If `y=a x^2+b x+c` represents the curve given in the figure and `b^2=2(b+2a c),` where `a!=0` and `A P=3` units, then `O P=` `3/2` (b) `3/4` (c) 3 (d) 6

Area of the region bounded by the curves y=2^x, y=2x-x^2, x=0 and x=2 is given by (A) 3log2-4/3 (B) 3/log2-4/3 (C) 3log2+4/3 (D) 3/log2+4/3

If (a+b+2c+3d)(a-b-2c+3d)=(a-b+2c-3d)(a+b-2c-3d) , then 2b c is equal to 3/2 (b) (3a)/(2d) (c) 3a d (d) a^2d^2

The point on the curve y=x^2-3x+2 where tangent is perpendicular to y=x is (0,2) (b) (1,\ 0) (c) (-1,\ 6) (d) (2,\ -2)

If (a)/(b)=(4)/(3), then (3a+2b)/(3a-2b)=?( a) -1 (b) 3 (c) 5(d)6

The equation of the tangent to the curve y=2.e^((-x)/(3)) where it crosses the y- axis is (A) 2x+3y=0 (B) 2x+3y=9 (c) 2x+3y=4 (D) 2x+3y=6

a,b,c are in G.P. and a+b+c=xb, x can not be (a) 2 (b) -2 (c) 3 (d) 4

If 2a=3b=4c, then a:b:c=2:3:4(b)3:4:64:3( d) 6:4:3

The line parallel to the x-axis and passing through the intersection of the lines a x+2b y+3b=0 and b x-2y-3a=0 , where (a , b)!=(0,0) , is (a)above the x-axis at a distance of 3/2 units from it (b)above the x-axis at a distance of 2/3 units from it (c)below the x-axis at a distance of 3/2 units from it (d)below the x-axis at a distance of 2/3 units from it

If a,b,c are in A.P; a,x,b are in G.P.and b,y,c are in G.P.then x^(2),b^(2),y^(2) are in

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a)1 (b) 2 (c) 3 (d) 4