Home
Class 11
MATHS
For any two numbers theta and phi ...

For any two numbers `theta and phi ` , we define ` theta R phi ` if and only if ` sec^(2) theta - tan ^(2) phi =1 ` the relation R is -

A

Reflexive but not transitive

B

Symmetric but not reflexive

C

Both reflexive and symmetric but not transitive

D

At equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos
  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos
  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

For any real numbers theta and phi we define theta R phi if and only if sec^(2) theta - tan^(2) phi =1 the relation R is

cos 2 (theta+ phi) +4 cos (theta + phi ) sin theta sin phi + 2 sin ^(2) phi=

If tan^(2)theta=2tan^(2)phi+1, then cos2 theta+sin^(2)phi is equal to

If sin 2 theta + sin 2 phi =1/2 and cos 2 theta + cos 2 phi =3/2, then cos ^(2) (theta - phi)=

If 0 lt theta , phi lt pi and 8 cos theta cos phi cos (theta + phi)+1=0 find theta and phi

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. On the set N of all natural numbers define the rational R by aRb iff t...

    Text Solution

    |

  2. Let W denote the words in the english dicitionary define the relatio...

    Text Solution

    |

  3. For any two numbers theta and phi , we define theta R phi ...

    Text Solution

    |

  4. If the function f :N to N is defined by f (x)= sqrtx, then (f (25))/(f...

    Text Solution

    |

  5. If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le...

    Text Solution

    |

  6. Let f : R to R satisfy f (x) (2) =4, then f ((1)/(2))=

    Text Solution

    |

  7. If f(x) = cos (log (e) x), then f (x) f(y) -1/2 [f(xy) +f((x)/(y))] ha...

    Text Solution

    |

  8. The values of ba n dc for which the identity of f(x+1)-f(x)=8x+3 is sa...

    Text Solution

    |

  9. Given the function f (x) =(a ^(x) + a ^(-x))/(2), a gt 2, then f (x+y)...

    Text Solution

    |

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

    Text Solution

    |

  11. If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(...

    Text Solution

    |

  12. If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest...

    Text Solution

    |

  13. Prove that if f (x) is periodic function with period T, then the funct...

    Text Solution

    |

  14. If the graph of the function y = f(x) is symmetrical about the line x ...

    Text Solution

    |

  15. Let f {(1,1), (2,4), (0,-2), (-1,-5)} be a linear function from Z into...

    Text Solution

    |

  16. If f (x) =log ""(1+x)/(1-x) then-

    Text Solution

    |

  17. The real valued function f(x)=(a^x-1)/(x^n(a^x+1)) is even, then the v...

    Text Solution

    |

  18. The function f(x) = sec[log(x + sqrt(1+x^2))] is

    Text Solution

    |

  19. The function f(x)= sin | log (x+ sqrt(x^(2) +1)) | is-

    Text Solution

    |

  20. If f(x)+2f((1)/(x))=3x, x ne 0 and S={x in R: f(x) = f(-x)}, " then ...

    Text Solution

    |