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NDA 2018 Maths · Mathematics · Straight Lines · medium

The lines kx+2y=3 and 4x-y=7 are perpendicular when k equals

Single correct option

The lines kx+2y=3kx+2y=3 and 4x−y=74x-y=7 are perpendicular when kk equals
  1. A. 22
  2. B. −12-\frac12
  3. C. 12\frac12
  4. D. 88
Show answer and solution

Answer: (C) 12\frac12

The slopes are −k2-\frac k2 and 44. Perpendicularity needs −k2⋅4=−1-\frac k2\cdot4=-1, so k=12k=\frac12. Using the coefficient condition aa′+bb′=0aa'+bb'=0 gives the same: 4k−2=04k-2=0. The value 8 comes from the parallel condition gone wrong.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake