Home
Class 12
MATHS
Let f(x)={[x-1,x" is even,[2x,"x is odd"...

Let `f(x)={[x-1,x" is even,[2x,"x is odd"]:} in N` .If for some `a in N,f(f(f(a)))=21` ,then `lim_(x rarr a^(-)){(|xx^(3))/(a)-[(x)/(a)]}`,where "[t]" denotes the greatest integer less than or equal to "t" ,is equal to:

A

144

B

225

C

121

D

169

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

lim(x rarr a_(-)){(|x|^(3))/(a)-[(x)/(a)]^(3)},(a<0) where [x] denotes the greatest integer less than or equal to x is equal to:

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

Let f(x)=(x^(2)-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x), then

The lim it lim_(x rarr0)(sin[x])/(x), where [x] denotes greatest integer less than or equal to x, is equal to

Let f(x)=[x^(2)]+[x+2]-8 , where [x] denotes the greater integer than or equal to x , then

Let f(x)=(x-[x])/(1+x-[x]), where [x] denotes the greatest integer less than or equal to x,then the range of f is

Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer less than or equal to x, then int_(-2)^(2) f(x) is equal to

Let f(x)=[x^(2)+1],([x] is the greatest integer less than or equal to x) . Ther

If f(x)=|x-1|-[x] (where [x] is greatest integer less than or equal to x ) then.

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. Consider "10" observations x(1),x(2),...,x(10) such that sum(i=1)^(10)...

    Text Solution

    |

  2. Let f(x)=|2x^(2)+5|x|-3|,x in R .If "m" and "n" denote the number of p...

    Text Solution

    |

  3. Let f(x)={[x-1,x" is even,[2x,"x is odd"]:} in N .If for some a in N,f...

    Text Solution

    |

  4. The number of solutions of the equation 4sin^(2)x-4cos^(3)x+9-4cos x=0...

    Text Solution

    |

  5. The value of int0^1(2x^3-3x^2-x+1)^(1/3)dx is equal to

    Text Solution

    |

  6. Let the system of equations x+2y+3z=5,2x+3y+z=9,4x+3y+lambda z=mu have...

    Text Solution

    |

  7. Let alpha be a non-zero real number.Suppose f:R rarr R is a differenti...

    Text Solution

    |

  8. Consider a /ABC where A(1,3,2),B(-2,8,0) and C(3,6,7) .If the angle bi...

    Text Solution

    |

  9. Let S(n) denote the sum of the first "n" terms of an arithmetic progre...

    Text Solution

    |

  10. "P" be a point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 .Let the line ...

    Text Solution

    |

  11. If (dx)/(dy)=(1+x-y^(2))/(y),x(1)=1 ,then 5x(2) is equal to.

    Text Solution

    |

  12. If three successive terms of a G.P.with common ratio r(r>1) are the le...

    Text Solution

    |

  13. Let vec a= hat i+hat j+hat k,vec b=-hat i-8 hat j+2 hat k and vec c=4 ...

    Text Solution

    |

  14. Let A=I(2)-2MM^(T),where "M" is a real matrix of order 2times1 such th...

    Text Solution

    |

  15. The lines L(1),L(2),...,L(20) are distinct.For n=1,2,3,...,10 all the ...

    Text Solution

    |

  16. 3 point O(0,0),P(aa^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2....

    Text Solution

    |

  17. If y=((sqrt(x)+1)(x^(2)-sqrt(x)))/(x sqrt(x)+x+sqrt(x))+(1)/(15)(3cos^...

    Text Solution

    |

  18. Let "ABC" be an isosceles triangle in which "A" is at (-1,0),/A=(2 pi)...

    Text Solution

    |

  19. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

    Text Solution

    |

  20. The sum of squares of all possible values of "k" ,for which area of th...

    Text Solution

    |