Sequences and S...

Find the number .

 There is a specific relationship between the numbers that are given in the following figures. On the basis of the relationship choose the correct alternative to replace the question mark.

If three lines $$x-3y=p,ax+2y=q$$ and $$ax+y=r$$ form a right angled triangle, then 

If in a progression $${a_1},{a_2},{a_3},...,etc.,\left( {{a_r} - {a_{r + 1}}} \right)$$ bears a constant ratio with $${a_r}.{a_{r + 1}}$$ then the term of the progression are in 

If the tangent at $$\theta =\frac { \pi  }{ 4 } $$ to the curve $$x=a\cos ^{ 3 }{ \theta  } ,y=a\sin ^{ 3 }{ \theta  } $$ meets the x and y axes in A and B then the area of the triangle OAB is

$$\dfrac { 7 } { 11 } : \dfrac { 336 } { 110 } : ? \quad : \quad \dfrac { 720 } { 272 }$$

A line L passes through the points $$ (1,1)  $$and $$ (2,0)  $$ and another line $$  L^{\prime}  $$ passes through $$ \left(\frac{1}{2}, 0\right)  $$ and perpendicular to L.Then the area of the triangle formed by the lines $$  L, L^{\prime}  $$ and $$  y- $$ axis, is

If  $$A =  (-3,4) , B =(-1,-2) , C=(5,6) D= (x,-4) $$  are the vertices of a quadrilateral such that area triangle $$ABD= 2 \times$$ (area of a triangle $$ACD$$), then $$x =$$

Area of a triangle whose vertices are $$ (a \cos \theta, b \sin \theta),(-a \sin \theta, b \cos \theta)  $$ and$$ (-a \cos \theta,-b \sin \theta)  $$ is $$ - $$

The area of the triangle formed by the lines $$x=0;y=0$$ and $$x\sin { { 18 }^{ 0 } } +y\cos { { 36 }^{ 0 } } +1=0$$ is