Home
Class 12
MATHS
If f(x)=cos[pi^2]x +cos[-pi^2]x , where ...

If `f(x)=cos[pi^2]x +cos[-pi^2]x ,` where `[x]` stands for the greatest integer function, then

A

`f ((pi)/(2))= -1`

B

`f(pi)=1`

C

`f(-pi)=0`

D

`f((pi)/(4))= (-1)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Let `f(x) = cos` …………..
`2pi^(2)=19.72`
`3pi^(2)=29.58`
`:. [2pi^(2)]=19, [-3pi^(2)]= -30`
`f ((pi)/(2))= -1 , f(pi) = 0 , f(-pi) = 0 , f ((pi)/(4)) = (-1)/(sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

If f(x)=cos[pi^2]x , where [x] stands for the greatest integer function, then (a) f(pi/2)=-1 (b) f(pi)=1 (c) f(-pi)=0 (d) f(pi/4)=1/sqrt(2)

If f(x)=cos[pi^2]x , where [x] stands for the greatest integer function, then (a) f(pi/2)=0 (b) f(pi)=1 (c) f(-pi)=0 (d) f(pi/4)=1

If f(x) = cos [pi]x + cos [pi x] , where [y] is the greatest integer function of y then f(pi/2) is equal to

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

Let f(x) = (sin {pi[x-pi]})/(1+[x^(2)]) , where [.] stands for the greatest integer function. Then, f(x) is continuous or not?

If f(x)=cos[pi]^2x+cos[-pi^2]x ,\ w h e r e\ [x] denotes the greatest integer less than or equal to x , then write the value of f(pi)dot

If f(x)= cos [(pi^(2))/(2)] x + sin[(-pi^(2))/(2)]x,[x] denoting the greatest integer function,then

If f(x) = x+|x|+ cos ([ pi^(2) ]x) and g(x) =sin x, where [.] denotes the greatest integer function, then

Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. If f(x)=cos[pi^2]x +cos[-pi^2]x , where [x] stands for the greatest in...

    Text Solution

    |

  2. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x + tan x and f si the inverse of g, then g'(x) equals

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. The function f(x) = (x^(2) - 1)|x^(2) - 3x + 3|+cos (|x|) is not diffe...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

    Text Solution

    |

  15. The sum of the roots of the equation tan^(-1)(x+3)-tan^(-1)(x-3)="sin"...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

    Text Solution

    |