CSS · Applied Mathematics · Past Papers MCQs
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Use the difference of squares formula: (a + b)(a - b) = a^2 - b^2. Here, (7 + 3√5)(7 - 3√5) = 7^2 - (3√5)^2 = 49 - (9 * 5) = 49 - 45 = 4. The square root of 4 is 2.
In Euclidean geometry, a plane is uniquely determined by three non-collinear points. Therefore, three points are the minimum requirement to define a plane and ensure that a line containing these points lies within it.
The lateral surface area of a room (the area of the four walls) is calculated by multiplying the perimeter of the floor by the height of the room. Given the perimeter is 18 meters and the height is 3 meters, the calculation is 18 * 3 = 54 square meters. This formula assumes a rectangular room where all walls have the same height.
The volume of a cylinder is calculated using the formula V = π * r^2 * h. Substituting the given values, we have V = π * (4.2)^2 * 18.5. Calculating the square of the radius gives 17.64. Multiplying 17.64 by 18.5 results in 326.34. Finally, multiplying 326.34 by π (approximately 3.14159) yields approximately 1025.62 cubic centimeters, which matches the provided option.
The surface area of a cube is given by 6a^2, where 'a' is the side length. Setting 6a^2 = 216, we find a^2 = 36, so a = 6 meters. The volume of a cube is a^3, which is 6^3 = 216 cubic meters.
The minute hand of a clock completes one full circular rotation in exactly one hour. A full circle corresponds to 360 degrees, which is equivalent to 2π radians in circular measurement.
The relationship is defined by dividing the first number by 100 to obtain the second number (0.16 / 100 = 0.0016). Applying this same rule to 1.023, we divide by 100 to get 0.01023. Among the provided choices, 0.0102 is the closest approximation to this result.
To compare the fractions, convert them to decimals: 1/2 = 0.5, 4/5 = 0.8, and 5/8 = 0.625. Comparing these values, 0.8 is the largest. Therefore, 4/5 is the largest fraction.
A decimal fraction is considered terminating if it has a finite number of digits after the decimal point. Since 0.25, 3.125, and 0.625 all have a limited number of decimal places and do not continue infinitely, they are classified as terminating decimal fractions.
To find the square root of 0.4, we calculate the value which, when multiplied by itself, equals 0.4. Since 0.6 squared is 0.36 and 0.7 squared is 0.49, the value must lie between 0.6 and 0.7. Calculating further, 0.632 multiplied by 0.632 is approximately 0.3994, which is very close to 0.4. Thus, 0.632 is the most accurate approximation among the given choices.
