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Let a, b, x, y, be real numbers | Quantitative Aptitude – Algebra - Quadratic Equation

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Quadratic Equation: Let a, b, x, y, be real numbers

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills.

You may also find remaining question solution of CAT 2019, Slot 2 by searching the question in the search bar.

CAT 2019 - Slot 2 - Quantitative Aptitude - Quadratic Equation - Question 1 - Let a, b, x, y, be real numbers

Q. 1: Let a, b, x, y, be real numbers such that a^2 + b^2 = 25, x^2 + y^2 = 169, and ax+by = 65. if k = ay-bx, then?

1. k>5/13

2. k=0

3. k=5/13

4. 0 < k < = 5/13

As a,b, x , y are real and as we know 3^2 + 4^2 = 25 or 5^2 + 0= 25 also 13^2 + 0= 169 and 5^2 + 12^2 = 169

 

ax+ by = 65 is possible only when (a,b) = (0,5) and (x,y)= (0,13)

 

Thus k = 0*13 – 0*5 =0

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