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

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

|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 answer is 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.

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com