If `y^2=4b(x-c)` and `y^2 =8ax` having common normal then `(a,b,c)` is (A) `(1/2,2,0)` (B) `(1,1,3)` (C) `(1,1,1)` (D) `(1,3,2)`

If x^(2)+3x+3=0 and ax^(2)+bx+1=0 ,a,b in Q have a common root,then value of (3a +b) is equal to : (A) (1)/(3) (B) 1 (C) 2 (D) 4

If the given equation ax^2+bx+c=0 and the equation x^2+2x+9=0 have a common root, then a:b:c is (A) 1:2:9 (B) 1:2:3 (C) 1:1:1 (D) none of these

The number of normal (s) to the parabola y^(2)=8x through (2,1) is (B) 2(A)1(D)3(C)0

Match the following. (A) 1-c, 2-b, 3-a (B) 1-b, 2-c, 3-a (C) 1-a, 2-b, 3-c (D) 1-a, 2-c, 3-b

A normal is drawn at a point " (x_(1),y_(1)) " of the parabola " y^(2) - 16x " and this normal makes equal angle with both "x" and "y" axes,Then point " (x_(1),y_(1)) " is (a) " (4,-4) ," (b) " (2,-8) " (c) " (4,-8) " (d) " (1,-4) "

If the quadratic equations 3x^(2)+ax+1=0 and 2x^(2)+bx+1=0 have a common root then the value of expression |2a^(2)-5ab+3b^(2)| is where (2a!=3b) (A) 0 (B) 1 (C) -1 (D) None of these

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

if |[2a,x_1,y_1],[2b,x_2,y_2],[2c,x_3,y_3]|=(abc)/2!=0 then the area of the triangle whose vertices are (x_1/a,y_1/a),(x_2/b,y_2/b),(x_3/c,y_3/c) is (A) (1/4)abc (B) (1/8)abc (C) 1/4 (D) 1/8

If the family of curves y=ax^2+b cuts the family of curves x^2+2y^2-y=a orthogonally, then the value of b = (A) 1 (B) 2/3 (C) 1/8 (D) 1/4

D.E., having the solution y=c_(1)+c_(2)e^(3x) , is A) y_(2)=3y B) y_(2)=3y_(1) C) y_(3)+3y_(1)=0 D) y_(2)+3y=0