Multiple Choice Question: Find the sum of the first terms of the progression 2, 4, 8, 16,…

Find the sum of the first terms of the progression 2, 4, 8, 16,…

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

Find the value of $x = \sin^2 \varphi - \cos^2 \varphi$ if $\varphi$ is $\pi / 4$ or $45^\circ$.
It is a point formed by intersecting the three perpendicular bisectors of the sides of the triangle.
Find x if the point (x, 2) is equidistant from (3, 2) and (7, 2).
Allan and Bernard start at the same time from two places 136 km apart and travel toward each other. Allan travels 10 kph and Bernard 8 kph. If Bernard rests 1 hour on the way, in how many hours will they meet?
The geometric mean of two numbers is 8 and the arithmetic mean is 17. Find one of the numbers.
It is the tensile force required on a tape to eliminate the effects of sag during tape surveys.
Find the area bounded by the y-axis and the lines y = 6x - 1 and y = 0.25x + 3.
An airplane flew from Davao whose latitude is 14° N and longitude of 121° 30' E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?
When the population growth of a certain city was first studied, the population was 22,000.
A certain university gives 4 points per credit for a grade A, 3 points per credit for B, 2 points per credit for grade C, a point per credit for grade D, and zero for an F.
Calculate $\sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$
Three boys and two girls are to be picked from a class of 15 in which 9 are girls. How many ways can this be done?
In how many ways can 5 engineers and 4 nurses be arranged in a round table if the nurses insisted to be sitting side by side?
Solve for $x^2$ if $48^{1/x} = 4 \times 3^{1/x}$.
The vena contracta of a sharp-edged hydraulic orifice usually occurs:

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