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Q.

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the path of the man?

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a

B only

b

A only

c

C only

d

All the three

answer is A.

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Detailed Solution

xa+yb=1ha+kb=1----(1)1a+1b2=14∴1a+1b=12-----(2)∴ Line passes through fixed point (2,2). (from (1) and (2))

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A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the path of the man?