Home
Class 12
MATHS
Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+...

Let `f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tanx)xsgnx` be an even function for all `x in Rdot` Then the sum of all possible values of `a` is (where `[dot]a n d{dot}` denote greatest integer function and fractional part function, respectively). `(17)/6` (b) `(53)/6` (c) `(31)/3` (d) `(35)/3`

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tan)x sin x be an even function for all x in R Then the sum of all possible values of a (where [.] and {.} denot greatest integer function and fractional part function,respectively). (a) 17/6 (b) 53/6 (c) 31/6 (d) 35/3

Solve 2[x]=x+{x},where [.] and {} denote the greatest integer function and the fractional part function, respectively.

Number of solutions of the equation [2x] - 3{2x} = 1 is (where [/] and {.} denote greatest integer and fractional part function respectively)

Solve : 4{x}= x+ [x] (where [*] denotes the greatest integer function and {*} denotes the fractional part function.

The value of int_0^1.5 [x^2] dx is : where [x] denotes greatest integer function.

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. Solve: [x]^2-5[x]+6=0.

Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer function less than or equal to x and the fractional part function, respectively).

Number of solution of equation [x]^2=x+2{x} is/are , where [.] and {.} denote the greatest integer and the fractional part functions, respectively

Discuss the differentiability of f(x) =[x]+ sqrt({x})), where [.] and {.} denote the greatest integer function and fractional part repectively .

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If f(x^2-6x+6)+f(x^2-4x+4)=2x ,AA x in R then f(-3) + f(9) -5f(1)= ? ...

    Text Solution

    |

  2. Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not eq...

    Text Solution

    |

  3. Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tanx)xsgnx be an even fun...

    Text Solution

    |

  4. f(x)=sin^2x+cos^4x+2 and g(x)=cos(cosx)+cos(sinx) Also let period f(x)...

    Text Solution

    |

  5. A continuous, even periodic function f with period 8 is such that f(0)...

    Text Solution

    |

  6. If a and b are natural numbers and f(x)=sin(sqrt(a^2-3))x+cos(sqrt(b^2...

    Text Solution

    |

  7. What is the fundamental period of f(x) = (sin x+ sin 3x)/(cos x+ cos ...

    Text Solution

    |

  8. Which of the following functions is/are bounded ? f(x)=(2x)/(1+x^2), [...

    Text Solution

    |

  9. The domain of the function f(x)=sqrt(10-sqrt(x^4-21 x^2)) is a. [5...

    Text Solution

    |

  10. Number of integers in domain of function f(x) =log(|x^2|)(4-|x|)+log2...

    Text Solution

    |

  11. Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log4x))-pi/2)+sin^(- 1)...

    Text Solution

    |

  12. The range of the function tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R is ...

    Text Solution

    |

  13. The function f(x)=cos^(-1)((2[|sinx|+|cosx|])/(sin^2x+2sinx+11/4)) is ...

    Text Solution

    |

  14. Which of the folllowing functions are defined for all x (A) sin[x]+ ...

    Text Solution

    |

  15. The domain of the function f(x)=log(e){sgn(9-x^(2))}+sqrt([x]^(3)-4[x]...

    Text Solution

    |

  16. Number of integers in the range of f(x)=1/pi(sin^(-1)x+tan^(-1)x)+(x+1...

    Text Solution

    |

  17. If f(x) is an invertible function and g(x)=2f(x)+5, then the value of ...

    Text Solution

    |

  18. Which of the following functions is one-one ? (1)f:R->R defined as f...

    Text Solution

    |

  19. Which of the following statements are incorrect? I. If f(x) and g(x) a...

    Text Solution

    |

  20. Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) wher...

    Text Solution

    |