Home
Class 12
MATHS
Let f(x)={b^(2)+(a-1)b-(1)/(4)}x+int(0)^...

Let `f(x)={b^(2)+(a-1)b-(1)/(4)}x+int_(0)^(x)(sin^(4)theta+cos^(4)theta)d theta` If `f(x)` be a non- decreasing function `AA x in R` and `AA b in R` then "a" can belong to

Text Solution

Verified by Experts

The correct Answer is:
`a in [0, 2]`
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)|125 Videos

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(ab-b^(2)-2)x+int_(0)^(x)(cos^(4)theta+sin^(4)theta)d theta is a decreasing function of x for all x in R and b in R, b being independent of x, then

Let f(x) be a funtion defined by f(x)=(ab-a^(2)-2)x-int_(0)^(x)(cos^(4)t+sin^(2)t-2)dt If f(x) is a decreasing function for all x in R and for all a in R where a is independent of x then b belongs to

If f(x)= (ab+b^2+1)x+int_(0)^(x)(cos^4theta+sin^4theta)" d"theta is an incrasing function of x for all x in R and b in R , b being independent of x then

f(x)=[-c^(2)+(b-1)c-2)]x+int(sin^(2)x+cos^(4)x)dx If f(x) be an increasing function of x AA x in R then all possible values of b if (c in R)

If f(x)=int_(0)^((pi)/(2))(ln(1+x sin^(2)theta))/(sin^(2)theta)d theta,x>=0 then :

Let f be a differentiable function AA x in R where f(1)=1&f(3)=4&f'(x)>=1 AA x in R then f(2) can be equal to

Let |f (x)| le sin ^(2) x, AA x in R, then

f(theta)=int_0^1 (x+sin theta)^2 dx

Let f(a)>0, and let f(x) be a non- decreasing continuous function in [a,b]. Then,(1)/(b-a)int_(a)^(b)f(x)dx has the

let f:R rarr R be a continuous function AA x in R and f(x)=5,AA x in irrational. Then the value of f(3) is

FIITJEE-TIPS-NUERICAL DECIMAL BASED QUATIONS
  1. Let f(x)={b^(2)+(a-1)b-(1)/(4)}x+int(0)^(x)(sin^(4)theta+cos^(4)theta)...

    Text Solution

    |

  2. If {x} denotes the fractiona part of x, then {(4^(2n))/(15)}, n in N, ...

    Text Solution

    |

  3. Period of sin.(pi)/(4)[x]+sin.(pix)/(2)+tan.(pi)/(3)+sin.(pit)/(4) is

    Text Solution

    |

  4. The period of the function f(t)=sin.(pit)/(3)+sin.(pit)/(4) is

    Text Solution

    |

  5. The value of lim(xrarroo)(x^(3)sin(1//x)-2x^(2))/(1+3x^(2)) is

    Text Solution

    |

  6. Let fp(alpha)=(cos(alpha/p^2)+i sin(alpha/p^2))+((cos)(2alpha)/p^2+isi...

    Text Solution

    |

  7. Evaluate underset(xto0)lim(1-cos(1-cosx))/(x^(4)).

    Text Solution

    |

  8. The value of int(-1)^(1)g(x)-g-(-x)+[x]dx where [.] is the greatest fu...

    Text Solution

    |

  9. Tet alpha, beta and gamma be the roots of f(x) = x^3 + x^2 - 5x - 1 = ...

    Text Solution

    |

  10. If a, b, c, d, e and f are non negative real numbers such that a +b+...

    Text Solution

    |

  11. Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of...

    Text Solution

    |

  12. If int(sqrt(cotx))/(cosx cos x)dx=a sqrt(cotx)+b, then

    Text Solution

    |

  13. If f(x+1)+f(x+7)=0, x in R , then possible value of t for which inta^(...

    Text Solution

    |

  14. f(x)={{:(3[x]-5(|x|)/(x)",",x ne0),(2",", x=0):}, then int(-3//2)^(2)f...

    Text Solution

    |

  15. If f(x)=x(x-1), 0 le x le 1, and f(x+1)=f(x) AA x in R, then |int(2)^(...

    Text Solution

    |

  16. int2^3(x^2dx)/(2x^2-10 x+25)

    Text Solution

    |

  17. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

    Text Solution

    |

  18. Let f:(0, oo) rarr R and F(x^(2))=int(0)^(x^(2))f(t)dt. " If "F(x^(2))...

    Text Solution

    |

  19. intx^6sin(5x^7)dx=k/5cos(5x^7)+c ,then k=

    Text Solution

    |

  20. If int(sqrt(cotx))/(sinx cos x)dx=A sqrt(cotx)+B, then A is equal to

    Text Solution

    |

  21. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...

    Text Solution

    |