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6.

 If   [a×b.b×c.c×a]=λ[abc]2  then λ  is equal to


A) 0

B) 1

C) 2

D) 3



7.

The image of the line   \frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}    in the plane 2x-y+z+3=0 is the line


A) \frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}

B) \frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}

C) \frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}

D) \frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}



8.

 The slope of the line touching both the parabola   y^{2}=4x    and x^{2}=-32y is 


A) \frac{1}{2}

B) \frac{3}{2}

C) \frac{1}{8}

D) \frac{2}{3}



9.

 Let C be the circle with centre at (1,1) and radius 1. If T is the circle centred at (0,y)  passing through the origin and touching the circle C externally, then the radius of T is equal to 


A) \frac{\sqrt{3}}{\sqrt{2}}

B) \frac{\sqrt{3}}{2}

C) \frac{1}{2}

D) \frac{1}{4}



10.

 The locus of the foot of perpendicular drawn from the centre of the ellipse    x^{2}+3y^{2}=6 on any tangent to it is


A) (x^{2}-y^{2})^{2}=6x^{2}+2y^{2}

B) (x^{2}-y^{2})^{2}=6x^{2}-2y^{2}

C) (x^{2}+y^{2})^{2}=6x^{2}+2y^{2}

D) (x^{2}+y^{2})^{2}=6x^{2}-2y^{2}



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