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

The straight lines represented by x^2+m x y-2y^2+3y-1=0 meet at (a) (-1/3,2/3) (b) (-1/3,-2/3) (c) (1/3,2/3) (d) none of these

If sin^2theta=(x^2+y^2+1)/(2x) , then x must be -3 (b) -2 (c) 1 (d) none of these

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 if (a) theta=npi,n in I Q (b) A=(2n+1)pi,n in I (c) theta=2npi,n in I (d) none of these

The straight lines represented by the equation 135 x^2-136 x y+33 y^2=0 are equally inclined to the line (a) x-2y=7 (b) x+2y=7 (c) x-2y=4 (d) 3x+2y=4

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If y=a e^(m x)+b e^(-m x), then (d^(2y))/(dx^2)-m^2y is equal to m^2(a e^(m x)-b e^(-m x)) 1 (c) 0 (d) none of these

The line y=m x-((a^2-b^2)m)/(sqrt(a^2+b^2m^2)) is normal to the ellise (x^2)/(a^2)+(y^2)/(b^2)=1 for all values of m belonging to (a) (0,1) (b) (0,oo) (c) R (d) none of these

If the straight lines (x-1)/(1)=(y-2)/(2)=(z-3)/(m^(2))and(x-3)/(1)=(y-2)/(m^(2))=(z-1)/(2) are coplanar, find the distinct real values of m.

The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a) a pair of straight lines and a circle (b) a pair of straight lines and a parabola (c) a set of four straight lines forming a square (d) none of these