1)The triangle formed by the tangent to the curve f(x) = x^{2} + bx - b at the point (1,1) and the co-ordinate axes lie in the first quadrant. If it's area is 2 then the value of b is:

a)-1 b)3 c)-3 d)1

ans c

2)If the normals from any point to the parabola x^{2} = 4y cuts the line y = 2 in points whose abscissae are in AP , then the slopes of the tangents at the three co-normal points are in:

a) AP b)GP c) HP d) None of these

ans b

3)A line L passing through the focus of the parabola y^{2} = 4(x-1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then:

a) m E (-1,1) b) m E (-∞,-1) U (1 , ∞) c) m E R d) None of these

ans d

4)The latus rectum of the parabola x = at^{2} + bt + c and y = a't^{2} + b't + c' is

a)(aa' - bb')^{2}(a^{2} + a'^{2})^{3/2} b)(ab' - a'b)^{2}(a^{2} + a'^{2})^{3/2} c) (bb' - aa')^{2}(b^{2} + b'^{2})^{3/2} d)(a'b - ab')^{2}(b^{2} + b'^{2})^{3/2}

ans b

5)**answer not matching**

If the tangents to to the parabola y^{2} = 4ax at the points (x_{1} , y_{1}) and (x_{2} , y_{2}) meet at (x_{3} , y_{3}) then:

a)y^{3} = √y_{1}y_{2} b) 2y_{3} = y_{1} + y_{2} c)2y_{3} = 1y_{1} + 1y_{2} d) None of these.

book answer a my answer b

** 1 to 4 are doubts (please give the solutions) and 5 I am not getting the answer as given by the book..(someone please confirm which is the correct answer)**