Mathematics

Since Naeem sold the computer at a 20% loss for Rs 25,000, the selling price is 80% of the purchase price. Therefore, purchase price = 25000 ÷ 0.8 = Rs 31,250, which matches option C.

To find 80% of 700, multiply 700 by 0.80, which equals 560. Therefore, option B is correct.

Blaise Pascal was a French mathematician, physicist, inventor, writer, and Catholic theologian, best known for his contributions to mathematics and science.

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.

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.

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

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.

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.

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 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.

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.

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.

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

Euclid is known as the Father of Geometry because of his foundational work 'Elements,' which systematically organized the principles of geometry.

A right-angled prism, commonly known as a rectangular prism or cuboid, has 6 faces. These include the top, bottom, front, back, and two side faces.

The Ciprian Foias Prize is awarded in the field of Mathematics, recognizing outstanding contributions in this area. Ciprian Foias was a renowned mathematician, and the prize named after him honors achievements in mathematical research.

"Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa’l-muqābala" (The Compendious Book on Calculation by Completion and Balancing) was written by Al-Khwarizmi, who is considered the father of algebra. This work laid the foundations for algebra as a discipline.

The formula (7-3) × (1+6) / 4 evaluates as follows: (7-3) = 4, (1+6) = 7, so 4 × 7 = 28, then 28 / 4 = 7. Therefore, the correct answer is 7, which corresponds to option A.

25% of 150 is calculated as (25/100) × 150 = 37.5. Therefore, the correct answer is 37.5.

The pattern in the sequence is that each number is multiplied by 2 and then 1 is added: 16×2+1=33, 33×2-1=65, 65×2+1=131, 131×2-1=261, 261×2+1=523. Thus, the missing number is 523.

To cut one roll into 10 pieces, the tailor needs 9 cuts per roll. In 24 minutes at 45 cuts per minute, he makes 24 × 45 = 1080 cuts. 1080 cuts ÷ 9 cuts per roll = 120 rolls.

The pattern in the sequence is: add 3, 5, 7, 9, 11, 13, and 15 to each previous number. The last number should be 65 (50 + 15), not 64. Therefore, 64 is the odd one out.

“5 percent” means 5/100. So 5% of 5 = (5/100)×5 = 25/100 = 0.25, which matches option A.