CAT 2024 Coordinate Geometry Question (Hard)

Question

Consider the system of two linear equations as follows: $3x + 21y + p = 0, \quad qx + ry - 7 = 0;$ where $p, q, r$ are real numbers.

Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?

Optima Learn · Accepted Answer

For the two lines to coincide, their coefficients must be proportional. So there exists a nonzero real lambda such that q 3 lambda, quad r 21 lambda, quad -7 lambda p Rightarrow p - lambda . Analyse each statement 1. Sign of p and q since q 3 lambda and p -7 lambda, p and q always have opposite sign

CAT 2024 Coordinate Geometry — Previous Year Question

CAT 2024

Quantitative

Coordinate Geometry

Hard

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