Home
Class 11
MATHS
ABCD is a convex quadrilateral and 3, 4,...

ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked on the sides AB, BC, CD, and DA, respectively. The number of triangles with vertices on different sides is a. `270` b. `220` c. `282` d. `342`

A

220

B

270

C

282

D

342

Text Solution

Verified by Experts

`=` Number of triangales with vertices on sides PQ, QR, and RS
+ Number of triangles with vertices on sides QR, RS and PS
+ Number of triangles with vertices on sides RS, PS and PQ
+ Number of triangles with vertices on sides PS, PQ and QR
`=""^(3)C_(1)xx""^(4)C_(1)xx""^(5)C_(1)xx""^(4)C_(1)xx""^(5)C_(1)xx""^(6)C_(1)+""^(5)C_(1)xx""^(6)C_(1)xx""^(3)C_(1)+""^(6)C_(1)xx""^(3)C_(1)xx""^(4)C_(1)`
`=60+120+90+72+=342`.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|9 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|136 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

Similar Questions

Explore conceptually related problems

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

If D(3,-2) , E(-3,1) and F(4,-3) are the mid-points of the sides BC, CA and AB respectively of Delta ABC , find the co-ordinates of point A , B and C .

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD and FE bisect each other.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.

ABCD is a quadrilateral in which AB=AD . The bisector of BAC and CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.

P,Q,R and S are the mid points of sides AB,BC , CD and DA respectively of rhombus ABCD. Show that PQRS is a rectangle. Under what conditions will PQRS be a square ?

The coordinates of the mid points of the sides "BC", "CA" and "AB" of a △ ABC are (3,3), (3, 4) and (2,4) respectively. Then the triangle "ABC" is

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Section I - Solved Mcqs
  1. There are three coplanar parallel lines. If any p points are taken ...

    Text Solution

    |

  2. In a polygon no three diagonals are concurrent. If the total number of...

    Text Solution

    |

  3. ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked...

    Text Solution

    |

  4. The number of ways in which we can select four numbers from 1 to 30...

    Text Solution

    |

  5. The number of four-digit numbers that can be made with the digits 1...

    Text Solution

    |

  6. The number of 5-digit number that can be made using the digits 1 and 2...

    Text Solution

    |

  7. The number of ways of dividing 20 persons into 10 couples is

    Text Solution

    |

  8. Find the number of ways in which 10 condidates A(1),A(2),......,A(10) ...

    Text Solution

    |

  9. There are n white and n black balls marked 1, 2, 3,…..,n. The number o...

    Text Solution

    |

  10. The number of ways in which we can distribute m n students equally ...

    Text Solution

    |

  11. The total number of 6-digit numbers in which the sum of the digits is ...

    Text Solution

    |

  12. The number of integers solutions for the equation x+y+z+t=20, where x,...

    Text Solution

    |

  13. The number of integral solutions of x+y+z=0 with xgeq-5,ygeq-5,zgeq-5 ...

    Text Solution

    |

  14. The number of non-negative integral solutions of x+y+z<=n, where n in ...

    Text Solution

    |

  15. If n objects are arrange in a row, then the number of ways of select...

    Text Solution

    |

  16. There are three piles of identical red, blue and green balls and each ...

    Text Solution

    |

  17. If n objects are arrange in a row, then the number of ways of select...

    Text Solution

    |

  18. Between two junction stations A and B there are 12 intermediate statio...

    Text Solution

    |

  19. In how many ways can 30 marks be allotted to 8 question if each que...

    Text Solution

    |

  20. The number of points in space, whose each co-ordinate is a negative in...

    Text Solution

    |