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

Let `f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)-5{a}+1)x-(tanx)xx"sgn " x ` be an even function for all ` x in R.` Then the sum of all possible values of a is (where `[*]` and `{*}` denote greatest integer function and fractional part function, respectively)

Text Solution

Verified by Experts

The correct Answer is:
C
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise MCQ_TYPE|31 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise COMPREHENSION_TYPE|6 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise MATCH THE COLUMN|2 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

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

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

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.

The value of int_(0)^(|x|){x} dx (where [*] and {*} denotes greatest integer and fraction part function respectively) is

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

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

f(x)=[x^(2)]-{x}^(2), where [.] and {.} denote the greatest integer function and the fractional part function , respectively , is

Find the solution of the equation [x] + {-x} = 2x, (where [*] and {*} represents greatest integer function and fractional part function respectively.

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

RESONANCE ENGLISH-RELATION, FUNCTION & ITF-INTEGER_TYPE
  1. The domain of f(x) such that the f(x) = [[x + 1/2]] / [[x - 1/2]] is p...

    Text Solution

    |

  2. Number of integers in the range of the function f(x) = (x^3 + 2x^2 + ...

    Text Solution

    |

  3. Range of the function f(x)=|sinx|cosx|+cosx|sinx||is [a,b] then (a+b) ...

    Text Solution

    |

  4. If fa n dg are two distinct linear functions defined on R such that th...

    Text Solution

    |

  5. If f(x)=(1)/((1-x)),g(x)=f{f(x)}andh(x)=f[f{f(x)}]. Then the value of ...

    Text Solution

    |

  6. If f9x)=a x^7+b x^3+c x-5,a , b , c are real constants, and f(-7)=7, t...

    Text Solution

    |

  7. If f(x) = (4a-7)/3 x^3+(a-3)x^2 +x+5 is one-one function find the rang...

    Text Solution

    |

  8. Number of solutions of the equation e^(-sin^2x) = tan2x in [0, 10pi] i...

    Text Solution

    |

  9. Let f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)-5{a}+1)x-(tanx)xx"sgn " x be...

    Text Solution

    |

  10. Let f be a one-one function with domain (21, 22, 23) and range {x,y,z)...

    Text Solution

    |

  11. Let f:[-sqrt(2)+1,sqrt(2)+1]to[(-sqrt(2)+1),2,(sqrt(2)+1)/2] be a func...

    Text Solution

    |

  12. The number of real solutions of the equation x^3+1=2\ root(3)(2x-1), i...

    Text Solution

    |

  13. If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, prove that x^2+y^2+z^2+2x y z=1.

    Text Solution

    |

  14. The sum of absolute value of all possible values of x for which cos t...

    Text Solution

    |

  15. If cot^(-1). (n)/(pi) gt (pi)/(6), n in N, then the maximum value of n...

    Text Solution

    |

  16. If x in (0,1) and f(x)=sec{tan^(-1)((sin(cos^(-1)x)+cos(sin^(-1)x))/(c...

    Text Solution

    |

  17. If 1/2 sin^(-1)((3sin2theta)/(5+4cos2theta))=(pi)/4, then tan theta is...

    Text Solution

    |

  18. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

    Text Solution

    |

  19. The number of solution (s) of the equation sin^-1x + cos^-1(1-x)=sin^-...

    Text Solution

    |

  20. Find the value of 3sum(n=1)^(oo) {1/(pi) sum(k=1)^(oo) cot^(-1)(1+2sqr...

    Text Solution

    |