These are Multiple Choice Questions (MCQ) from Exams posted before May 2024. These MCQs get orphaned after the system upgrade.
What is the integral of (3 cos^5 x) dx with limits from 0 to pi/2.
Company X has a fixed expense of P1.5M monthly and each unit is produced at P20
A pipe can alone fill a tank in 5 hours, while a drain could do the contrary in 12 hours.
A stone is projected from the ground with a velocity of 15 m/s at an angle of 30 deg; with the horizontal ground. How high will it rise?
What is the full capacity in cubic meter of a water tank having the shape of a frustum of a pyramid with lower and upper base areas of 32 m^2 and 8 m^2 and altitude of 6 m?
In a class experiment, a student needs 5 liters of 6% solution. He found a 4% and a 10% solution in the laboratory. How many liters of each solution should he mix in order to obtain 5 liters of 6% solution?
Find the compounded interest of P7,000 for 10 years at 6% compounded monthly.
Find the angle subtended by the line segment through (0, 0, 0) and (3, 8, 5) from the xy-plane.
A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of water in cubic meters.
A time deposits of P110,000 for 31 days earns P890.39 on maturity date after deducting the 20% withholding tax on interest income. Find the rate of interest per annum.
Find the area bounded by the y-axis and the lines y = 6x - 1 and y = 0.25x + 3.
The total surface area of a closed cylindrical tank is 153.94 square meter. If the volume is to be maximum, what is its height in meters.
A right spherical triangle ABC of a sphere of radius 50 cm has angle C = 90 deg, A = 56 deg and side b = 47 deg. Find the area of the triangle in square centimeter.
What time after 3:00 o’clock would the hour-hand and the minute-hand of a continuously driven clock subtends an angle of 45deg; for the second time?
Find the length of the latus rectum of the following ellipse: 25x^2 + 9y^2 - 300x - 144y + 1251 = 0.
Water is flowing into a conical cistern at the rate of 5 m^3/min. The height of the cone is 10 m and the radius of the upper base 5 m.
Find the volume generated by revolving the area on the 1st and 4th quadrants by the ellipse y^2 / 9 + x^2 / 4 = 1 about the line x = 3.
Determine the radius of the circle tangent to the coordinate axes and to another circle with center at (5, 5) and of radius 5.
A cone was formed by rolling a thin sheet of metal in a form of a sector of a circle 72 cm in diameter with a central angle of 150 deg. Find the volume of the cone.
A hollow glass bowl in the shape of a sphere of radius 4” is filled with water to a depth of 3”. If the water flows out through a small hole in the bottom so that the level drops 2”, how much water has escaped in in^3?
A car that accelerates uniformly passes at point A with a speed of 30 kph. It reaches point B, 21 km from A, after 18 minutes. Find the acceleration of the car.
What annuity over a 10 year period at 8% interest is equivalent to a present worth of P10,000?
Ernie’s average in 6 subjects is 83. If his lowest grade is disregarded, his remaining subject is 84. What is his lowest grade?
A product has a current selling price of P325. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?
Find x if the point (x, 2) is equidistant from (3, 2) and (7, 2).
In a company meeting, coffee and cake were served during the break. Of the 50 people who attended the meeting, 30 ate cake while 34 took coffee.
The front wheel of a bicycle has a diameter of 50 cm. Approximately how many times has the front wheel turned if the bicycle has traveled 1 km?
When an irregular shaped object is placed in a cylindrical vessel of water whose radius is 8 cm, the water rises 6 cm. What is the volume of the rock if it is completely submerged?
A highway has a gradient of 0.087. How many meters would an automobile rise vertically if it traveled 2 miles along the way?
A large sewer system will cost P8,750,000 annually. There will be favorable consequences to the general public of P25,000,000 annually and adverse consequences to a small segment of the public of P2,500,000 annually. What is the benefit to cost ratio?
Point (3, 4) is the center of the circle that is tangent to the x-axis. What is the point of tangency?
The ratio of two numbers is 6:7. If the large number is 42, what number is the smaller one?
An arch 18 m high has a form of a parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. Find the width at the bottom.
Circle a has circumference numerically equal to its area. If the certain square has the same area with the circle a, then what would be the length of its sides?
Find the equation of the line through (4, -7) parallel to the y-axis.
A decagon has how many diagonals?
What is the value of x in trigonometric substitution with an integrand involving (a^2 - x^2)?
Find the equation of the line whose slope is -3 and the x-intercept is 5.
Find C so that the line y = 4x + 3 is tangent to the curve y = x^2 + C.
Convert the equation (3a + 2b)^2 into a polynomial.
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?
If three coins are tossed, how many possible ways are there of at least one coin showing tails?
The triangle defined by the points A(6, 1), B(2, 4), C(-2, 1) is…
A flywheel is brought from rest up to a speed of 1500 rpm in 1 minute. What is the average angular acceleration, alpha?
Jojie was sent to the store to get 11 cans of spam. Jojie could carry only two cans at a time. How many trips would Jojie have to make?
Spherical degree is a unit of a spherical area taken as 1/720 of the surface of the sphere. How many spherical degrees hemispheres have?
Which of the following is the value of x^2 + 1/x^2 when x + 1/x = 5?
A factory is running at 80% efficiency with a fixed cost of P78,000.00, variable cost per unit of P130.00, selling price per unit of P416.00, and production capacity of 5000 units.
Instead of multiplying the number by 17, Fred divided it by 17. If the answer he obtained was 1, what should have been the correct answer?
An equilateral triangle has an altitude of $5\sqrt{3}$ cm long. Find its area.