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

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

A

cos 3

B

0

C

cos 4

D

cos 5

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - C) Objective Type Questions (More than one option are correct)|17 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - D) Linked Comprehension Type Questions|17 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos

  • PROBABILITY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|13 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

Similar Questions

Explore conceptually related problems

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

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 [] denotes the greatest integer function then f(x) is

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

Let f(x)=cos x and g(x)=[x+1],"where [.] denotes the greatest integer function, Then (gof)' (pi//2) is

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

If f:R to R is function defined by f(x) = [x]^3 cos ((2x-1)/2)pi , where [x] denotes the greatest integer function, then f is :

f(x)=2^(cos^(4)pi x+x-[x]+cos^(2)pi x), where [.] denotes the greatest integer function.

AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. If |x + 4| + |x-4|=2|x| and |x+1|+|5-x|=6 then x belongs to

    Text Solution

    |

  2. If [] and {} represents the greatest integer function and fractional f...

    Text Solution

    |

  3. If f(x) = cos [pi]x + cos [pi x], where [y] is the greatest integer fu...

    Text Solution

    |

  4. Range of function (1)/(3- sin 3x) is

    Text Solution

    |

  5. If -1 le [2x^2 -3] lt 2, then x belongs to

    Text Solution

    |

  6. Range of f(x) = (x+2)/(|x+2|)

    Text Solution

    |

  7. If f(x) = log ((1+x)/(1-x)), then f((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  8. The domain of f(x) = log |x| + 1/sqrt|x| + 1/log|x| is R - A where A i...

    Text Solution

    |

  9. The largest set of real values of x for which f(x)=sqrt((x + 2)(5-x))...

    Text Solution

    |

  10. The domain of the function f(x) = (x^(2) + 1)/(ln (x^(2) + 1)) is

    Text Solution

    |

  11. The domain of definition of the function f(x) = log(3//2) log(1//2) lo...

    Text Solution

    |

  12. The domain of the function f(x) = sqrt(log(10) cos (2pi x)) is

    Text Solution

    |

  13. Domain of log([x+1]) (x-1) is ( [.] represents greatest integer func...

    Text Solution

    |

  14. Range of the f(x) = (e^(x) - 1)/(e^(x) + 1)

    Text Solution

    |

  15. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  16. The domain of the function f(x)=sqrt(x-sqrt(1-x^2)) is

    Text Solution

    |

  17. The range of f(x) = 2+2x +x^(2) is

    Text Solution

    |

  18. The range of the expression 2^(x) + 2^(-x) + 3^(x) + 3^(-x) for x in R...

    Text Solution

    |

  19. Let [], and {} denotes the greatest integer function and fractional fu...

    Text Solution

    |

  20. The range of the function y = f(x) if (34)^(x) + (34)^(y) = 34 equals

    Text Solution

    |