These are Multiple Choice Questions (MCQ) from Exams posted before May 2024. These MCQs get orphaned after the system upgrade.
Find the value of x if $x = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi}$.
Which of the following is equal to $\dfrac{\sin \theta}{1 + \cos \theta}$.
Find the value of $x = \sin^2 \varphi - \cos^2 \varphi$ if $\varphi$ is $\pi / 4$ or $45^\circ$.
Find the area of the sector inside the square ABCD.
Area outside equilateral triangle available for grazing by the goat.
From the given right triangle what is the value of $3 \sin^2 \varphi \, \sec \varphi$ in terms of $x$.
Find $\tan \beta$ from the given figure.
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 $x$.
Solve for b as shown in the figure.
From the following figure, which of the following is equal to $\tan (\theta/2)$?
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.
Find the exact value of $\cos [ \, \arcsin (2/3) \, ]$.
Evaluate the $\tan (\arctan 3 - \arctan 2)$.
Evaluate the $\tan (\arctan 3 + \arctan 4)$.
Find the exact value of $\arccos (\tan 45^\circ)$
Solve for $x$ if $\arcsin (x + 2) = \pi/6$.
In the figure, $\varphi$ represents the angle subtended by a 5 ft picture when viewed from point P that is 7 ft below the picture and 14 ft away from the wall on which the picture hangs.
Find the 8th term of the sequence $-3, ~ 4, ~ 5/3, ~ … \, , ~ \dfrac{n + 2}{2n - 3}$.
Find the 6th term of $1, ~ 2, ~ 5, ~ ... \, , ~ \frac{1}{2}(1 + 3^{n - 1})$.
Find $\displaystyle \sum_{n = 1}^5 S_n$ where $S_n = 2/n$.
Find $\displaystyle \sum_{n = 1}^4 (2k + 1)$.
Compute the following: $\displaystyle \sum_{n = 1}^3 \left( \dfrac{n + 1}{n} \right) - \sum_{n = 1}^3 \left( \dfrac{n}{n + 1} \right)$.
Compute the following: $\displaystyle \sum_{j = 1}^6 \left[ -3 + 5(j - 1) \right]$.
Compute the sum of the integers from 1 to 1000.
The sequence 1, 1, 2, 3, 5, 8, 13 is called the Fibonacci sequence. What is then the tenth term?
A pyramid of blocks has 26 blocks in the bottom row and 2 fewer blocks in each successive row thereafter. How many blocks are there in the pyramid?
Find the sum of the arithmetic sequence 2, 4, 6, 8, 10, 12.
Find the 7th term of the geometric sequence beginning with 6, 9, 27/2, …
A certain bacterial culture doubles in number every day. If there were 1000 bacteria at the end of the 1st day, how many will there be after 10 days?
A steel pipe is being carried down a hallway 9 ft wide.
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 cm and 4 cm if two sides of the rectangle lie along the legs.
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river.
A cylindrical can is to be made to hold 1 liter of oil. Find the radius that will minimize the cost of the metal to manufacture the can.
A Norman window has the shape of a rectangle surmounted by a semicircle.
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?
A closed cylindrical tank having a volume of 71.57 m^3 is to be constructed. If the surface area is to be minimum, what is the required diameter of the tank?
If 1200 cm^2 of material is available to make a box with a square base and open top, find the largest possible volume of the box.
A corner lot, triangular in shape, has perpendicular sides measuring 90 m and 120 m, respectively.
A triangle has a variable sides x, y, and z subject to the constraint that the perimeter P is fixed to 18 cm. What is the maximum possible area of the triangle?
A wall 10 ft high along the property line is 8 ft from a house.
A ship lies 6 miles from a straight shore, and opposite a point 10 miles farther along the shore, another ship lies 18 miles offshore.
Find the area of the largest rectangle that can be inscribed in the ellipse x^2/25 + y^2/16 = 1.
Solve for x: log_3 67 = 2x.
How many 3-digit numbers greater than 300 can be made out from digits 0, 1, 2, 3, 4, 5, and 6 if repetition of digit is not allowed?
What is the equation of the line with y-intercept = 2 and slope = -3?
What is the length of the latus rectum of the curve y^2 = -16x?
The sum of the interior angles of a polygon of n sides is four times the sum of its exterior angles. Find the value of n.
Find the perimeter of the ellipse with major-axis = 10 and minor-axis = 8.
The volume of the sphere is 7238 m^3, find the radius.
At what value of x will the slope of the curve x^3 - 9x - y = 0 be 18?