Mathematics

John Napier developed logarithms in 1614, which is the year he published his work introducing the concept. This makes option B the correct answer.

William Oughtred is credited with inventing the slide rule in the early 17th century, building upon the logarithmic concepts introduced by John Napier. The slide rule became a fundamental calculation tool before electronic calculators.

The problem states that the sum of two numbers is 28 and their difference is 4. Let the two numbers be x and y, where x > y. Then we have the system of equations: x + y = 28 and x - y = 4. Adding these two equations gives 2x = 32, so x = 16. Substituting x = 16 into the first equation gives 16 + y = 28, so y = 12. Therefore, the two numbers are 16 and 12. Checking the options, option A (12,16) satisfies both conditions: 12 + 16 = 28 and 16 - 12 = 4. Option D (14,12) does not satisfy the sum condition (14 + 12 = 26). Hence, the correct answer is A.

The analogy Cube : Cuboid relates a three-dimensional shape to another three-dimensional shape where the first is a special case of the second (a cube is a special type of cuboid). Similarly, Square : Cube relates a two-dimensional shape to a three-dimensional shape where the first is the base shape of the second (a square is the base of a cube). Option C (Sphere : Ellipsoid) relates two 3D shapes but neither is a special case of the other in the same way. Therefore, option B is the best analogous pair.

Mensuration is the branch of mathematics that deals with the measurement of geometric figures, including lengths, areas, and volumes of both two-dimensional and three-dimensional shapes. While trigonometry specifically relates to triangles, mensuration broadly covers the measurement of areas and volumes of various geometric figures, including polygons, circles, and solids. Therefore, the best analogy is that mensuration is related to areas (option C), as it involves calculating areas and volumes of shapes, not limited to polygons only.

The arithmetic mean is calculated by summing all the data points (3 + 6 + 9 + 12 + 15 = 45) and dividing by the number of data points (5), resulting in 45/5 = 9.

When rolling two dice, the total number of outcomes is 6 × 6 = 36. The pairs that sum to 8 are (2,6), (3,5), (4,4), (5,3), and (6,2), totaling 5 favorable outcomes. Therefore, the probability is 5/36.

1 inch is exactly equal to 2.54 centimeters, which is the standard conversion factor used internationally.

Given n(U) = 60 and n((A ∪ B)') = 10, the number of elements in the union is n(A ∪ B) = n(U) - n((A ∪ B)') = 60 - 10 = 50. Using the formula for union of two sets: n(A ∪ B) = n(A) + n(B) - n(A ∩ B), substitute the values: 50 = 35 + 24 - n(A ∩ B). Simplifying, n(A ∩ B) = 35 + 24 - 50 = 59 - 50 = 9. Therefore, n(A ∩ B) = 9, which corresponds to option C.

If P is 5 times as large as Q, then P = 5Q. The difference between P and Q is 5Q - Q = 4Q. To find what percent less Q is than P, we calculate (difference ÷ P) × 100 = (4Q ÷ 5Q) × 100 = 80%. Therefore, Q is 80% less than P, making option C the correct answer.