Straight Lines ...

The area of a triangle whose sides are $$ a , b $$ and $$ c $$ is

The arrangement of the areas of the triangles formed by the following points in ascending order is 
i) P(0,0), Q(4,0), R(0,3)
ii) P(0,0), Q(5,0), R(0,2)
iii) P(0,0), Q(0,5), R(6,0)
iv) p(3,0), Q(0,6), R(0,0)

two medians drawn from the acute angles of a right angled  triangle interect at the angle $$\pi /6$$ if thelength the hypotenuse of the triangle is 3 units then the area of the triangle is

If $$m_1$$ and $$m_2$$ are the roots of the equation $$x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0 $$, then the area of the triangle formed by the lines $$y=m_1x,y=-m_2x$$ and $$y=1$$ is:

In $$\triangle ABC,A(1,2);B(5,5),\angle ACB={ 90 }^{ 0 }$$. If area of $$\triangle ABC$$ is to be 6.5 sq. units, then the possible number of points for C is 

The area inside the parabola $$5x^2 - y = 0 $$ but outside the parabola $$2x^2 - y + 9 = 0$$ is

The inclination of the line y=$$\sqrt { 3 } x+3$$ is 

Area of the triangle formed by co-ordinate axes and the line x + y = 5 is

The centroid and two vertices of a triangles are (4,-8), (-9,7), (1,4) then the area of the triangle is 

In a conference hall 10  executive are to be seated on 10 chairs placed left to right. Executive $$E_1$$ wants to sit to the right of $$E_2$$ Also, $$E_4$$ wants to sit the left of $$E_1$$ and $$E_5$$ wants to sits to the left of ways $$E_4$$ Number of ways the executives can be seated on the 10 chairs, is