The straight lines represented by `(y-m x)^2=a^2(1+m^2)` and `(y-n x)^2=a^2(1+n^2)` form (a) rectangle (b) rhombus (c) trapezium (d) none of these

If sum_(i=1)^4(x_i^2+y_ i^2)lt=2x_1x_3+2x_2x_4+2y_2y_3+2y_1y_4, the points (x_1, y_1),(x_2,y_2),(x_3, y_3),(x_4,y_4) are (a) the vertices of a rectangle (b)collinear (c)the vertices of a trapezium (d)none of these

The differential equation of all straight lines which are at a constant distance p from the origin, is (a) (y+xy_1)^(2)=p^(2) (1+y_(1)^2) (b) (y-xy_(1)^(2))=p^(2) (1+y_(1))^(2) ( c ) (y-xy_(1))^(2)=p^(2) (1+y_(1)^(2)) (d) None of these

If the angle between the two lines represented by 2x^2+5xy+3y^2+2y+4=0 is tan ^(-1) (m) , then m is equal to

The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines represented by (1+lambda)x^(2)-8xy+y^(2)=0 are equally inclined, then

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((z y)/(x r))+tan^(-1)((x z)/(y r))+tan^(-1)((x y)/(z r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

The lines given by the equation (2y^2+3xy-2x^2)(x+y-1)=0 form a triangle which is

The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n d(x-2)/1=(y-1)/(-3)=(z+3)/2dot Statement 1: the given lines are coplanar. Statement 2: The equations 2x_1-y_1=1,x_1+3y_1=4a n d3x_1+2y_1=5 are consistent.

The differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(1+y')^(2)=(x+yy')^(2) (b) (x-y)^(2)(1+y')^(2)=(x+y')^(2) ( c ) (x-y)^(2)(1+y')=(x+yy')^(2) (d) None of these

If the straight line joining the origin and the points of intersection of y=mx+1 and x^2+y^2=1 be perpendicular to each other , then find the value of m.

If x >1,y >1,z >1 are in GP, then 1/(1+lnx),1/(1+lny),1/(1+lnz) are in (1998, 2M) (a) AP (b) HP (c) GP (d) none of these