# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 18

CAT 2023 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 18 : A rectangle with the largest possible area is drawn inside a semicircle of radius $2 $mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is 1. $2 : 1$ 2. $$sqrt{5} : 1$ 3. $1 : 1$ 4. $\sqrt{2} : 1$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Let the length of the longer side$the side resting on the diameter$ be equal to 2a.
Then the shorter side is given by $$sqrt { 2 ^ { 2 } - a ^ { 2 } }$ Area of the rectangle = $A = 2 a $sqrt { 4 - a ^ { 2 } }$ To maximize A, let us maximize A2 $A ^ { 2 } = 4 a ^ { 2 } \left$ 4 - a ^ { 2 } $right$$ $= 16 a ^ { 2 } - 4 a ^ { 4 }$ $= - 4 $left$ a ^ { 4 } - 4 a ^ { 2 } $right$$ $= - 4 $left$ a ^ { 4 } - 2 $times 2 \times a ^ { 2 } + 4 - 4 \right$ = 16 - 4 $left$ a ^ { 2 } - 2 $right$ ^ { 2 }$ The maximum value of $A ^ { 2 } = 16$ when $a = $sqrt { 2 }$ The shorter side will then be $\sqrt { 4 - a ^ { 2 } } = \sqrt { 4 - 2 } = \sqrt { 2 } = a$ Hence the ratio of longer to shorter side will be $2 a : a = 2 : 1$ The question is " A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is " ##### Hence, the answer is '$2 : 1$' Choice A 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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