Multiple Choice Question: Which of the following equations is true for all angles $\theta$?

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Orphaned Multiple Choice Questions (MCQ) due to changes of exam system.

At a point A that is 50 m from the base of a monument, the angle of elevation to the top of the monument is twice as large as the angle of elevation from a point B that is 150 m from the monument.
The value of $10^{\log_{10} 7}$ is:
A sequence of numbers is defined by the relation $\dfrac{a_{n + 1}}{a_n} = 3^n$ and it is known that $a_1 = 1$. Find the value of $\log_3 a_{100}$.
Find the product of the roots of the quadratic equation $4x^2 + 2x - 1 = 0$.
Two casks A and B were filled with two kinds of sherry. In cask A, the ratio of the two kinds of sherry is 2:7 while in B, it is 1:5.
Find the capacity of a conical vessel that is made from a semi-circular tin of radius 2.5 m.
What is the integral of (3 cos^5 x) dx with limits from 0 to pi/2.
If $a^x = c^q = b$ and $c^y = a^z = d$, then:
It is the property of a material to absorb energy from a continuously applied load until it yields.
FYrh97O-1 Find x in meters.
Solve for the value of x if |x - 2| < 3.
The volume of fluid passing a section of the stream per unit time is known as:
If 8 men can cut 22 trees in a day, how many trees can 20 men cut in a day?
If three coins are tossed, how many possible ways are there of at least one coin showing tails?
A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average rate of 42%, what minimum rate of return, before payment of taxes, must the investment offer to be justified?

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