CAT 2021 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 11

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 11 : Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle ∠ADC is equal to 30° then the area of the parallelogram, in sq. cm, is

1. $$frac{25$$sqrt{3}+$sqrt{15}$}{2}$ 2. $25$$sqrt{5}+$sqrt{15}$$ 3. $$frac{25$$sqrt{5}+\sqrt{15}$}{2}$ 4. $25$$sqrt{3}+$sqrt{15}$$ 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 Revising the Cosine rule and the area of the triangle using the Sine rule… We draw the described parallelogram ABCD. Applying the cosine rule in triangle ADC, 202 = 102 + DC2 - 2$10)(DC) cos(30)
400 = 100 + DC2 - 2(10)(DC)($$frac { $sqrt { 3 } } { 2 }$$ 300 = DC2 -$10)(DC)($$sqrt { 3 }$) DC2 -$10)($$sqrt { 3 }$)$DC) - 300 = 0
DC = $$frac {$ $sqrt { 3 } )$ 10 ) $pm $sqrt {$ $sqrt { 3 } 10$ ^ { 2 } - 4$ 1 ) ( - 300 ) } } { 2 }$
DC is the length of one of the sides of the parallelogram, hence it can’t be negative.
DC = $$frac {$ $sqrt { 3 } )$ 10 ) + $sqrt {$ 300 ) 5 } } { 2 }$
DC = $$frac { $sqrt {$ 300$ 5 } + ( $sqrt { 3 } )$ 10 ) } { 2 }$
DC = $$frac { 10 $sqrt { 15 } + 10 \sqrt { 3 } } { 2 }$ DC = 5$$$sqrt { 15 } + \sqrt { 3 }$$ The are of the triangle ADC = ½ × DC × 10 × sin$300) (Applying the sine rule)
Area(ADC) = ½ × DC × 10 × sin(300)
Area(ADC) = $$frac { 10 $mathrm { DC } } { 4 }$= $\frac { 5 D C } { 2 }$ Area of the parallelogram ABCD = 2 × Area$ADC$
Area of the parallelogram ABCD = 2 × $$frac { 5 D C } { 2 }$ Area of the parallelogram ABCD = 5$DC)
Area of the parallelogram ABCD = 5 ( 5($$sqrt { 15 } + $sqrt { 3 }$$) Area of the parallelogram ABCD = 25$$$sqrt { 15 } + $sqrt { 3 }$$ The answer is '$25$$sqrt{3}+$sqrt{15}$$' Choice D is the correct answer. 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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