Home
Class 12
MATHS
A, B and C are the points (a, p), (b,q) ...

A, B and C are the points (a, p), (b,q) and (c,r) respectively such that a, b and c are in AP and p,q and r in GP. If the points are collinear, then

A

`p=q=r`

B

`p^(2)=q`

C

`q^(2)=r`

D

`r^(2)=p`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • RECTANGULAR COORDINATES, STRAIGHT LINES, FAMILY OF LINES

    ARIHANT PUBLICATION BIHAR|Exercise EXAM BOORSTER FOR CRACKING EXAM |30 Videos
  • RATIONAL EXPRESSIONS

    ARIHANT PUBLICATION BIHAR|Exercise EXAM BOOSTER (FOR CRACKING EXAM)|22 Videos
  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION BIHAR|Exercise Exam Booster For Cracking Exam|25 Videos

Similar Questions

Explore conceptually related problems

If a, b, c, are in A.P. ., p , q,r, are in H.P. and ap ,bq, cr are in G.P. then

If P, Q, R are three points with respective position vectors hati + hatj, hati -hatj and a hati + b hatj + c hatk . The points P, Q, R are collinear, if

The pth, qth and rth terms of an A.P. are a, b and c respectively. Show that a(q – r) + b(r-p) + c(p – q) = 0

Let a,b,c be in A.P and x,y,z be in G.P.. Then the points (a,x),(b,y) and (c,z) will be collinear if

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)

Ifa,b,c are in A.P., a,x,b,are in G.P and b,y,c are also in G.P then the point (x,y) lies on

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

ARIHANT PUBLICATION BIHAR-RECTANGULAR COORDINATES, STRAIGHT LINES, FAMILY OF LINES-EXAM BOORSTER FOR CRACKING EXAM
  1. The vertices of a DeltaABC are (lamda,2-,2lamda),(-lamda+1,2lamda) and...

    Text Solution

    |

  2. The area of a triangle is 5 and two of its vertices are A(2,1),B(3,-2)...

    Text Solution

    |

  3. If the co-ordinates of points A,B,C,D are (6,3),(-3,5),(4,-2) and (x,3...

    Text Solution

    |

  4. The points (-a,-b),(0,0),(a,b) and (a^(2),ab) are

    Text Solution

    |

  5. If the points (2k, k), (k, 2k) and (k, k) with kgt0 enclose in a trian...

    Text Solution

    |

  6. The distance between the points (acosalpha,asinalpha) and (acosbeta,as...

    Text Solution

    |

  7. The points (x,2x),(2y,y) and (3,3) are collinear

    Text Solution

    |

  8. Line L is perpendicular to the lines 5x-y=1. The area of triangle form...

    Text Solution

    |

  9. If m(1) and m(2) are the roots of an equation x^(2)+(sqrt3+2)x+(sqrt3-...

    Text Solution

    |

  10. The equation of the base of an equilateral triangle is x+y=2 and the v...

    Text Solution

    |

  11. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

    Text Solution

    |

  12. A, B and C are the points (a, p), (b,q) and (c,r) respectively such th...

    Text Solution

    |

  13. The equations of perpendicular bisectors of the sides AB and AC of a D...

    Text Solution

    |

  14. A point P(h, k) lies on the straight line x + y +1 = 0 and is at a dis...

    Text Solution

    |

  15. The equations of the straight lines through (3, 2) which make acute an...

    Text Solution

    |

  16. The number of integral values of m for which the x-coordinate of the p...

    Text Solution

    |

  17. The equation of the straight line which makes angle of 15^(@) with the...

    Text Solution

    |

  18. The equation of straight line passing through the point of intersectio...

    Text Solution

    |

  19. The diagonals of a parallelogram ABCD are along are the lines x+3y=4 a...

    Text Solution

    |

  20. The orthocentre of triangle with vertices (2,(sqrt3-1)/2) , (1/2,-1/2)...

    Text Solution

    |