# CAT 2023 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 2

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. 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 2 : The sum of all possible values of $x$ satisfying the equation $2^{4 x^2}-2^{2 x^2+x+16}+2^{2 x+30}=0$, is

1. $$frac{3}{2}$ 2. $$frac{5}{2}$ 3. $\frac{1}{2}$ 4. 3 ## 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 $2 ^ { 4 x ^ { 2 } } - 2 ^ { 2 x ^ { 2 } + x + 16 } + 2 ^ { 2 x + 30 } = 0$ $\div$ by $2 ^ { 2 x ^ { 2 } + x + 16 }$ on both sides. $2 ^ { 2 x ^ { 2 } - x - 16 } + 2 ^ { - 2 x ^ { 2 } + x + 14 } = 1$ $2 ^ { 2 x ^ { 2 } - x - 16 } + 2 ^ { - 2 x ^ { 2 } + x + 16 - 2 } = 1$ $2 ^ { 2 x ^ { 2 } - x - 16 } + 2 ^ { - \left$ 2 x ^ { 2 } - x - 16 $right$ - 2 } = 1$ let $y = 2 ^ { 2 x ^ { 2 } - x - 16 }$ $y + $frac { 1 } { 4 y } = 1$ $4 y ^ { 2 } - 4 y + 1 = 0$ $4 y ^ { 2 } - 2 y - 2 y + 1 = 0$ $2 y$ 2 y - 1$ - 1 ( 2 y - 1 ) = 0$
$( 2 y - 1 ) ^ { 2 } = 0$
$$therefore 2 y = 1$ $2 $times 2 ^ { 2 x ^ { 2 } - x - 16 } = 1 = 2 ^ { 0 }$ $2 ^ { 2 x ^ { 2 } - x - 15 } = 2 ^ { 0 }$ $2 x ^ { 2 } - x - 15 = 0$ $2 x ^ { 2 } - 6 x + 5 x - 15 = 0$ $2 x$ x - 3$ + 5 ( x - 3 ) = 0$
$( 2 x + 5 ) ( x - 3 ) = 0$
$$therefore x = 3$ or $x = - 5 / 2$ Sum of all possible values of x $= 3 +$ - 5 / 2 ) = $frac { 1 } { 2 }$ The question is " The sum of all possible values of $x$ satisfying the equation $2^{4 x^2}-2^{2 x^2+x+16}+2^{2 x+30}=0$, is " ##### Hence, the answer is '$$frac{1}{2}$' Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## 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? Mobile:$91$ 99626 48484 / 94459 38484
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