12.188. two planes leave manila for a southern city, a distance of 900km. Plane A 12.188. travels at a ground speed of 90kph faster than the plane B. plane A arrives in their destination 2 hours and 15minutes ahead of plane B. what is the ground speed of plane A? A. 205kph B. 315kph C. 240kph D. 287kph 15.196. a man left his home at past 3:00 o’clock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hands of the clock interchanged. At what time did the man leave his home? A. 3:31:47 B. 3:21:45 C.3:46:10 D. 3:36:50 51.285. there are 5 main roads between the cities A & B, and 4 between B & C. in how 51.285. many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice? A. 260 B. 240 C. 120 D. 160 76.315. find the sum 76.315. inscribed in a circle A. 150
of
the
interior
B. 160
angles
of
the
vertices
of
a
C. 170
5
pointed
star
D. 180
93.380. a regular octahedron has an edge 2m. find its volume (in m3) 93.380. A. 3.77 B. 1.88 C. 3.22
D. 2.44
118.530. point P(x,y) moves with a distance from point (0,1) one-half of its distance 118.530. from line y=4. The equation of its locus is A. 2x2-4y2=5 B. 4x2+3y2=12 C. 2x2+5y3=3 D. x2+2y2 =4 121.533. find the major axis of the ellipse x2+4y2-2x-8y+1=0 121.533. A. 2 B. 10 C. 4 122.534. the length of 122.534. A. 2
D. 6
the latus rectum for the ellipse x2/64 + y2/16 =1 is equal to: B. 3 C. 4 D. 5
123.535. an ellipse with an eccentricity of 0.65 and has one of its foci 2 units from 123.535. the center. The length of the latus rectum is nearest to A. 3.5 units B. 3.8 units C. 4.2 units D. 3.2 units 124.536. an earth satellite has an apogee of 40,000km and a perigee of 6,600km. 124.536. assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci? A. 0.46 B. 0.49 C. 0.52 D. 0.56 125.537. the major axis of the elliptical path in which the earth moves around the sun 125.537. is approximately 186,000,000 miles and the eccentricity is 1/60 determine the apogee of the earth. A. 93x10^6 miles B. 91.45x10^6 miles C. 94.3351x10^6 miles D. 94.55x10^6 127.539. an ellipse with center at the origin has a length of major axis 20units. If 127.539. the distance from the center of the ellipse to its focus is 5, what is the equation of its directix? A. x= 18 B. x= 20 C. x=15 D. x=16 130.543. how far from the x-axis is the focus F of the hyperbola x2-2y2+4x+4y+4=0? 130.543. A. 4.5 B. 3.4 C. 2.7 D. 2.1 132.545. what is the equation of the asymptote of the hyperbola x2/9 – y2/4 =1? 132.545. A. 2x-3y=0 B. 3x-2y=0 C. 2x-y=0 D. 2x+y=0 133.546. find the equation of the hyperbola whose asymptotes are y= +-2x and which 133.546. passes through (5/2,3) A. 4x2+y2+16=0 B. 4x2+y2-16=0 C. x2-4y2-16=0 D. 4x2-y2=16
134.547. find the equation of the hyperbola with the vertices at (-4,2) and (0,2) and foci at (-5,2) and (1,2) A. 5x2-4y2+20x+16y-16=0B.5x2-4y2+20x-16y-16=0C.5x2-4y2-20x+16y+16=0D.5x2+4y2-20x+16y-16=0 136.552. find the polar equation of the circle, if its center at(4,0) and the radius 4. A. r-8cosϴ=0 B. r-6cosϴ=0 C. r-12cosϴ=0 D. r-4cosϴ=0 137.554. find the polar equation of radius 3 units and center at (3,0) A. r-3cosϴ=0 B. r-3sinϴ=0 C. r-6cosϴ=0
D. r-9sinϴ=0
140.595. find the radius of curvature at any point in the curve y+lncosx = 0 A. cosx B. 1.5707 C. secx D. 1 149.668. find the area of the curve r2= a2cos2ϴ A. a B. 2a C. a2
D. a3
150.670. find the coordinates of the centroid of the plane bounded by the parabola y= 4-x2 and the x-axis A. 0,1 B. 0,1.6 C. 0,2 D. 1,0 151.671. locate the centroid of the plane area bounded by the equation y2=4x, x=1 and the x-axis on the first quadrant A. ¾, 3/5 B. 3/5, 3/4 C. 3/5, 3/5 D. 3/5, 2/3 152.672. find the length of the arc of the parabola x2= 4y from x=-2 to x=2 A. 4.2 units B. 4.6 C. 4.9 D. 5.2 153.673. find the surface area generated by rotating the parabola arc y=x2 about the x-axis from x=0 to x=1 A. 5.33 B. 4.98 C. 5.73 D. 4.73 154.674. the area enclosed by the ellipse x2/9 + y2/4 =1 is revolved about the line x=3. What is the volume generated? A. 355.3 B. 360.1 C. 370.3 D. 365.1 155.675. the area in the 2nd quadrant of the circle x2+y2= 36 is revolved about the line y+10 =0. What is the volume generated? A. 2218.33 B. 2228.83 C. 2233.43 D. 2208.53 156.676. the area bounded by the curve y2= 12x and the line x=3 is revolved about the line x=3. What is the volume generated? A. 179 B. 181 C. 183 D. 185 157.677. given the area in the first quadrant bounded by x2=8y, the line y-2=0 and the y-axis. What is the volume generated when the area is revolved about the line y-2=0? A. 28.41 B. 27.32 C. 25.83 D. 26.81 158.678. find the volume generated by rotating a circle x2+y2+6x+4y+12=0 about the yaxis A. 39.48 B. 47.23 C. 59.22 D. 62.11 159.679. given the area in the first quadrant by x 2=8y, the line x=4 and the x-axis. What is the volume generated by revolving this area about the y-axis A. 53.26 B. 52.26 C. 51.26 D. 50.26 160.680. find the moment if inertia, with respect to x-axis of the area bounded by the parabola y2= 4x and the line x=1 A. 2.03 B. 2.13 C. 2.33 D. 2.53 162.688. solve (cos(x)cos(y)- cot(x))dx –sin(x)sin(y)dy= 0 A.sinxcosy= ln(c cosx)B.sinxcosy= ln(csinx)C.sinxcosy=-ln(csinx)D.sinxcosy=-ln(c cosx)
163.691. solve (y- (x2+ y2)1/2) dx –xdy =0 A. (x2+ y2)1/2 + y= C B. (x2+ y2 +y)1/2= C
C. (x+ y)1/2+y= C
171.739. evaluate the determinant 2 14 3 1 1 5 -1 3 1 -2 2 -3 3 -4 -3 -4 A. 489 B. 389
C. 326
D. 452
172.755. the laplace transform of coswt is A. s/s2+ w2 B. w/s2+w2
C. w/s+w
D. s/s+w
D. (x2- y)1/2+ y=C
182.790. a tennis ball moving horizontally to the left at 40m/s hits a racket and rebounds horizontally to the right at 30m/s. if the mass of the ball is 100g, find the impulse of the force (in kg-m/s) exerted on the ball by the racket A. 1 B. -1 C. 7 D. 12 184.792. a 50g mass hangs at the end of the spring. When 20g more are added to the end of the spring, it stretches 7cm more. Find the spring constant. A. 2.8 B. 2.9 C. 4.3 D. 2.5 188.796. a hollow cylinder 1m in diameter and 2m high weighs 3825N. how many kN of lead weighing 110kN/m3 must be fastened to the outside bottom of the cylinder to make it float with 1.5m submerged in water? A. 8.5kN B. 6.5 C. 10.5 D. 9.5 196.819. at what angle does the force F= 6.23i-2.38j+4.92k N makes A. 39.2 B. 40.2 C. 41.3
with the x-axis? D. 42.2
198.841. an automobile moving at a constant velocity of a 15m/s passes a gasoline station. 2 seconds later, another automobile leaves the gasoline station and accelerates at a constant rate of 2m/s 2. How soon will the second automobile overtake the first? A. 15.3s B. 16.8 C. 13.5 D. 18.6 202.859. a stone is thrown upward at an angle measured horizontally and 2m below measured Determine the initial velocity of the stone in A. 22.35 B. 23.35
of 30 with the horizontal. It lands 60m vertically from its point of release. m/s C. 24.35 D. 25.35
203.860. a wooden block having a weight of 50N is placed at a distance of 1.5m from the center of a circular platform rotating at a speed of 2radians per second. Determine the minimum coefficient of friction of the blocks so that it will not slide. Radius of the circular platform is 1.5m A. 0.55 B. 0.58 C. 0.61 D. 0.65 212.869. a hi-way curve has a super elevation of 7degrees. What is the radius of the curve such that there will be no lateral pressure between the tires and the roadway at a speed of 40mph? A. 265.71m B. 438.34 C. 345.34 D. 330.78 213.870. traffic travels at 65mi/hr around a banked highway curve with a radius of 3000ft. what banking angle is necessary such that friction will not be required to resist the centrifugal force? A. 3.2 B. 2.5 C. 5.4 D. 18 214.871. determine the angle of the super elevation for a 200m hi-way curve so that there will be no side thrust at a speed of 90kph A. 19.17 B. 17.67 C.18.32 D. 20.11
215.873. a cyclist on a circular track of radius r= 800 ft is travelling at 27fps. His speed in the tangential direction increases at the rate of 3fps2. what is the cyclist total acceleration? A. 2.8 fps2 B. 3.1 C. 3.8 D. 4.2 216.874. a concrete hi-way curve with a radius of 500ft is banked to give lateral pressure equivalent to f= 0.15. for what coefficient of friction will skidding impend for a speed of 60mph? A. μ > 0.36
B. μ < 0.31
C. μ > 0.31
D. μ < 0.36
218.876. a car weighing 40tons is switched to a 2% upgrade with a velocity of 30mph. if the train resistance is 10lb/ton, how far up the grade will it go? A. 1124ft on slope B. 2014ft C. 1204ft D. 1402ft 221.879. a body weighing 40 lbs starts from rest and slides down a plane at an angle of 30 with the horizontal for which the coefficient of friction μ= 0.3. how far will it move during the third second? A. 19.63ft B. 19.33 C. 18.33 D. 19.99 223.881. an iron column of annular cross section has an outer diameter of 200mm and is subjected to a force of 74kN. Find the thickness of the wall if the allowable compressive stress is 10MPa. A. 12.75mm B. 12.57 C. 17.75 D. 15.75 230.894. a solid shaft 48.2cm long is used for a transmission of mechanical power at rate of 37kW running at 1760rpm. The stress is 8.13MPa. Calculate the diameter A. 30mm B. 35 C. 40 D. 50 232.896. a 2 inch solid shaft is driven by a 36inch gear and transmits power at 120rpm. If the allowable shearing stress is 12ksi, what horsepower can be transmitted? A. 29.89 B. 35.89 C. 38.89 D. 34.89 233.897. a hollow shaft has an inner diameter of 0.035m and an outer diameter of 0.06m. compute for the torque in N-m, if the stress is not to exceed 120MPa A. 4500 B. 4100 C. 4300 D. 4150 234.898. compute the nominal shear stress at the surface in MPa for a 40mm diameter shaft that transmits 750kW at 1500rpm. Axial and bending loads are assumed negligible. A. 218 B. 312 C. 232 D. 380 237.907. a simple beam 10m long carries a concentrated load of 200kN at the midspan. What is the maximum moment of the beam? A. 250kN-m B. 500 C. 400 D. 100 238.909.a simply supported beam, 10m long carries uniformly distributed load 20kN/m. what is the value of maximum shear of the beam due to this load? A. 250kN B. 100 C. 1000 D. 500
of
239.910. a simply supported beam, 10m long carries uniformly distributed load 20kN/m. what is the value of maximum moment of the beam due to this load? A. 10000kN-m B. 5000 C. 2000 D. 250
of
