# CAT 2021 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 8

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 8 : If r is a constant such that |x2 - 4 x - 13| = r has exactly three distinct real roots, then the value of r is

1. 15
2. 18
3. 17
4. 21

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|x2 - 4x - 13| = r has exactly three distinct real roots.
Let's complete the squares of the quadratic equation.
|(x - 2)2 - 17| = r
(x - 2)2 - 17 = r and (x - 2)2 - 17 = -r
(x - 2)2 = r + 17 and (x - 2)2 = -r + 17
Hence, we get exactly three roots when r = 17.

The question is " If r is a constant such that |x2 - 4 x - 13| = r has exactly three distinct real roots, then the value of r is "

##### Hence, the answer is '17'

Choice C is the correct answer.

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