JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q73

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MathematicsSingle correct+4 / -1Question 73 of 90

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 $\dfrac14$ . 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 ?

A only

B only

C only

All the three

Answer and worked solution

Official answer: B

Intercepts a, b with $\frac1a+\frac1b=\frac12$ , so $\frac2a+\frac2b=1$ : the line always passes through (2, 2). Only B is certain to lie on the path.

(B)

Topics:Family of lines and pair of lines

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 73