# CAT 2022 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 17

CAT 2022 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 17 : The number of integer solutions of the equation $$left$x^2-10$right)^{$left$x^2-3 x-10$right$}=1$ is ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer We have $$left$ x ^ { 2 } - 10 $right$ ^ { $left$ x ^ { 2 } - 3 x - 10 $right$ } = 1$. Whenever $a ^ { b } = 1$. It could be because of one of the three cases… Case 1) b = 0 $x ^ { 2 } - 3 x - 10 = 0$ x = 5 or x = -2 Case 2) a = 1 $x ^ { 2 } - 10 = 1$ $x ^ { 2 } = 11$ x is not an integer. Case 3) a = -1 & b is even. $x ^ { 2 } - 10 = - 1$ $x = $pm 3$ For both values of x, $x = \pm 3$ b = $x ^ { 2 } - 3 x - 10$ is even. Therefore x can be 5, -2, +3 or -3. The question is " The number of integer solutions of the equation $\left$x^2-10$right$^{$left$x^2-3 x-10$right$}=1$ is " ##### Hence, the answer is '4' ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### 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? Mobile:$91) 99626 48484 / 94459 38484
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