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 4a x+3b y+c=0 passes through which point? , where a+b+c =0 (a) (4,3) (b) (1/4,1/3) (c) (1/2,1/3) (d) none of these

In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0), 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

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

The line x/a+y/b=1 meets the x-axis at A , the y-axis at B , and the line y=x at C such, that the area of "Delta"A O C is twice the area of "Delta"B O C . Then the coordinates of C are (b/3, b/3) (b) ((2a)/3,(2a)/3) (c) ((2b)/3,(2b)/3) (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

If the angle between the lines represented by 2x^2+5xy+3y^2+7x+13y-3=0 is tan^(-1) (m) , then m is equal to

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

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