Home
Class 12
MATHS
Let a>0, a!=0. Then the set S of all pos...

Let `a>0, a!=0`. Then the set S of all positive real numbers b satisfying `(1+a^2)(1+b^2)=4ab` is

A

an empty set

B

a singleton set

C

a finite set containing more than one element

D

`(0,infty)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SOLVED PAPER 2018

    KVPY PREVIOUS YEAR|Exercise EXAMPLE|27 Videos

Similar Questions

Explore conceptually related problems

The set of all real numbers satisfying e^(((1)/(x)-1))<1 is

The set of all real numbers x satisfying x^(2)-|x+2|+x>0 is

The number of pairs (a, b) of positive real numbers satisfying a^(4)+b^(4)lt1" and "a^(2)+b^(2)gt1 is

Let S be a relation on the set R of all real numbers defined by R:a^(2)+b^(2)=1}. Prove S={(a,b)in R xx R:a^(2)+b^(2)=1}. Prove that S is not an equivalence relation on R .

For a complex z , let Re(z) denote the real part of z . Let S be the set of all complex numbers z satisfying z^(4)- |z|^(4) = 4 iz^(2) , where I = sqrt(-1) . Then the minimum possible value of |z_(1)-z_(2)|^(2) where z_(1),z_(2) in S with Re (z_(1)) gt 0 and Re (z_(2)) lt 0 , is ....

On the set Q^(+) of all positive rational numbers a binary operation * is defined by a*b=(ab)/(2) for all a,b in Q^(+). The inverse of 8 is (1)/(8) (b) (1)/(2)(cc)2(d)4

Let S be a relation on the set R of all real numbers defined by S={(a,b)epsilon RxR:a^(2)+b^(2)=1}. Prove that S is not an equivalence relation on R.

Let S be the set of all real numbers. Then the relation R= {(a,b):1+abgt0} on S is

Let S be the set of all real numbers sjow that the relation R={(a,b):a^(2)+b^(2)=1} is symmetric but neither reflextive nor transitive .

Let a,b and c be positive real numbers such that a+b+c=6. Then range of ab^(2)c^(3) is

KVPY PREVIOUS YEAR-SOLVED PAPER 2019-EXAMPLE
  1. Let f(x)={(xsin(1/x), whenx!=0),(1, when x=0):} and A={x inR:f(x)=1}. ...

    Text Solution

    |

  2. Let S be a subset of the plane defined by:S={(x,y):|x|+2|y|=1} Then th...

    Text Solution

    |

  3. The number of solutions of the equation sin(9x)+sin(3x)=0 in the close...

    Text Solution

    |

  4. Among all the parallelograms whose diagonals are 10 and 4, the one hav...

    Text Solution

    |

  5. The number of ordered pairs (a,b) of positive integers such that(2a-1)...

    Text Solution

    |

  6. Let z=x+iy and w=u+iv be two complex numbers, such that |z|=|w|=1 and ...

    Text Solution

    |

  7. Let sigma1,sigma2,sigma3 be planes passing through the origin. Assume ...

    Text Solution

    |

  8. Ravi and Rashmi are each holding 2 red cards and 2 black cards (all fo...

    Text Solution

    |

  9. Let A1,A2 and A3 be the region on R^2 defined by A1={(x,y):xge0,yge0,2...

    Text Solution

    |

  10. Let f:RrarrR be a continuous function such that f(x^2)=f(x^3) for all ...

    Text Solution

    |

  11. Suppose a continuous function f:[0,infty)rarrR satisfies f(x)=2int0^xt...

    Text Solution

    |

  12. Let a>0, a!=0. Then the set S of all positive real numbers b satisfyin...

    Text Solution

    |

  13. Let f:RrarrR be function defined by f(x)={(sin(x^2)/2, ifx!=0),(0,if x...

    Text Solution

    |

  14. The points C and D on a semicircle with AB as diameter are such that A...

    Text Solution

    |

  15. Let f(x)=x^6-2x^5+x^3+x^2-x-1 and g(x)=x^4-x^3-x^2-1 be two polynomial...

    Text Solution

    |

  16. The number of solutions to sin(pisin^2(theta))+sin(picos^2(theta))=2co...

    Text Solution

    |

  17. Let J=int0^1x/(1+x^8)dx. Consider the following assertions: I.J>1/4 II...

    Text Solution

    |

  18. Let f:(-1,1)rarrR be a differentiable function satisfying (f'(x))^4=16...

    Text Solution

    |

  19. Let A be the set of vectors veca=(a1,a2,a3) satisfying (sum(i=1)^3ai/2...

    Text Solution

    |

  20. Let f:[0,1]rarr[0,1] be a continuous function such that x^2+(f(x))^2le...

    Text Solution

    |