$A$ pair of lines $S=0$ together with the lines given by the equation $8 x^2-14 x y+3 y^2+10 x+10 y-25=0$ form a parallelogram. If its diagonals intersect at the point $(3,2)$,then the equation $S=0$ is

If the pair of lines represented by $3 x^2 - 5 x y + P y^2 = 0$ and $6 x^2 - x y - 5 y^2 = 0$ have one line in common,then the sum of all possible values of $P$ is

$\frac{(1+i)^{2011}}{(1-i)^{2009}}$ is equal to

Which of the following compounds is the least ionic?

The area (in sq units) of the quadrilateral formed by two pairs of lines $\lambda^2 x^2 - m^2 y^2 - n(\lambda x + m y) = 0$ and $\lambda^2 x^2 - m^2 y^2 + n(\lambda x + m y) = 0$ is:

An object $2.4 \, m$ in front of a lens forms a sharp image on a film $12 \, cm$ behind the lens. $A$ glass plate $1 \, cm$ thick,of refractive index $1.50$,is interposed between the lens and the film with its plane faces parallel to the film. At what distance (from the lens) should the object be shifted to be in sharp focus on the film? (in $m$)