Multiple Choice Question: How many prime numbers are there from 1 to 100, inclusive?

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

A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?
Find the area of a sector of a circle of radius 6 cm and a central angle of 60°.
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
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.
A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly towards the sun, what is the length of the pole?
Two vertices of a rectangle are on the positive x-axis. The other two vertices are on the lines y = 4x and y = 6 - 5x. What is the maximum possible area of the rectangle?
For a given GP, a1 = 5/21 and r = 1.2. Calculate the product of the first 21 terms.
A line of levels 9.36 km is run to check the elevation of BM 2 which been found to be 31.388 meters with BM 1 of elevation at sea level.
The Design Basis Earthquake (DBE) has a return period of 475 years with 10% probability of exceedance in how many years?
Find the non-zero solution to the equation $3x^4 - 27x^3 = 0$.
If $\theta$ is an acute angle of a right triangle where $\sin \theta = x/2$, compute the value of $\sin 2\theta$ in terms of $x$.
A hole 10 inches in diameter is to be punched out from a sphere having a diameter of 16 inches. Determine the volume punched out if the center of the hole is along the diameter of the sphere.
A circle with radius r has a circumference equal to the perimeter of a square whose side is S. Which of the following is true?
Ten stones are placed in a straight line on the ground, at intervals of two feet.
Solve for the value of x if |x - 2| < 3.