TCS Company Numerical Ability Geometry

Two vertical poles 2 metres and 8 metres high stand apart on a horizontal plane . the height in metres of the point of intersection of the lines joining the top of each pole to the bottom of the other pole is.
1. 5.6
2. 1.6
3. 1.8

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TCS Other Question

A semicircle is drawn with AB as its diameter . From c, a point on AB, a line perpendicular to AB is drawn , meeting the circumference of the semicircle at D. Given that AC=2 cm, CD= 6cm, the are of the semicircle ( in sq. cm ) will be:
1. 82pi
2. 50pi
3. 31pi
4. 55pi
In this question A^B means A raised to the power B. Let f(X)=1+X+X^2+.....X^6.
The reamainder when f(X^7) is divided by f(X) is:
1. 7
2. 0
3. 6