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

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

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these

The slopes of the common tanents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are (a) +-1 (b) +-sqrt(2) (c) +-sqrt(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

If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c) are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

Area enclosed between the curves |y|=1-x^2a n dx^2+y^2=1 is (3pi-8)/3 (b) (pi-8)/3 (2pi-8)/3 (d) None of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these