Home
Class 12
MATHS
If a,b,c,d and p are distinct non -zero ...

If a,b,c,d and p are distinct non -zero real numbers such that `:`
`( a^(2) + b^(2) +c^(2))p^(2) - 2 ( ab + bc + cd) p + ( b^(2) + c^(2) + d^(2)) le 0`, then a,b,c,d `:`

A

are in A.P.

B

are in G..

C

are in H.P.

D

satisfy ad =bc

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise LATEST QUESTIONS|11 Videos
  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos
  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos
  • RELATIONS

    MODERN PUBLICATION|Exercise RCQS|6 Videos
  • SETS

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|6 Videos

Similar Questions

Explore conceptually related problems

If a, b, c, d and p are different real numbers such that (a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd) p + (b^2 + c^2 + d^2) le 0 , then show that a, b, c and d are in GP.

If a,b,c,d are in H.P., then :

If a, b and c real numbers such that a^(2) + b^(2) + c^(2) = 1, then ab + bc + ca lies in the interval :

If a, b, c are distinct positive real numbers and a^(2)+b^(2)+c^(2)=1 , then ab+bc+ca is :

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

If a,b,c,d are distinct integers in an A.P. such that d=a^(2)+b^(2)+c^(2) , then find the value of a+b+c+d.

If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca) , than a,b,c are in

If a + b +c =9 and ab + bc + ca =26, then find a ^(2) + b ^(2) + c ^(2).

If a,b,c,d are positive real numbers such that a+b+c +d = 12 , then M = ( a+ b ) ( c + d ) satisfies the relation :

Prove that {:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2)

MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) +...

    Text Solution

    |

  2. The minimum sum of the series : 20 + 19(1)/(3)+ 18(2)/( 3) +"..." i...

    Text Solution

    |

  3. If a,b,c,d and p are distinct non -zero real numbers such that : ( a...

    Text Solution

    |

  4. If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and d...

    Text Solution

    |

  5. Let a(1), a(2),"…..",a(10) be in A.P. and h(1) ,h(2),"…….",h(10) be in...

    Text Solution

    |

  6. The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)...

    Text Solution

    |

  7. If x(1), x(2),"……….",x(n) are n non zero real numbers such that (x(1)^...

    Text Solution

    |

  8. For 0 lt theta lt ( pi )/(2) , if x = sum(n=0)^(oo)cos^(2n) theta, y =...

    Text Solution

    |

  9. If a(1), a(2) ,a(3)"….." is an A.P. such that : a(1) + a(5) + a(10)+...

    Text Solution

    |

  10. If f(x) is a function satisfying f(x+y) = f(x) f(y) for all x,yin N su...

    Text Solution

    |

  11. If sin alpha, sin^(2) alpha, 1,sin^(4) alpha, sin^(5) alpha, ( - pi lt...

    Text Solution

    |

  12. If A,G and H are respectively A.M.,G.M. and H.M. of three positive num...

    Text Solution

    |

  13. x+y+z = 15 if 9, x,y,z,a are in A.P., while (1)/( x) + ( 1)/( y) + ( ...

    Text Solution

    |

  14. If p,q,r are in A.P. and are positive, the roots of the quadratic equa...

    Text Solution

    |

  15. Let a^(n) be the nth term of the G.P. of positive numbers. Let sum(n=1...

    Text Solution

    |

  16. Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N ...

    Text Solution

    |

  17. For any odd integer n ge1, n^(3) - ( n - 1)^(3) + "….." + ( -1)^(n-1)1...

    Text Solution

    |

  18. The sum to infinity of the series : 1+2 ( 1-(1)/( n )) + 3( 1 - ( 1)...

    Text Solution

    |

  19. If a,b,c are digits, then the rational number represented by 0.c ab ab...

    Text Solution

    |

  20. If I(n) = int(0)^(n) ( 1- sin 2nx)/( 1-cos 2n)dx then I(1) , I(2) , I(...

    Text Solution

    |