100%- CAT 2026 & OMETs

📚 Answer Key & Explanation of the Quiz Q1. 12 : 12 + 7√3 APQ is an equilateral △. Since PQ ∥ BC, ∠QRC = 90° and △QRC is a 30°–60°–90° triangle. Let the side of the square be a. Therefore, QR = a and AQ = AP = PQ = a. In △QRC, QR/QC = √3/2 So, QC = 2a/√3 Hence, AC = AQ + QC = a + 2a/√3 Area of the equilateral △ABC: = √3/4 × AC² = √3/4 × (a + 2a/√3)² = √3/4 × (a²/3)(4 + 3 + 4√3) = (7 + 4√3)/12 × √3a² = (12 + 7√3)/12 × a² Area of the square = a² Therefore, the required ratio of the area of the square to the area of the equilateral △ABC is: a² : [(12 + 7√3)/12 × a²] = 12 : 12 + 7√3 Q2. 60 kmph Let V₁, V₂ and V₃ be the speeds of the three cars. The second car reaches C 1 hour earlier than the first car: ²⁴⁰/V₁ − ²⁴⁰/V₂ = 1 The third car covers 240 + 80 = 320 km when the first car covers 240 − 80 = 160 km. Therefore, ³²⁰/V₃ = ¹⁶⁰/V₁ ⇒ V₃ = 2V₁ Condition 1 states that the cars leave at equal intervals of time and arrive at the same time. Hence, ²⁴⁰/V₁ − ²⁴⁰/V₂ = ²⁴⁰/V₂ − ²⁴⁰/V₃ Substituting V₃ = 2V₁: ²⁴⁰/V₁ − ²⁴⁰/V₂ = ²⁴⁰/V₂ − ²⁴⁰/(2V₁) ⇒ ³(²⁴⁰)/(2V₁) = ²(²⁴⁰)/V₂ ⇒ V₂ = ⁴V₁/3 Now, using: ²⁴⁰/V₁ − ²⁴⁰/V₂ = 1 ⇒ ²⁴⁰/V₁ − ¹⁸⁰/V₁ = 1 ⇒ ⁶⁰/V₁ = 1 ⇒ V₁ = 60 kmph Therefore, V₂ = 80 kmph V₃ = 120 kmph. The difference is 60 kmph.

Q2. Three cars leave A for B at equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

Quiz ~

📚 Answer Key & Explanation of the Quiz *📍PARA SUMMARY* Q1. 2 There are three important keywords in this paragraph: the challenge posed by rural-urban continuum, the objective methodology with one or two metrics may not be enough to capture the wide diversity, it may require an element of human judgement. 2 captures all the keywords succinctly. 1 misses the element of human judgement, 3 also misses on the same. 4 goes out because it is not about the judgment of objective methodology, but human judgement coming as an additional factor to aid the methodology. Q2. 3 For summary questions we must learn to pick the broader keywords and connect them together to form the summary. In this paragraph the author uses two broad keywords "genetic theory and metabolic theory. The genetic theory was successful because of the diversity of genetic models, and the same might happen for metabolic theory, which would provide a conceptual foundation for much of ecology." The contrast in choice 2 makes the choice an incorrect one because the author stresses on similarity, not contrasts. Option 1 says "metabolic theory must have the wide range of theoretical models". The word "must" makes this choice an incorrect one. The author talks about a possibility, not a necessity. Option 4 goes out it because it misses discussing the keyword "metabolic theory" and how it is compared with genetic theory. 3 is the right choice.

Question 2

Question 1

Para Summary Quiz ~

📚 Answer Key & Explanation of the Quiz *📍ODD ONE OUT* Q1. 1 Statement 2 says that 'others believe that complex identities.... This statement suggests that there must be a similar but slightly contrary belief immediately in the sentence preceding sentence 2. 5 says complex identities are beneficial, while 2 says that complex identities confuse. Thus 5 and 2 form a pair. 4 introduces the idea of identity and thus becomes the opening sentence of the paragraph. Since 3 introduces the idea of 'complex identities', it must come before 52 pair. Thus we have 4352 coming together to form a coherent paragraph. 1 is the odd one out. Q2. 2 To quickly answer this question, we must form pairs. 1 says 'his idea to use sign language.... We must find the noun to which the possessive pronoun 'his' refers. Logically it refers to Pedro Ponce, as he is the one who created the sign language. Thus 4 and 1 form a pair. Also, only 5 can be the opening sentence, as it introduces the idea that for millennia, people with hearing impairment encountered marginalization. How they were marginalized can be seen in statement 3. Thus 5 and 3 form a pair. 5341 form a coherent para. There is no place for statement 2.

Question 2

Question 2

Question 1

Odd One Out Quiz ~