Home
Class 12
MATHS
Let alpha,beta,gamma and delta are four ...

Let `alpha,beta,gamma and delta` are four positive real numbers such that their product is unity, then the least value of `(1+alpha)(1+beta)(1+gamma)(1+delta)` is :

A

6

B

16

C

0

D

32

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta,gamma,delta be four real numbers such that alpha^(2)+gamma^(2)=9 and beta^(2)+delta^(2)=1 ,then the maximum value of 3(alpha beta-gamma delta)+4(alpha delta+beta gamma) is

If alpha,beta,gamma,delta are four complex numbers such that (gamma)/(delta) is real and alpha delta-beta gamma!=0 then z=(alpha+beta t)/(gamma+delta t) represents a

If alpha,beta,gamma and delta are roots of equation x^(4)-7x^(2)+x-5=0, then the value of (alpha+beta+gamma)(alpha+beta+delta)(beta+gamma+delta)(alpha+gamma+delta) is equal to

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0, then the value of (alpha-(1)/(beta gamma))(beta-(1)/(gamma alpha))(gamma-(1)/(alpha beta)) is

Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma are non zero real numbers such that (alpha+beta+gamma)(alpha+beta-gamma)=3alphabeta then value of gamma

Let alpha,beta and gamma are the angles of a right angle triangle,then the value of sin alpha*sin beta*sin(alpha-beta)+sin beta*sin gamma*sin(beta-gamma)+sin gamma*sin alpha*sin(gamma-beta)+sin(beta-gamma)*sin(gamma-gamma)*sin(gamma-

RESONANCE-DPP-QUESTION
  1. Suppose alpha, beta, gammaand delta are the interior angles of regula...

    Text Solution

    |

  2. If y=1costheta+2cos2theta+3cos3theta++99 cos 99theta , the maximum val...

    Text Solution

    |

  3. Let alpha,beta,gamma and delta are four positive real numbers such tha...

    Text Solution

    |

  4. If the sum of the series S=1+5/11+12/((11)^2)+22/((11)^3)+35/((11)^4)+...

    Text Solution

    |

  5. Let [x] denote the greatest integer part of a real number x, if M sum(...

    Text Solution

    |

  6. Then sum sum(r=1)^(50) r.(2^(r)+2^(50-r)) equals

    Text Solution

    |

  7. lf abcd=1 where a,b,c,d are positive reals then the minimum value of ...

    Text Solution

    |

  8. Solve for x:log(2)(sin""(x)/(2))lt-1

    Text Solution

    |

  9. Suppose that P(x) is a quadratic polynomial such that P(0)=cos^3 40^@,...

    Text Solution

    |

  10. Let y=ax^2+ bx + c be a quadratic expression having its vertex at (3,-...

    Text Solution

    |

  11. Let y=ax^(2)+bx+c be a quadratic expression have its vertex at (3-2) a...

    Text Solution

    |

  12. Through the centriod of an equilateral triangle a line parallel to the...

    Text Solution

    |

  13. Let 'X' denotes the value of the product.(1+a+a^2+a^3+.........oo)(1+b...

    Text Solution

    |

  14. 50th term of the sequence 3+12+25+42+ is 5145 b. 5148 c. 5142 d. 5195

    Text Solution

    |

  15. Consider two quadratic expression f(x)=ax^(2)+bx+c and g(x)=ax^(2)+px+...

    Text Solution

    |

  16. Let alpha, beta be the roots of x^(2)-x+p=0and gamma,delta"be the root...

    Text Solution

    |

  17. Let f(theta) = 1/2 + 2/3 cosec^(2)theta + 3/8 sec^(2) theta. The least...

    Text Solution

    |

  18. If f(x)=(1-s in2x+cos2x)/(2cos2x) , then the value of f(16^0)dotf(29^0...

    Text Solution

    |

  19. If P = (tan(3^(n+1)theta) - tan theta) and Q = sum(r=0)^(n) (sin(3^(r)...

    Text Solution

    |

  20. Let a sequence whose n^(th) term is {a(n)} be defined as a(1) = 1/2 ...

    Text Solution

    |