Assistant/Auditor Government Secretariat 2018 — Kerala PSC PYQ Practice with Answers

Correct answer (Option B):\nLet any four consecutive natural numbers be n, n+1, n+2, and n+3.\nThe product of n consecutive integers is always divisible by n! (n factorial).\nFor 4 consecutive natural numbers, the product is always divisible by 4!.\nCalculation: 4! = 4 × 3 × 2 × 1 = 24\nTherefore, 24 is the largest natural number that exactly divides the product.\nOption B is correct.\n\nWhy others are wrong:\nOption A (120) is 5!, which is too large for just 4 numbers (e.g., 1×2×3×4 = 24, which is not divisible by 120).\nOptions C and D (12 and 6) are factors of 24, but they are not the largest natural number.\n\nStudy tip:\nAlways remember that the product of 'n' consecutive integers is always a multiple of n!.

Correct answer (Option C):\nWe can solve this problem using the unitary method.\nCost of 520 mangoes = ₹600\nStep 1: Find the number of mangoes per rupee = 520 / 600\nStep 2: Number of mangoes for ₹1500 = (520 / 600) × 1500\nStep 3: Simplify the expression = 520 × (1500 / 600) = 520 × 2.5 = 1300\nAnswer: 1300\nOption C is correct.\n\nWhy others are wrong:\nOptions A, B, and D do not match the correct calculation derived from the direct proportion equation.\n\nStudy tip:\nIn direct variation, the ratio of two quantities remains constant: X₁/Y₁ = X₂/Y₂.

Correct answer (Option C):\nLet the total number of candidates appeared be x.\nGiven: Percentage of passed candidates = 86%\nStep 1: Find the percentage of failed candidates = 100% - 86% = 14%\nStep 2: Set up the equation: 14% of x = 224\nStep 3: (14 / 100) × x = 224\nStep 4: x = (224 × 100) / 14\nStep 5: x = 16 × 100 = 1600\nAnswer: 1600\nOption C is correct.\n\nWhy others are wrong:\nOptions A, B, and D are incorrect values that do not satisfy the relation where 14% equals 224.\n\nStudy tip:\nAlways calculate the remaining percentage first when the problem relates total parts to a specific absolute subgroup.

Correct answer (Option A):\nLet the total work be the LCM of 10, 12, and 15, which is 60 units.\nStep 1: One day work of Raju + Tom = 60 / 10 = 6 units\nStep 2: One day work of Tom + Appu = 60 / 12 = 5 units\nStep 3: One day work of Appu + Raju = 60 / 15 = 4 units\nStep 4: Total work per day when combined = 2 × (Raju + Tom + Appu) = 6 + 5 + 4 = 15 units\nStep 5: One day work of Raju + Tom + Appu = 15 / 2 = 7.5 units\nStep 6: Days required together = 60 / 7.5 = 8 days\nOption A is correct.\n\nWhy others are wrong:\nOptions B, C, and D are incorrect values that result from calculation errors or forgetting to divide the sum of pairs by 2.\n\nStudy tip:\nWhen pairs of workers are given, adding their rates counts every individual twice, so remember to divide the combined rate by 2.

Correct answer (Option B):\nThe largest triangle inscribed in a semicircle has the diameter as its base and the radius as its height.\nGiven: Radius (r) = 2 cm\nStep 1: Base of the triangle = Diameter = 2 × r = 2 × 2 = 4 cm\nStep 2: Height of the triangle = Radius = 2 cm\nStep 3: Formula for Area = (1/2) × base × height\nStep 4: Area = (1/2) × 4 × 2 = 4 cm²\nOption B is correct.\n\nWhy others are wrong:\nOption A represents half the required value. Option C uses an incorrect geometric relation. Option D includes π, which belongs to circle areas, not triangles.\n\nStudy tip:\nFor any semicircle of radius r, the maximum area of an inscribed triangle is always r².