Home
Class 12
MATHS
There are three coplanar parallel lines....

There are three coplanar parallel lines. If any `p` points are taken on each of the lines, the maximum number of triangles with vertices on these points is a. `3p^2(p-1)+1` b. `3p^2(p-1)` c. `p^2(4p-3)` d. none of these

A

`3n^(2)(n-1)+1`

B

`3n^(2)(n-1)`

C

`n^(3)`

D

`n^(2)(4n-3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise LEVEL-2|88 Videos
  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|50 Videos
  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|50 Videos
  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
  • PROBABILITY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|102 Videos

Similar Questions

Explore conceptually related problems

There are p coplanar parallel lines. If any 3 points are taken on each of the lines, the maximum number of triangles with vertices at these points is:

P is a point on the line y+2x=1, and Q and R are two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If p be the length of the perpendicular from the origin on the line x//a+y//b =1, then p^2=a^2+b^2 b. p^2=1/(a^2)+1/(b^2) c. 1/(p^2)=1/(a^2)+1/(b^2) d. none of these

Find the reflection of the point P(-1,3) in the line x = 2

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) 1/(sqrt(2)) (d) none of these

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If the point(p,5) lies on the parallel to y-axis and passing thorugh the intersection of the lines 2(a^(2) +1) x+ by + 4(a^(3) + a) = 0 , the p is equal to

A(1,1) , B (-2,3) are two points . If a point P forms a triangle of are 2 square units with A, B then find the locus of P.

If p_(1),p_(2),p_(3) are altitudes of a triangle ABC from the vertices A,B,C and ! the area of the triangle, then p_(1).p_(2),p_(3) is equal to

Let L_1 and L_2 be two lines intersecting at P If A_1,B_1,C_1 are points on L_1,A_2, B_2,C_2,D_2,E_2 are points on L_2 and if none of these coincides with P, then the number of triangles formed by these 8 points is

VMC MODULES ENGLISH-PERMUTATION & COMBINATION-LEVEL-1
  1. There are 15 points in a plane, no three of which are in a straight li...

    Text Solution

    |

  2. The straight lines I(1),I(2),I(3) are parallel and lie in the same pla...

    Text Solution

    |

  3. There are three coplanar parallel lines. If any p points are taken ...

    Text Solution

    |

  4. The no. of integral solutions of x1+x2+x3=0 with xk, >=-5 is

    Text Solution

    |

  5. The number of ways in which 30 coins of one rupee each be given to six...

    Text Solution

    |

  6. The number of positive integral solutions of x+y+z=n,n in N, n >= 3 is

    Text Solution

    |

  7. The number of negative integral solution of equation x+y+z=-12 is

    Text Solution

    |

  8. The number of ordered triplets, positive integers which are solutions ...

    Text Solution

    |

  9. If a,b, and c are positive integers such that a+b+cle8, the number of ...

    Text Solution

    |

  10. If a, b, c are three natural numbres in A.P. such that a+b+c =21, then...

    Text Solution

    |

  11. In how many ways te sum of upper faces of four distinct dices can be ...

    Text Solution

    |

  12. If x, y, z are integers such that x >=0, y >=1, z >=2 and x + y + z = ...

    Text Solution

    |

  13. The total number of positive integral solution of 15<x1+x2+x3lt=20 is ...

    Text Solution

    |

  14. If a,b,c and d are odd natural numbers such that a+b+c+d=20, the numbe...

    Text Solution

    |

  15. The total number of non-negative integral solutions of x(1)+x(2)+x(3)+...

    Text Solution

    |

  16. The number of non-negative integral solutions of x(1)+x(2)+x(3)+x(4) l...

    Text Solution

    |

  17. Find the number of non-negative integral solutions of x1+x2+x3+4x4=20.

    Text Solution

    |

  18. The number of positive integral solutions of the equation x(1)x(2)x(3)...

    Text Solution

    |

  19. The number of ways in which 20 different pearls of two colours can be ...

    Text Solution

    |

  20. Six boys and six girls sit along a line alternately in x ways, and alo...

    Text Solution

    |