Home
Class 12
MATHS
Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0...

Let `g(x)=3f((x)/(3))+f(3-x)` and `f''(x)>0` for all `x in(0,3)`. If `"g"` is decreasing in `(0,alpha)` and increasing in `(alpha,3)` ,then `8 alpha` is :

A

24

B

0

C

20

D

18

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos
  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

Similar Questions

Explore conceptually related problems

For "x"in(0,3) g(x)=3f(x/3)+f(3-x) and f''(x)gt0A"x"in(0,3) If g(x) is increasing in (alpha,3) and decreasing in (0,alpha) then find alpha

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let g(x)=f(log x)+f(2-log x) and f'(x)<0AA x in(0,3) Then find the interval in which g(x) increases.

Let varphi(x)=f(x)+f(2a-x) and f"(x)>0 for all x in [0, a] . Then, varphi(x) (a) increases on [0, a] (b) decreases on [0, a] (c) increases on [-a , 0] (d) decreases on [a , 2a]

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

If f(x)=ln(sin x) and g(x)=sin^(-1)(e^(-x)) for all x in(0,pi) and f(g(alpha))=b and (f(g(x))' at x=alpha is a then which is true.

Let g(x)=x^(2)-2x-2 and f(x)=x^(2)+x+alpha . If f(g(x))=0 has no real solution then the set of values of alpha is.

Let f(x)=(sinx)/x and g(x)=|x.f(x)|+||x-2|-1|. Then, in the interval (0,3pi) g(x) is :

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. The values of alpha ,for which [[1,(3)/(2),alpha+(3)/(2)],[1,(1)/(3),a...

    Text Solution

    |

  2. The integral int((x^(8)-x^(2))dx)/((x^(12)+3x^(6)+1)tan^(-1)(x^(3)+(1)...

    Text Solution

    |

  3. Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0 for all x in(0,3). If "g" is ...

    Text Solution

    |

  4. If y=y(x) is the solution curve of the differential equation (x^(2)-4)...

    Text Solution

    |

  5. Let "A" and "B" be two finite sets with "m" and "n" elements respectiv...

    Text Solution

    |

  6. If the point (a^2,a+1) lies in the angle between the lines 3x-y+1=0 an...

    Text Solution

    |

  7. If alpha,beta are the roots of the equation,x^(2)-x-1=0 and S(n)=2023 ...

    Text Solution

    |

  8. If the solution curve,of the differential equation (dy)/(dx)=(x+y-2)/(...

    Text Solution

    |

  9. Consider a circle (x-alpha)^(2)+(y-beta)^(2)=50 ,where alpha,beta>0 .I...

    Text Solution

    |

  10. Let the complex numbers alpha and (1)/(bar(alpha)) lie on the circles ...

    Text Solution

    |

  11. The mean and standard deviation of "15" observations were found to be ...

    Text Solution

    |

  12. A is the area of region 0leylemin(2x,6x-x^2), then find 12A

    Text Solution

    |

  13. The lines (x-2)/(2)=(y)/(-2)=(z-7)/(16) and (x+3)/(4)=(y+2)/(3)=(z+2)/...

    Text Solution

    |

  14. If the sum of squares of all real values of "alpha" ,for which the lin...

    Text Solution

    |

  15. f(x)=int(0)^(x)g(t)log(e)((1-t)/(1+t))dt ,where "g" is a continuous od...

    Text Solution

    |

  16. The coefficient of x^2012 in the expansion of (1 - x)^2008 (1+x+x^2)...

    Text Solution

    |

  17. Let "A" be a 2times2 real matrix and "I" be the identity matrix of ord...

    Text Solution

    |

  18. Let A=[[1,0,0],[0,alpha,beta],[0,beta,alpha]] and abs(2A^(3))=2^(21) w...

    Text Solution

    |

  19. Let "PQR" be a triangle with "R(-1,4,2)" .Suppose "M(2,1,2)" is the mi...

    Text Solution

    |

  20. Let "R" be a relation on Z times Z defined by (a,b)R(c,d) if and only ...

    Text Solution

    |