MSTE

Question 1

In the equation x^2 - kx + 9 = 0, find the k if the roots are equal.
a. 8
b. 6
c. 7
d. 9

Answer 1

B

Question 2

In the quadratic equation I ax^2 + bx + c =0, when b^2 is equal to 4ac, then the roots are
a. equal
b. real and unequal
c. imaginary
d. extraneous

Answer 2

A

Question 3

The equation whose roots are the reciprocals of the roots of the equation 2x^2 - 3x - 5 = 0
a. 2x^2 - 5x - 3 = 0
b. 5x^2 - 2x - 3 = 0
c. 5x^2 + 3x - 2 = 0
d. 3x^2 - 5x - 2 = 0

Answer 3

C

Question 4

In a quadratic equation problem, a student made a mistake in copying the coefficient of x^2 and got roots of 2 and 3. Another student made a mistake in copying the constant term and got roots of 4 and 6. Find the value of the smaller of the two roots.
a. 1.4
b. 10.6
c. 8.6
d. -1.4

Answer 4

A

Question 5

When you divide x to the 10 plus 1 by the quantity x minus square root of 2, the remainder is?
a. 13
b. 34
c. 33
d. 43

Answer 5

C

Question 6

If the polynomial x^3 + 4x^2 - 3x + 8 is divided by x-5, determine the remainder.
a.218
b. 45
c. 42
d. 210

Answer 6

A

Question 7

If the polynomial ax^3 + bx^2 + 8x + 7 is divided by x-2, the remainder is 63. If it is divided by x=3, the remainder is -62. FInd the value of “a”.
a. 3
b. 4
c. 5
d. 6

Answer 7

A

Question 8

Roots which are equal to zero are called the
a. trivial solution
b. extraneous roots
c. imaginary roots
d. zero of an equation

Answer 8

A

Question 9

They are the equations whose memberss are only for certain (or possibly) no values of the unknown
a. conditional equations
b. inequalities
c. fix equation
d. temporary equation

Answer 9

A

Question 10

A statement which is accepted as true proof without proof
a. postulate
b. lemma
c. theorem
d. corollary

Answer 10

A

Question 11

When a certain polynomial p(x) is divided by (X-1), the remainder is 12. When the same polynomial is divided by (x-4), the remainder is 3. Find the remainder when the polynomial is divided by (x-1)(x-4)
a. x+5
b. -2x-8
c. -3x+15
d. 4x-1

Answer 11

C

Question 12

If (x+3) is a factor of x^3 + 3x^2 +4x + k, find k
a. 12
b. 14
c. -12
d. -14

Answer 12

A

Question 13

When all x is replaced by y and all y are replaced by x and the equation remains the same, then equations is said to be:
a. equivalent
b. identical
c. symmetric
d. consistent

Answer 13

C

Question 14

FInd the value of x if the square root of the quantity x plus so on close quantity is equal to two
a. 1
b. 2
c. 3
d. 4

Answer 14

B

Question 15

Solve for x and y in the following equations:
27^x = 9^y
(81^y)(3^-x) = 243
a. (1,3)
b. (3,1)
c. (1,1.5)
d. (1.5,1)

Answer 15

C

Question 16

Solve for the value of x in the following equation
x^3logx = 100x
a. 10
b. 100
c. 1000
d. 10000

Answer 16

A

Question 17

Kaye is now thrice as old as Koy. Five years ago, Kaye was 5 times as old as Koy. How old is Kaye?
a. 10
b. 20
c. 30
d. None of the choices

Answer 17

C

Question 18

Mary is 24 years old. Mary was twice as old as Ana was when Mary was as old as Ana is now. How old is Ana?
a. 20
b. 16
c. 19
d. 18

Answer 18

B

Question 19

Diophantus spent 1/12 of his life in childhood, 1/6 in youth and 1/7 as a bachelor. Five years after his marriage was born a son who died four years before him at half his final age. How old was Diophantus when he died?
a. 84
b. 108
c. 72
d. 94

Answer 19

A

Question 20

How much gold and how much silver must be added to 100kg of an alloy containing 40 percent gold and 10 percent silver to produce an alloy containing 50 percent gold and 20 percent silver?
a. 43.33kg gold and 23.33kg silver
b. 37.33kg gold and 42.11kg silver
c. 45.23 kg gold and 23.33 silver
d. 24.4kg silver and 21.41kg gold

Answer 20

A

Question 21

A 100kg salt solution originally 4% by weight NaCl in water is evaporated until the concentration is 5% by weight NaCl. What percentage of the water in the original solution is evaporated?
a. 20.83%
b. 12.56%
c. 78%
d. 100%

Answer 21

A

Question 22

MCMXCIV is equivalent to what number?
a. 2974
b. 1974
c. 2174
d. 1994

Answer 22

D

Question 23

The difference in the squares of the digits of a two-digit positive number is 27. If the digits are reversed in order and the resulting number subtracted from the original number, the difference is also 27. What is the product of the digits of the number?
a. 61
b. 62
c. 63
d. 18

Answer 23

D

Question 24

A man left their office at past 3 oclock for merienda. After 20 minutes on his return, he noticed that the minute hand is ahead of the hour hand exactly by as much as it was behind when he left. At what time did he leave?
a. 3:07.36
b. 3:08.36
c. 3:06.16
d. 3:06.36

Answer 24

D

Question 25

An equilateral lot of side 10m is fenced all around. If a goat tied by a rope to a midpoint of one side
grazes over four fifths of the lot, find the length of the rope?
a. 2m
b. 3m
c. 4m
d. 5m

Answer 25

D

Question 26

A point “A” on the south bank of a river 2km wide and flowing due east is to be connected by a bridgeand a road to a town “T” which is at a perpendicular distance of 4km north measured from the north bank of the river. A preliminary survey indicated that the bridge can be built from point “A” on the south bank to a point “P” on the north bank lying N220W from point “A” or alternately to a point “Q” downstream from point “P” with a bearing of 𝑁410𝐸 from point “A”. The town “T” lies 𝑁120𝐸 from
point “A”. If the bridge costs P160000 per km to build and the road P40000 per km, which route is more economical and how much?
a. Route AQT is more economical by P32600.00
b. Route APT is more economical by P65200.00
c. Route AQT is more economical by P65200.00
d. Route APT is more economical by P32600.00

Answer 26

B

Question 27

Two towers A and B of equal height on dangerous rocks bear respectively southeast and southwest from a battleship. The angle of elevation of A’s top is viewed from the battleship is 125′ that of B is 154′. What course should the battleship take to pass midway between the towers?
a. The battleship should take 𝑆3
*19′𝑊 course
b. The battleship should take 𝑆8
*25′𝑊 course course
c. The battleship should take 𝑆1
39′𝐸 course
d. The battleship should take 𝑆1009′𝐸 course

Answer 27

B

Question 28

A corner lot of land is 35m on one street and 25m on the other street, the angle between the two lines
of the street being 82*25′. The other two lines of the lot are respectively perpendicular to the lines of
the streets. What is the worth of the lot at P180 per square meter?
a. P320950.8
b. P139270
c. P176950.8
d. P282034

Answer 28

B

Question 29

The Flagship of the Naval Fleet guarding the Sulu Sea is 4 nautical miles from the destroyer, 3 nautical miles from the cruiser and 5 nautical miles from the battleship. The flagship is within the triangle formed by the three ships. If the line connecting the destroyer and the cruiser is perpendicular and equal to the line joining the cruiser and the battleship, determine the distance between the destroyer
and the battleship.
a) 6. 04n.m
b) 8. 55n.m
c) 6. 77n.m
d) 8. 07n.m

Answer 29

B

Question 30

Having a certain unknown distance measured and the angle of elevation of the cliff, a civil engineer walked 60m on a level towards the cliff. The angle of elevation from this second station was the compliment of the former angle. The civil engineer then walks 20m nearer the cliff, on the same line and found the angle of elevation from the third station to be doubled the first angle. How high is the
cliff?
a) 44.17m
b) 64.17m
c) 54.17m
d) 74.17m

Answer 30

D

Question 31

A lighthouse at the edge of a cliff is due south and in line with the three ships anchored at the bay. The farthest ship is 600 nautical miles from the 2nd ship while the nearest ship is 500 nautical miles
from the lighthouse. The three ships are colinear with the position of the lighthouse. A naval boat approaches the position of the three ships but not in line with the position of the three ships. The farthest boat and the 2nd boat subtend an angle of 30degrees from the naval boat, while that of the 2nd boat and the nearest boat to the lighthouse subtends an angle of 45degrees and the nearest boat and the lighthouse subtends an angle of 60degrees. Find the distance of the nearest ship from the 2nd ship.
a) 155.5n.m
b) 255.5n.m
c) 355.5n.m
d) 455.5n.m

Answer 31

B

Question 32

The position of the lighthouse is equidistant from the destroyer battleship, flagship and the cruiser. The lighthouse is also colinear with the destroyer and the cruiser. If the distance between the destroyer and battleship is 3 nautical miles, between the battleship and the flagship is 4nautical miles while that of the flagship and the cruiser is 5 nautical miles, determine the distance from the destroyer to the flagship.
a) 4. 03n.m
b) 7. 48n.m
c) 6. 32n.m
d) 5. 42n.m

Answer 32

C

Question 33

Two sounding ships left port A to port B with the faster ship making a stop at another port C and stayed there for 2 days to load sounding equipment before proceeding to port B. The slower ship left
port A one day after the first ship left. They arrived port B at the same time. Port A is at longitude 120036′𝐸 and latitude 14023′𝑁; port B lies at the equator with longitude 105024′𝐸; port C is at longitude 108032′𝐸 and latitude 10036′𝑁. Determine the speed of the faster ship if the other is cruising
at a speed of 10knots.
a) 12.49knots
b) 11.03knots
c) 15.12knots
d) 14.11knots

Answer 33

D

Question 34

An airplane flew from Davao whose latitude is 140𝑁 and longitude of 121030′E on a course 𝑆300𝑊and maintaining a uniform altitude. At what point will the plane cross the equator?
a) 7057′𝐸
b) 60059′𝑊
c) 11333’E
d. 12901’W

Answer 34

C

Question 35

A Philippine Airlines plane on one of its trips is to fly from Manila (14035′𝑁, 120059′𝐸) to Sydney, Australia (33052′𝑆, 151012′𝐸) if it flies at an average speed of 221 nautical miles per hour. At what
course will the pilot take at Manila?
a) S49022’E
b) 𝑆29032′𝐸
c) 𝑁19012′𝑊
d) 𝑁59042′𝑊

Answer 35

A

Question 36

Twenty-five potatoes are placed on the ground 4ft apart in a straight row. In line with the potatoes and 10ft. from the first one is a basket. A runner starting from the basket picks up the potatoes and carries them one at a time to the basket. If he runs at an average rate of 5yards per second. how many potatoes can be put into the basket in one minute and 16seconds?
a) 20potatoes
b) 15potatoes
c) 30potatoes
d) 35potatoes

Answer 36

B

Question 37

Three numbers whose sum is 42 in geometric progression. If one subtracted from the first, 3 from the second and 11 from the third, the remainders will be in arithmetic progression. Find one of the
numbers.
a) 13
b) 3
c) 20
d) 8

Answer 37

A

Question 38

The sum of the sides of 2polygon is 12 and their diagonals is 19. Identify one of the polygons.
a) Hexagon
b) Heptagon
c) Octagon
d) Nonagon

Answer 38

B

Question 39

The Philippine Army recruited new trainees for its armed forces. The new trainees were formed into a hollow square, three deeps, when it was observed by the commanding officer; that with the addition of 25 to their number, a solid square might be formed, of which the number of men in each side
would be greater by 22 than the square root of the number of men in each side of the hollow square. Determine the number of men that were recruited originally.
a) 936men
b) 1026men
c) 596men
d) 706men

Answer 39

A

Question 40

Solve the given Diophantine Problem: Find the smallest number which when you divide by 2, the remainder is 1, you divide by 3, the remainder is 2, you divide by 4, the remainder 3, you divide by 5, the remainder is 4 and when you divide by 6, the remainder is 5.
a) 49
b) 59
c) 69
d) 79

Answer 40

B

Question 41

Which explains why the spherical triangle with angles 800, 1700 𝑎𝑛𝑑 1000 is not possible?
a) Sum of three angles must be more than 540 degrees
b) Sum of three angles must be less than 360 degrees
c) Sum of two angles less than the third must be less than 180 degrees
d) Sum of three angles must be 180 degrees or less

Answer 41

C

Question 42

The sun was observed in the eastern sky from Manila (1210𝐸, 140𝑁). By using a sextant, it was found that the sun has a declination of 500𝑁. If the altitude of the sun is 400, find the local apparent time.
a) 9:09
b) 11:12
c) 10.36
d) 2.51

Answer 42

A

Question 43

One side of a regular octagon is 2. Find the area of the region inside the octagon.
a) 19.3
b) 21.4
c) 13.9
d) 31.0

Answer 43

A

Question 44

The area of a regular polygon inscribed in a circle is to the area of the circumscribed regular polygon of the same number of sides as 7.5 is to 10. What is the regular polygon?
a) Octagon
b) Heptagon
c) Hexagon
d) Pentagon

Answer 44

C

Question 45

A rectangle ABCD which measures 18 by 24units is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.
a) 45/2
b) 2
c) 7/2
d) 54/2

Answer 45

A

Question 46

A man rowing upstream drop his hat at a point A. Thirty minutes later at B, he notices its lost and rows back at the same rate with respect to still water, picking up the hat at C, one fourth of a mile below
A. Determine how long the hat was in the water?
a) 0.5hr
b) 1hr
c) 1.5hrs
d) 2hrs

Answer 46

B

Question 47

𝐼𝑓 𝑠𝑖𝑛3𝐴 = cos 6𝐵, then which of the following expression is correct?
a) A + B = 90
b) A + 2B = 30
c) A + B = 180
d) A + B = 270

Answer 47

B

Question 48

In a purse are nickels, dimes and quarters amounting to $9.85. There are twice as many dimes as quarters, and the number of nickels is two more than twice the number of dimes. Determine the number of nickels.
a) 16
b) 34
c) 54
d) 62

Answer 48

D

Question 49

An open-air auditorium is so designed with partial conical roof top extending to the ground as shown. The width of the base of the 45 degrees parabolic opening is 20m. The radius of the circular base is 12m. If an elevated concrete platform is constructed 1.5m above the ground, determine the floor area of the platform.
a. 346.36 sq.m
b. 276.47 sq.m
c. 46.99 sq.m
d. 69.89 sq.m

Answer 49

B

Question 50

Points A, B and C has elevations of 30m, 33m and 27m, respectively Point B is between A and C and is 160m from A and 90m from C. Find the elevation of the highest point of the parabolic curve formed by joining the three points A, B and C.
a. 33.94m
b. 23.94m
c. 43.94m
d. 53.94m

Answer 50

A

Question 51

A satellite orbits around the earth in an elliptical path of eccentricity 0.60 and semi-minor axis length of 12000 miles. If the center of the earth is at one of the foci, find the maximum altitude of the satellite
a. 15000miles
b. 9000miles
c. 24000miles
d. 12000miles

Answer 51

C

Question 52

An earth satellite has an apogee of 2450 miles and perigee of 410 miles. Assuming that the Earth’s radius is 400miles, what is the value of the eccentricity of ellipse which is form with the center of the earth at one focus and whose apogee and perigee satisfy the condition above?
a. 0.247
b. 0.367
c. 0.447
d. 0.557

Answer 52

D

Question 53

A conical vessel 6m across the top and 4m deep is filled with water. A portion was spilled by slanting it to the position where one of its slant side is in y-axis. Determine the volume spilled.
a. 37.70m^3
b. 32.11m^3
c. 26.87m^3
d. 28.92m^3

Answer 53

B

Question 54

An arch in the form of a semi-ellipse has a span of 60m and its greatest height is 15m. There are two vertical supports equidistant from each other and the ends of the arc. Find the height of the supports.
a. 5 sqrt of 2
b. 10 sqrt of 2
c. 6 sqrt of 2
d. 3 sqrt of 2

Answer 54

B

Question 55

Find the equation of the line normal to the tangent at (4,0) on the curve x^2 + 16y = 32 - 4x - y^2
a. 4x - 3y = 16
b. 3x - 4y = 16
c. 2x - 5y = 23
d. 5x - 2y = 23

Answer 55

A

Question 56

Find the equation of the circle inscribed in the triangle whose sides are 4x + 3y - 21 = 0; 3x - 4y - 22 = 0 and x + 6 = 0
a. x^2 + y^2 + 2x - 24 = 0
b. x^2 + y^2 + 4x + 6y - 20 = 0
c. x^2 + y^2 - 3x - 6y + 16 = 0
d. x^2 + y^2 = 5^2

Answer 56

A

Question 57

Find the area bounded by the equation (x/5) + (y/2) = 1 on the first quadrant and line x = 10
a. 20 sq units
b. 30 sq units
c. 40 sq units
d. 50 sq units

Answer 57

C

Question 58

Find the bisectors of the angles between the lines x + 7y = 8 and x - y = 10
a. 2x + 6y + 21 = 0
b. 2x - 6y + 21 = 0
c. 2x + 6y - 21 = 0
d. 2x - 6y - 21 = 0

Answer 58

D

Question 59

Find the area bounded by the lines x - 2y - 2 = 0 and 3x - y - 11 = 0
a. 2 sq units
b. 3 sq units
c. 4 sq units
d. 5 sq units

Answer 59

D

Question 60

An arch in the form of a parabolic curve with a vertical axis is 60m across the bottom. The highest point is 16m above the horizontal base. What is the length of the beam placed horizontally across the arch 3m below the top?
a. 22m
b. 24m
c. 26m
d. 28m

Answer 60

C

Question 61

A line perpendicular to a plane
a. is perpendicular to only two intersecting lines in the plane
b. makes a right angle with every line in the plane which passes through its foot
c. is perpendicular to every line in the plane
d. makes a right angle with every line in the plane

Answer 61

B

Question 62

In the story about the crow that wanted to drink water form a cylindrical can but could not reach the water. It is said that the crow dropped a pebble which was a perfect sphere 3cm in radius into the can. If the can was 6cm radius, what was the rise in water level inside the cylindrical can after the pebble was dropped?
a. 2cm
b. 1cm
c. 3cm
d. 2.5cm

Answer 62

B

Question 63

The area of three adjacent surfaces of a rectangular block are 8sq.cm, 10sq.cm and 20sq.cm. The volume of the rectangular block is
a. 200cc
b. 40cc
c. 10cc
d. 20cc

Answer 63

B

Question 64

Four grapefruits (considered spheres) 6cm in diameter were placed in a square box whose inside base diameter are 12cm by 12cm. In the space between the first four grapefruit, a fifth of the same diameter was then placed on top of them. How deep must the box be so that the top will just touch the fifth grapefruit?
a. 10.24cm
b. 12.24cm
c. 15.24cm
d. 11.24cm

Answer 64

A

Question 65

A spherical ball of radius 3cm was dropped into a conical vessel of depth 8cm and radius of base 6cm. What is the area of the portion of the sphere which lies above the circle of contact with the cone?
a. 25.48 cm^2
b. 90.48cm^2
c. 80.48cm^2
d. 75.48cm^2

Answer 65

B

Question 66

Find the volume of the solid common to two cylinders intersecting at 90* angle if radius of cylinders are both 3cm.
a. 125cc
b. 135cc
c. 144cc
d. 154cc

Answer 66

C

Question 67

What is the distance in cm between two vertices of a cube which are farthest from each other, if an edge measures 8cm?
a. 12.32cm
b. 13.86cm
c. 8.66cm
d. 6.93cm

Answer 67

B

Question 68

A metal washer 1 inch in diameter is pierced by 1/2 inch hole. What is the volume of the washer if it is 1/8 inch thick?
a. 0.082
b. 0.047
c. 0.074
d. 0.028

Answer 68

C

Question 69

A group of children playing with marbles placed 50 pieces of the marbles inside a cylindrical container with water filled to a height of 20cm. If the diameter of each marble is 1.5cm and that of the cylindrical container 6cm, what would be the new height of water inside the cylindrical container after the marbles were placed inside?
a. 56.456cm
b. 65.345cm
c. 23.125cm
d. 45.657cm

Answer 69

C

Question 70

A horizontal cylindrical tank with hemispherical ends is to be filled with water to a height of 762mm. If the inside diameter of the cylinder is 1016mm and the total inside length of the cylinder is 3600mm, find the volume of water in cubic meters, that will be filled into the tank up to the required height.
a. 2.81
b. 1.55
c. 67.23
d. 123.6

Answer 70

A

Question 71

A conoid is a solid having a circular base that every plane section perpendicular to the diameter of the base is an isosceles triangle. Find the volume of the conoid having a radius of 2m and an altitude of the isosceles triangle is 4
a. 8pi
b. 4pi
c. 16pi
d. 12pi

Answer 71

A

Question 72

A frustum of a sphere has base diameters of 20cm and 12cm and thickness of 3.6cm. What is the volume of the frustum?
a. 744.6cc
b. 793.5cc
c. 752.9cc
d. 789.5cc

Answer 72

B

Question 73

The cross section of a semi-elliptical trough has a top diameter of 18 inches and a height of 12 inches. Determine the width oif water surface in the trough if the depth of water is 8inches.
a. 15.91in
b. 14.35 in
c. 15.28in
d. 16.97in

Answer 73

D

Question 74

Given x = ( y^3/3) + y, find dx/dy
a. 3y^2 + 1
b. y^2 + 3
c. y^2 - 1
d. y^2 + 1

Answer 74

D

Question 75

Find dy/dx of the function y = (x^6 - 2x3 - 3)/x^2
a. y’ = (4+3x^2)/(4-3x^2)^2
b. y’ = (2/3)x^(-1/3) - x^(-2/3)
c. y’ = (3/x^2)(2/x + 1)
d. y’ = 4x^3 + (6/x^3) - 2

Answer 75

D

Question 76

Find the inflection point to the right of the y-axis of the curve defined by the y = (x^2)/2 + (1/2)sin2x
a. (pi/6 , 0.234)
b. (pi/12 , 0.284)
c. (7pi/12 , 0.75)
d. (pi/4 , 0.4)

Answer 76

B

Question 77

Find the radius of curvature of the curve 4x^2-y^2 = 0 at point (1.2)
a. 1.56
b. 7.32
c. 4.556
d. 5.675

Answer 77

D

Question 78

Find the first derivative of the function y = sec(x^2 + 2)
a. 2xsec(x^2 + 2) tan(x^2 + 2)
b. 2xsin(x^2 + 3) tan (x^2 + 4)
c. 4xcos(x^2 + 3 ) csc (x^2 + 2)
d. 6xsec(5x^2 + 2) cot (5x^2 + 2)

Answer 78

A

Question 79

A right circular cylinder has base radius of 4 cm and height of 12 cm. Find the approximate increase in volume of the cylinder if the radius is increased by 0.2 cm and the height by 0.3
a. 24pi
b. 36pi
c. 12pi
d. 8pi

Answer 79

A

Question 80

A rectangular parallelepiped is measured with 5cm length, 3cm width and 2cm thickness. If there were errors in measurements of 0.01cm, 0.002cm and 0.001cm, respectively. What is the percentage error in computed volume?
a. 0.023
b. 0.056
c. 0.0032
d. 0.0025

Answer 80

C

Question 81

Find the 7th derivative of x^7
a. 5040
b. 5040x
c. 7x^7
d. 0

Answer 81

A

Question 82

Find the 3rd derivative of ln x
a. -1/x^2
b. 1/x^4
c. 2/x^3
d. 0

Answer 82

C

Question 83

Find the 6th derivative of sinx
a. -cosx
b. cosx
c. sin(^3)x
d. -sinx

Answer 83

D

Question 84

A rectangular shape is inscribed in the segment cut from the parabola y^2 = 4x by the line x=3, one side of the rectangle lying on the line. Find the dimensions of the rectangle of maximum area.
a. 2 by 4
b. 3 by 6
c. 1.5 by 3
d. 4 by 8

Answer 84

A

Question 85

Find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2
a. 26.678
b. 32
c. 25
d. 30

Answer 85

B

Question 86

Two parabolas x^2 = 8y and x^2+4y = 16 intersects at each other, determine the area bounded by these two curves?
a. 12.56
b. 17.42
c. 19.23
d. 18.89

Answer 86

B

Question 87

What is the area confined by the curve y^2 = 8x and x^2 = 8y?
a. 27.333
b. 25.333
c. 29.333
d. 21.333

Answer 87

D

Question 88

Compute the total area constrained by the trigonometric function y = sinx and x-axis at the interval 0<x<2pi
a. 2
b. 4
c. 8
d. 3

Answer 88

B

Question 89

Compute the area bounded by the equilateral hyperbola xy=8, the line x=5 , y = 5x and y = 0
a. 12
b. 15
c. 6
d. 26

Answer 89

B

Question 90

A spherical ball of radius 2m is carefully lowered into a right circular cone full of water. Find the altitude of the cone of minimum volume in which the ball may barely be submerged.
a. 8
b. 9
c. 10
d. 7

Answer 90

A

Question 91

Find the radius of the base and altitude of a right circular cone of maximum volume that could be inscrived in a sphere of radius 10m
a. 6.43
b. 9.43
c. 6.34
d. 9.34

Answer 91

B

Question 92

Determine the radius and altitude of a right circular cone of minimum volume that can be circumscribed a sphere having a radius of 6m
a. 8.115
b. 8.345
c. 8.485
d. 8.568

Answer 92

C

Question 93

A sector is cut out of a circular disk of radius sqrt 3 and the remaining part of the disk is bent up so that the two edges join and the cone is formed/ What is the largest volume for the cone?
a. pi/3
b. 2pi/3
c. 3pi/3
d. 4pi/3

Answer 93

B

Question 94

A light is to be placed directly above the center of the circular plot of radius 30m, at such a height that the edge of the plot will get the maximum illumination. Find the height if the intensity at any point on the edge is directly proportional to the cosine of the angle of coincidence, (angle between the ray of light and the vertical and inversely proportional to the square of the distance from the source.
a. 15 sqrt5
b. 15 sqrt3
c. 14 sqrt2
d. 15 sqrt2

Answer 94

D

Question 95

A witness to a hit and run accident told the police that the license plate number contained letters VIB followed by three digits, the first of which was a five. If the witness cannot recall the last two digits, but is certain that all three digits are different, find the number of automobile registration that the police may have to check
a. 72
b. 15
c. 45
d. 10

Answer 95

A

Question 96

Four married couples have bought 8 seats in a row for a concert. In how many way can they be seated if all men sit together to the right side of all the women?
a. 40320
b. 384
c. 576
d. 70

Answer 96

C

Question 97

You know that the extension of a private telephone number is 343 but you have forgotten the last 4 digits. You can only recall that the last 4 digits are 3,6,8 and 9, but you do not know the order. What is the maximum number of telephone calls you will need to make in order to dial the correct number?
a. 35
b. 210
c. 126
d. 24

Answer 97

D

Question 98

A drug for the relied of asthma can be purchased from 5 manufacturers in liquid, tablet or capsule form, all of which come in regular and extra strength. In how many different ways can a doctor prescribe the drug for a patient suffering from asthma?
a. 5
b. 20
c. 30
d. 120

Answer 98

C

Question 99

A restaurant offers a dinner salad for 150 pesos. There is a choice of a lettuce salad or spinach salad. Then there is a choice of one topping from mushrooms, beans or cheese. Finally, there is a choice of dressing from ranch style or oil and vinegar. how many different salad combinations are possible?
a. 12
b. 8
c. 150
d. 2

Answer 99

A

Question 100

Kathy can choose gray or blue jeans, a navy, white, green or striped shirt and running shoes, boots or penny loafers. How many outfits can she form?
a. 24
b. 9
c, 3
d. 84

Answer 100

A

Question 101

A certain show comes in different styles with each style available in 4 distinct colors. If the store wishes to display pairs of these shoes showing all of each various styles and colors. How may different pairs would the store have on display?
a. 6
b. 4
c. 20
d. 16

Answer 101

C

Question 102

Police use photographs of various facial features to help, witnesses to identify the suspects. One basic identification kit contains 195 hairline, and the eyes and eyebrows of a suspect. How many different faces can be produced with this information?
a. 691532
b. 13349986650
c. 19305
d. 43071

Answer 102

A

Question 103

Calculate the probability of randomly guessing at least 7 correct answers on a 10 question true or false quiz to get a passing grade.
a. 0.172
b. 0.7
c. 0.467
d. 0.509

Answer 103

A

Question 104

In 2015, about 1 in 43 births resulted in twins. if a barangay has 2150 births that year. Find the probability that between 29 and 50 of them were twins?
a. 0.0135
b. 0.4987
c. 0.023
d. 0.037

Answer 104

B

Question 105

Health officials from COH who have studied a COVID-19 virus say that 50% of all the Filipino people have had a virus. If a random sample of 144 people is taken. What is the chances that fewer than 60 has the COVID-19 virus?
a. 0.023
b. 0.5
c. 0.417
d. 0.0833

Answer 105

A

Question 106

SM Megamall in EDSA provides guarantees of its products for 7 days. If not completely satisfied, a customer can return the product within that period and get a full refund. According to past records of the mall, an average of 2 of every 10 products sold by the mall are returned for a refund. find the probability that exactly 6 of the 40 products sold by this mall on a given day will be returned for a refund.
a. 0.1246
b. 0.15
c. 0.2
d. 0.1221

Answer 106

D

Question 107

The length of time (in hours) that a Civil Engineering student spend to study each week was the subject matter. it was found that the mean is 10.5 hours and the standard deviation is 4.3 hours. A random sample of 50 students were selected. Determine the probability that their mean weekly study time exceeds more than 11 hours.
a. 0.608
b. 0.79457
c. 0.20543
d. 0.95455

Answer 107

C

Question 108

A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encourage by this result, the company decided to market the new hamburger. Assume that 70% of all people like this hamburger. On a certain day, 8 customers bought it. Find the probability that exactly three of the eight customers will like this hamburger.
a. 0.375
b. 0.0467
c. 0.2625
d. 0.2541

Answer 108

B

Question 109

Sixty three percent of children which live with unmarried mothers live in poverty. Two children who live with unmarried mothers are selected at random at it is observed whether or not they live in poverty. Find the probability that in this sample of two children.
a. 0.63
b. 0.7938
c. 0.233
d. 0.603

Answer 109

D

Question 110

A survey conducted about job satisfaction showed that 20% of workers are not happy with the current jobs. Assume that this result is true for the population of all workers. Two workers are selected at random and it is observed whether or not they are happy with their current jobs. Find the probability that in this sample of two worker, at least one of them is happy with the current job.
a. 0.80
b. 0.20
c. 0.24
d. 0.64

Answer 110

D

Question 111

Three cards are drawn in succession without replacement from an ordinary deck of 52 playing cards. Find the probability that the event A and B occurs where A is the event that the first card is red Ace, B is the event that the 2nd card is a 10 or a Jack and C is the even that the third card is greater than 3 but less than 7
a. 0.001448
b. 0.4353
c. 0.07611
d. 0.24603

Answer 111

A

Question 112

In a cup there are 4 quarters, 5 dimes, 6 nickels and 10 pennies. if one coin is selected at random, what is the probability that the coin has a letter “n” in its name?
a. 0.096
b. 1
c. 0.00694
d. 0.64

Answer 112

D

Question 113

A dart target board consists of a center circle having a radius of 2 inches, a square section with dimension of 6in x 6in and the radius of the biggest circle is 6in. The three cross sections have the same center at 0. Assuming the dart is equally like to hit any point inside the target. Find the probabiity that a dart thrown at the circular target will hit outside the square.
a. 0.111
b. 0.207
c. 0.682
d. 0.571

Answer 113

C

Question 114

For a carnival game, Jhon is painting two circle V and M on a square dartboard. V is represented by the equation x^2 + y^2 = 25 and the circle M represented by the equation (x-8)^2 + (y+6)^2 = 4. A point (x,y) is randomly selected such that -10 < x < 10 and -10 < y < 10. What is the probability that point (x,y) lies outside both circle V and M?
a. 0.0889
b. 0.772
c. 0.804
d. 0.2278

Answer 114

B

Question 115

With 50 examination questions each of which has 4 given answers how many possible answer patterns are there?
a. 5527200
b. 6250000
c. 230300
d. 1.26x10^30

Answer 115

D

Question 116

In certain songs cannot be sung one after the other. How many ways are possible?
a. 120
b. 7
c. 72
d. 48

Answer 116

C

Question 117

With a throw of 3 dice, what is the probability of getting 9 or an 11?
a. 0.241
b. 0.6944
c. 0.1389
d. 0.023

Answer 117

A

Question 118

In a poker hand consisting of 5 cards, what is the probability of holding 2 aces and 2 kings?
a. 33/54145
b. 3/216580
c. 36/270725
d. 5/519792

Answer 118

A

Question 119

A small ball is dropped into the top of the maze and tumbles to the bottom. Each time the ball strikes an obstacle, there is a 50% chance that the ball will move to the left. What is the probability that the ball ends up in the middle of the slot?
a. 1/6
b. 1/5
c. 1/16
d. 3/8

Answer 119

D