Maths Aptitude Test

Average speed for a round trip is the total distance divided by total time. If distance is D, time is D/U + D/V. Average speed = 2D / (D/U + D/V) = 2UV / (U + V).

22/7 is approximately 3.1428. The square root of 10 is approximately 3.1622. Since 3.1428 < 3.1622, 22/7 is not greater than sqrt(10).

In the context of human biology, every person is categorized as either male or female. Therefore, the probability of being one or the other is 1 (certainty).

The distance formula in 3D is sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). Plugging in the points: sqrt((3-1)^2 + (5-2)^2 + (-3-3)^2) = sqrt(2^2 + 3^2 + (-6)^2) = sqrt(4 + 9 + 36) = sqrt(49) = 7.

In an Olympic 100-metre final with eight total competitors, each runner has an equal likelihood of winning assuming fair competition. Since there is one winner and eight total participants, the probability of you winning is 1/8.

The harmonic series 1 + 1/2 + 1/3 + ... diverges to infinity. Therefore, it will eventually exceed any finite number, including 8.

The expansion of (a - b)^2 is a^2 - 2ab + b^2 based on the binomial square identity.

By definition in mathematics, 0! (zero factorial) is equal to 1.