Solution to 2024 CAT Slot 1 (Past Year Question Paper) - QA (Quant Questions 6 to 10 Explained)

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Q.6 ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of ∆ADE is
Q.7 If x is a positive real number such that 4 log ⁡ 10 𝑥 + 4 log ⁡ 100 𝑥 + 8 log ⁡ 1000 𝑥 = 13 4log 10​x+4log 100​x+8log 1000​x=13, then the greatest integer not exceeding x, is...
Q.8 A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
Q.9 The sum of all real values of k for which ( 1/8 )^𝑘 × ( 1/32768 )^1/3 = 1/8 × ( 1/32768 )^1/𝑘 is...
Q.10 An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

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