''(24)+g''(24) is

If f'(x)=g(x) and g'(x)=-f(x) forall x and f(3)=5=f'(3) then f^((2))(119)+g^((2))(119)=

f(x) and g(x) are two real valued function.If f'(x)=g(x) and g'(x)=f(x)AA x in R and f(3)=5,f'(3)=4 .Then the value of (f^2(pi)-g^(2)(pi)) is equal to

If f(g(x)) = g(f(x)) = x for all real numbers x, and f(2) = 5 and f(5) = 3, then the value of g(3)+ g(f(2)) is

Q.5 If f(g(x))=g(f(x))=x for all real numbers x, and f(2)=5 and f(5)=3, then the value g(3)+g(f(2)) is

ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(...

    Text Solution

    |

  2. If f and g are the function whose graphs are as shown, let u(x)=f(g(x)...

    Text Solution

    |

  3. f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2...

    Text Solution

    |

  4. if f(x) = x +x^2/1! + x^3/3! +---+ x^n/n! then f(0) + f'(0) + f''(0) ...

    Text Solution

    |

  5. If y=(f(0)f(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

    Text Solution

    |

  6. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

    Text Solution

    |

  7. If y=f(x)andx=g(y) are inverse functions of each other, then

    Text Solution

    |

  8. If y is a function of x then (d^2y)/(dx^2)+y \ dy/dx=0. If x is a func...

    Text Solution

    |

  9. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive functi...

    Text Solution

    |

  10. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  11. If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))), where -pi/4 lt ...

    Text Solution

    |

  12. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(1)/(4) is equal to

    Text Solution

    |

  13. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

    Text Solution

    |

  14. If y=(sin^(-1)(sinalphasinx)/(1-cosalphasinx)), then y'(0) is equal to

    Text Solution

    |

  15. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

    Text Solution

    |

  16. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  17. If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...

    Text Solution

    |

  18. If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )(...

    Text Solution

    |

  19. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

    Text Solution

    |

  20. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

    Text Solution

    |