Let the parabolas `y=x(c-x)a n dy=x^2+a x+b` touch each other at the point (1,0). Then a) `a+b+c=0`, b) `a+b=2`, c) `b-c=1`, (d) `a+c=-2`

Let the parabolas y=x(c-x)and y=x^(2)+ax+b touch each other at the point (1,0), then-

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0

Two straight lines are perpendicular to each other. One of them touches the parabola y^2=4a(x+a) and the other touches y^2=4b(x+b) . Their point of intersection lies on the line. (a) x-a+b=0 (b) x+a-b=0 (c) x+a+b=0 (d) x-a-b=0

Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c 0 a+b-c >0 a b c<0

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, (a) C1 and C2 touch each other at one point (b) C1 and C2 touch each other exactly at two point (c) C1 and C2 intersect(but do not touch) at exactly two point (d) C1 and C2 neither intersect nor touch each other

Ifintxe^xcosx dx=a e^x(b(1-x)sinx+c xcosx)+d ,t h e n (a) a=1,b=1,c=-1 (b) a=1/2,b=-,c=1 (c) a=1,b=-1,c=1 (d) a=1/2, b=1,c=-1

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) where c_1 and c_2 are variables, touch each other. Locus of their point of contact is

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and (k+2)/(k+1) ,then (a+b+c)^2 is equal to 2b^2-a c b. a 62 c. b^2-4a c d. b^2-2a c

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)