Home
Class 12
MATHS
Statement-1 : If a1,a2,a3,….. an are pos...

Statement-1 : If `a_1,a_2,a_3`,….. `a_n` are positive real numbers , whose product is a fixed number c, then the minimum value of `a_1+a_2+…. + a_(n-1)+2a_n` is `n(2C)^(1/n)`
Statement-2 :A.M. `ge` G.M.

A

`n(2c)^(1//n)`

B

`(n+1)c^(1//n)`

C

`2nc^(1//n)`

D

`(n+1)(2c)^(1//n)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 1

    KVPY PREVIOUS YEAR|Exercise EXERCISE|26 Videos

  • MOCK TEST 2

    KVPY PREVIOUS YEAR|Exercise EXERCISE|25 Videos

Similar Questions

Explore conceptually related problems

If a_1,a_2 …. a_n are positive real numbers whose product is a fixed real number c, then the minimum value of 1+a_1 +a_2 +….. + a_(n-1) + a_n is :

If a_1, a_2, a_3,...a_20 are A.M's inserted between 13 and 67 then the maximum value of the product a_1 a_2 a_3...a_20 is

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

If a_1, a_2, a_3,...a_n are in A.P with common difference d !=0 then the value of sind(coseca_1 coseca_2 +cosec a_2 cosec a_3+...+cosec a_(n-1) cosec a_n) will be

If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

If a_1, a_2,......,a_n are n distinct odd natural numbers not divisible by any prime greater than 5, then prove that (1)/(a_1)+(1)/(a_2)+…..+(1)/(a_n) lt 2 .

KVPY PREVIOUS YEAR-MOCK TEST 10-EXERCISE
  1. Statement-1 : If a1,a2,a3,….. an are positive real numbers , whose pro...

    Text Solution

    |

  2. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

    Text Solution

    |

  3. The triangle PQR is inscribed in the circle x^2+y^2 = 25. If Q and R h...

    Text Solution

    |

  4. The ellipse E1:(x^2)/9+(y^2)/4=1 is inscribed in a rectangle R whose s...

    Text Solution

    |

  5. The smaller radius of the sphere passing through (1, 0,0),(0,1,0) and ...

    Text Solution

    |

  6. The number of real values of the parameter k for which (log(16)x)^2-(l...

    Text Solution

    |

  7. Let S be the set of complex number a which satisfyndof log(1/3) { log...

    Text Solution

    |

  8. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

    Text Solution

    |

  9. If P(x) is a polynomial of the least degree that has a maximum equal ...

    Text Solution

    |

  10. if 10! = 2^p3^q5^r7^s then

    Text Solution

    |

  11. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  12. If (vec a xx vec b)^2 + (veca .vecb)^2 = 676 and |vecb| = 2, then |ve...

    Text Solution

    |

  13. The equation (x^2)/(1-r)-(y^2)/(1+r)=1,r >1, represents an ellipse (b)...

    Text Solution

    |

  14. The graph of the function, cos x cos (x +2) -cos^2 (x+1) is

    Text Solution

    |

  15. If f(x)=cos{(pi)/(2)[x]-x^(3)},1ltxlt2, and [x] denotes the greatest i...

    Text Solution

    |

  16. The number of real solutions of the equation 1+|e^x - 1|= e^x (e^x ...

    Text Solution

    |

  17. If 2x-y+1=0 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(16)=1 the...

    Text Solution

    |

  18. If the equation (x^2)/3-4x+13=sin(a/x) has a solution then a is equal ...

    Text Solution

    |

  19. If m be the slope of common tangent of y = x^2 - x + 1 and y = x^2 – 3...

    Text Solution

    |

  20. If Sn=^nC0.^nC1+^nC1.^nC2+.....+^nC(n-1).^nCn and if S(n+1)/Sn=15/4 , ...

    Text Solution

    |