Home
Class 12
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

270

B

220

C

282

D

342

Text Solution

Verified by Experts

The correct Answer is:
D

The no. of triangles with vertices on sides AB, BC, CD is
`.^(3)C_(1)xx^(4)C_(1)xx^(5)C_(1)`
Similarly, for other cases, the total no. of triangle is
`.^(3)C_(1)xx^(4)C_(1)xx^(5)C_(1)+^(3)C_(1)xx^(4)C_(1)xx^(6)C_(1)+^(3)C_(1)xx^(5)C_(1)xx^(6)C_(1)`
`+^(4)C_(1)xx^(5)C_(1)xx^(6)C_(1)=342`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 3

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 5

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

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.

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 quadrilateral; P,Q,R and S are the points of trisection of side AB,BC,CD and DA respectively and are adjacent to A and C; prove that PQRS is parallelogram.

in any traingle ABC,3,4 and 5 are the interior points on side AB,BC, and CA respectively.then total number traingle, consider these points as vertices,are

The quadrilateral formed by joining the mid-points of the sides AB, BC, CD, DA of a quadrilateral ABCD is

Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

ABCD is a square. P, Q, R, S are points on the sides AB. BC, CD, DA respectively such that AP = BQ = CR = DS. What is angleSPQ equal to ?

In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is

Suppose ABCD is a rectangled and P,Q,R,S are points on the sides AB,BC,CD,DA respectively. Show that PQ+QR+RS+SP gt sqrt(2) AC .

CAREER POINT-MOCK TEST 4-MATHS
  1. ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked...

    Text Solution

    |

  2. Let a die is loaded in such a way that prime number faces are twice as...

    Text Solution

    |

  3. Sigma(r=1)^(n) (-1)^(r+1).(""^(n)C(r))/(r+1) " is equal to" -

    Text Solution

    |

  4. If p,q and r are three statements then negation of compound statement ...

    Text Solution

    |

  5. The ratio of 11^(th) term from the beginning and 11^(th) term the end ...

    Text Solution

    |

  6. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

    Text Solution

    |

  7. A vertical tower PQ subtends the same anlgle of 30^@ at each of two po...

    Text Solution

    |

  8. If |z1 + z2| = |z1| + |z2| is possible if :

    Text Solution

    |

  9. Let the equation of a curve passing through the point (0,1) be given b...

    Text Solution

    |

  10. If coses 0=(x^(2)-Y^(2))/(x^(2)+Y^(2)) is true iff-

    Text Solution

    |

  11. The area bounded by the curves y= "sin" x, y= cos x and y-axis in 1 qu...

    Text Solution

    |

  12. The solution of the DE (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))...

    Text Solution

    |

  13. A variable circle having fixed radius 'a' passes through origin and me...

    Text Solution

    |

  14. The chord A B of the parabola y^2=4a x cuts the axis of the parabola a...

    Text Solution

    |

  15. If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the...

    Text Solution

    |

  16. f(x) = ("tan" x^(5))e^(x^(3)"sgn"x^(7)) " is " -

    Text Solution

    |

  17. "if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)), where x in (0,(pi)/(2)...

    Text Solution

    |

  18. lim(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-

    Text Solution

    |

  19. If veca,vecb,vecc are three mutually perpendicular vectors, then the v...

    Text Solution

    |

  20. A straight line moves so that the sum of the reciprocals of its interc...

    Text Solution

    |