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

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• 1/2

• 1/4

The image of line  in the plane 2x-y+z+3 =0 is the line

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A.

Here, plane and line are parallel to each other. Equation of normal to the plane through the point (1,3,4) is

Any point in this normal is (2jk+2, -k+3,4+k)
Then,  lies on the plane.

hence, point through which this image pass is
(2k+1,3-k,4+k)
i.e., (2(-2) + 1, 3+2, 4-2) = (-3,5,2)
Hence equation of image line is

A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O n the ground is 45^o. It flies off horizontally straight away from the point O. After 1s, the elevation of the bird from O is reduced to 30^o. Then, the speed (in m/s of the bird is

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D.

A ray of light along  get reflected upon reaching X -axis, the equation of the reflected ray is 

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B.

Given equation of line

Slope of incident ray is  
So, slope of reflected ray must be  and the point of incident
So equation of reflected ray