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`

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

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

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

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

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+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

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 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)

If the planes x-c y-b z=0,c x-y+a z=0a n d b x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b c dot

If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coefficients, then n= (a c+a b+b c)/(b^2+a c) b. (2a c+a b+b c)/(b^2-a c) c. (a b+a c)/(b^2-a c) d. none of these