Home
Class 12
MATHS
If f (x) is a function such that f''(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)=3` then `g(8)=`

A

0

B

3

C

5

D

8

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2012

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|60 Videos
  • KARNATAKA CET 2014

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|60 Videos

Similar Questions

Explore conceptually related problems

If f(x)=2 x^(2)+x+1 and g(x)=3 x+1 then f o g(2)

Let f be twice differentiable function such that f^('')(x) = -f(x) and f^(')(x) = g(x) . Also h(x) = [f(x)]^(2) + [g(x)]^(2). If h(4) = 7, then h(7) =

If f(x) is a polynomial even function such that f(x).f(1/x)=f(x)+f(1/x) and f(2)=65 , then f(-3) =

If f(x) is a ploynomial function satisfying f(x) . f(1/x) = f(x) + f(1/x) and f(3)=28, then f(2) is

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If 2f(x) = f^(')(x) and f(0) = 3, then f(2) =

If f(x) = In (x), g(x) = x^3 then f(g(ab)) = …

If f (x) and g (x) are two functions with g(x)=x-(1)/(x) and fog (x)=x^(3)-(1)/(x^(3)) , then f'(x)=

If g is the inverse function of f and f'(x) = sin x then g'(x) =

KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2013-Mathematics
  1. f(x) = {(2a-x", when" a lt x lt a),(3x-2a ", when " a le x):}. Then wh...

    Text Solution

    |

  2. Let f(x) = cos^(-1) [(1)/(sqrt13) (2 cos x - 3 sin x)]. Then f(0.5) =

    Text Solution

    |

  3. If f (x) is a function such that f''(x)+f(x)=0 and g(x)=[f(x)]^(2)+[f'...

    Text Solution

    |

  4. If f(x) = f'(x) + f''(x) + f'''(x) + ….and f(0)=1, then f(x) =

    Text Solution

    |

  5. The function f(x) = (x)/(3) + (3)/(x) decreases in the interval

    Text Solution

    |

  6. If sin^(-1) a is the acture angle between the curves x^(2) + y^(2) =4x...

    Text Solution

    |

  7. The maximum area of a rectangle that can be inscribed in a circle of r...

    Text Solution

    |

  8. If the length of the sub-tanget at any point to the curve xy^(n) = a i...

    Text Solution

    |

  9. int(cos^(n-1)x)/(sin^(n+1)x)dx, n ne 0 is

    Text Solution

    |

  10. int((x-1)e^(x))/((x+1)^(3)) dx=

    Text Solution

    |

  11. If I(1) = underset(0)overset(pi//2)int x.sin xdx and I(20 = underset(0...

    Text Solution

    |

  12. The value of underset(-1)overset(2)int(|x|)/(x) dx is

    Text Solution

    |

  13. underset(0)overset(pi)int (cos^(4)x)/(cos^(4)x + sin^(4)x) dx=

    Text Solution

    |

  14. The area bounded by the curve y= sin((x)/(3)), x-axis and lines x=0 an...

    Text Solution

    |

  15. The general solution of the differential equation sqrt(1-x^(2)y^(2)).d...

    Text Solution

    |

  16. If 'm' and 'n' are the order and degree of the differential equation (...

    Text Solution

    |

  17. If ((x+1)^(2))/(x^(3) +x) = (A)/(x) + (Bx +C)/(x^(2) +1) , then sin...

    Text Solution

    |

  18. The sum of the series, (1)/(2.3) .2 + (2)/(3.4).2^(2) + (3)/(4.5).2^(3...

    Text Solution

    |

  19. If the roots of the equation x^(3) + ax^(2) + bx + c = 0 are in A.P., ...

    Text Solution

    |

  20. If the value of C(0) + 2C(1) + 3C(2) + ……. + (n+1) C(n) =576 then n i...

    Text Solution

    |