This is the Uncategorized Multiples Choice Questions Part 9 of the Series in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize each and every questions compiled here taken from various sources including past Board Exam Questions, Engineering Mathematics Books, Journals and other Engineering Mathematics References. In the actual board, you have to answer 100 items in Engineering Mathematics within 5 hours. You have to get at least 70% to pass the subject. Engineering Mathematics is 20% of the total 100% Board Rating along with Electronic Systems and Technologies (30%), General Engineering and Applied Sciences (20%) and Electronics Engineering (30%).

### The Series

Following is the list of multiple choice questions in this brand new series:

**Engineering Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART 2**

**MCQs from Number 101 – 150**Answer key:

**PART 3**

**MCQs from Number 151 – 200**Answer key:

**PART 4**

**MCQs from Number 201 – 250**Answer key:

**PART 5**

**MCQs from Number 251 – 300**Answer key:

**PART 6**

**MCQs from Number 301 – 350**Answer key:

**PART 7**

**MCQs from Number 351 – 400**Answer key:

**PART 8**

**MCQs from Number 401 – 450**Answer key:

**PART 9**

**MCQs from Number 451 – 500**Answer key:

**PART 10**

### Continue Part IX of the Series

**Choose the letter of the best answer in each questions.**

401. A circular water main 4 meter in diameter. is closed by a bulkhead whose center is 40 m below the surface of the water in the reservoir. Find the force on the bulkhead.

- a. 3419 kN
- b. 4319 kN
- c. 4931 kN
- d. 5028 kN

402. A plate in the form of parabolic segment is 12 m in height and 4m deep and is partly submerged in water so that its axis is parallel to end 3 m below the water surface. Find the force acting on the plate.

- a. 899.21 kN
- b. 939.46 kN
- c. 933.17 kN
- d. 993.26 kN

403. A cistern in the form of an inverted right circular cone is 20 m deep and 12 m diameter at the top. If the water is 16 m deep in the cistern, find the work done in Joules in pumping out the water. The water is raised to a point of discharge 10 m above the top cistern.

- a. 54883992 Joules
- b. 61772263 Joules
- c. 68166750 Joules
- d. 76177640 Joules

404. A bag containing originally 60 kg of flour is lifted through a vertical distance of 9 m. While it is being lifted, flour is leaking from the bag at such rate that the number of pounds lost is proportional to the square root of the distance traversed. If the total loss of flour is 12 kg find the amount of work done in lifting the bag.

- a. 4290 Joules
- b. 4591 Joules
- c. 5338 Joules
- d. 6212 Joules

405. According to Hooke’s law, the force required to stretch a helical spring is proportional to the distance stretched. The natural length of a given spring is 8 cm. a force of 4 kg will stretch it to a total length of 10 cm. Find the work done in stretching it from its natural length to a total length of 16 cm.

- a. 4.65 Joules
- b. 5.32 Joules
- c. 6.28 Joules
- d. 7.17 Joules

406. The top of an elliptical conical reservoir is an ellipse with major axis 6m and minor axis 4m. it is 6m deep and full of water. Find the work done in pumping the water to an outlet at the top of the reservoir.

- a. 473725 Joules
- b. 493722 Joules
- c. 554742 Joules
- d. 593722 Joules

407. A bag of sand originally weighing 144 kg is lifted at a rate of 3m/min. the sand leaks out uniformly at such rate that half of the sand is lost when the bag has been lifted 18 m. find the work done in lifting the bag of sand at this distance.

- a. 6351 Joules
- b. 4591 Joules
- c. 5349 Joules
- d. 5017 Joules

408. A cylindrical tank having a radius of 2 m and a height of 8 m is filled with water at a depth of 6 m. Compute the work done in pumping all the liquid out of the top of the container.

- a. 2 934 942 Joules
- b. 3 698 283 Joules
- c. 4 233 946 Joules
- d. 5 163 948 Joules

409. A right cylindrical tank of radius 2 m and a height 8m is full of water. Find the work done in pumping the tank. Assume water to weigh 9810 N/m^3.

- a. 3945 kN . m
- b. 4136 kN . m
- c. 2846 kN . m
- d. 5237 kN . m

410. A conical vessel 12 m across the top and 15 m deep. If it contains water to a depth of 10 m find the work done in pumping the liquid to the top of the vessel.

- a. 12 327.5 kN . m
- b. 14 812.42 kN . m
- c. 24 216.2 kN . m
- d. 31 621 kN . m

411. A hemispherical vessel of diameter 8 m is full of water. Determine the work done in pumping out the top of the tank in Joules.

- a. 326 740 pi
- b. 627 840 pi
- c. 516 320 pi
- d. 418 640 pi

412. A spring with a natural length of 10 cm is stretched by 1/2 cm by a Newton force. Find the work done in stretching from 10 cm to 18 cm. Express your answer in joules.

- a. 6.29 Joules
- b. 7.13 Joules
- c. 7.68 Joules
- d. 8.38 Joules

413. A 5 lb. monkey is attached to a 20 ft. hanging rope that weighs 0.3 lb/ft. the monkey climbs the rope up to the top. How much work has it done?

- a. 160
- b. 165
- c. 170
- d. 180

414. A bucket weighing 10 Newton when empty is loaded with 90 Newton of sand and lifted at 10 cm at a constant speed. Sand leaks out of a hole in a bucket at a uniform rate and one third of sand is lost by the end of the lifting process in Joules.

- a. 800 Joules
- b. 850 Joules
- c. 900 Joules
- d. 950 Joules

415. A conical vessel is 12 m across the top and 15 m deep. If it contains water to a depth of 10m find the work done in pumping the liquid to a height 3m above the top of the vessel.

- a. 560 pi w N.m
- b. 660 pi w N.m
- c. 520 pi w N.m
- d. 580 pi w N.m

416. A small in the sack of rice cause some rice to be wasted while the sack is being lifted vertically to a height of 30 m. The weight lost is proportional to the cube root of distance traversed. If the total loss was 16 kg, find the work done in lifting the said sack of rice which weighs 110 kg.

- a. 2369 kg.m
- b. 2409 kg.m
- c. 2940 kg.m
- d. 3108 kg.m

417. A hemispherical tank of diameter 20 ft. is full of oil weighing 20 pcf. The oil is pumped to a height of 10 ft. above the top of the tank by an engine of 1/2 horsepower. How long will it take the engine to empty the tank?

- a. 1 hr. 15.47 min
- b. 1 hr. 24.27 min
- c. 1 hr. 44.72 min
- d. 2 hrs.

418. A full tank consists of a hemisphere of radius 4 m surmounted by a circular cylinder of the same radius of altitude 8 m. Find the work done in pumping the water to an outlet of the top of the tank.

- a. (2255/3) pi w
- b. (2527/3) pi w
- c. (2752/3) pi w
- d. (5722/3) pi w

419. Determine the differential equation of a family of lines passing thru (h, k).

- a. (y-k) dx – (x-h) dy = 0
- b. (x-h) + (y-k) = dy/dx
- c. (x-h) dx – (y-k) dy = 0
- d. (x+h) dx – (y-k) dy = 0

420. What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis

- a. 2x dy – y dx = 0
- b. x dy + y dx = 0
- c. 2y dx – x dy = 0
- d. dy/dx – x = 0

421. Find the differential equations of the family of lines passing through the origin.

- a. ydx – xdy = 0
- b. xdy – ydx = 0
- c. xdx + ydy = 0
- d. ydx + xdy = 0

422. The radius of the moon is 1080 miles. The gravitation acceleration of the moons surface is 0.165 miles the gravitational acceleration at the earth’s surface. What is the velocity of escape from the moon in miles per second?

- a. 2.38
- b. 1.47
- c. 3.52
- d. 4.26

423. Find the equation of the curve at every point of which the tangent line has a slope of 2x.

- a. x = -y^2 + C
- b. y = -x^2 + C
- c. x = y^2 + C
- d. y = x^2 + C

424. The radius of the earth is 3960 miles. If the gravitational acceleration of earth surface is 31.16 ft/sec^2, what is the velocity of escape from the earth in miles/sec?

- a. 3.9266
- b. 5.4244
- c. 6.9455
- d. 7.1842

425. Find the velocity of escape of the Apollo spaceship as it is projected from the earth’s surface that is the minimum velocity imparted to it so that it will never return. The radius of the earth is 400 miles and the acceleration of the spaceship is 32.2 ft/sec^2.

- a. 30426 kph
- b. 50236 kph
- c. 40478 kph
- d. 60426 kph

426. The rate of population growth of a country is proportional to the number of inhabitants. If a population of a country now is 40 million and expected to double in 25 years, in how many years is the population be 3 times the present?

- a. 39.62 yrs.
- b. 28.62 yrs.
- c. 18.64 yrs.
- d. 41.2 yrs.

427. From the given differential equation xdx + 6y^5dy = 0 solve for the constant of integration when x = 0, y = 2.

- a. 27x dx + 4y^2 dy = 0
- b. 58
- c. 48
- d. 64

428. Find the equation of the curve which passes through points (1, 4) and (0, 2) if d^2 y/ dx^2 = 1

- a. 2y = x^2 + 3x + 4
- b. 4y = 2x^2 + x + 4
- c. 5y = x^2 + 2x + 2
- d. 3y = x^2 + x + 4

429. The rate of population growth of a country is proportional to the number of inhabitants. If a population of a country now is 40 million and 50 million in 10 years time, what will be its population 20 years from now?

- a. 56.19
- b. 71.29
- c. 62.18
- d. 59.24

430. The Bureau of Census record in 1980 shows that the population in the country doubles compared to that of 1960. In what year will the population trebles assuming that the rate of increase in the population is proportional to the population?

- a. 34.60
- b. 31.70
- c. 45.65
- d. 38.45

431. A tank contains 200 liters of fresh water. Brine containing 2 kg/liter of salt enters the tank at the rate of 4 liters per min, and the mixture kept uniform by stirring, runs out at 3 liters per min. Find the amount of salt in the tank after 30 min.

- a. 196.99 kg
- b. 186.50 kg
- c. 312.69 kg
- d. 234.28 kg

432. In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at rate of 2 liters per minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of 1 hour?

- a. 20.50
- b. 18.63
- c. 19.53
- d. 22.40

433. Determine the general solution of xdy + ydx = 0.

- a. xy = c
- b. ln xy = c
- c. ln x + ln y = c
- d. x + y = c

434. The inverse laplace transform of s/[(square) + (w square)] is:

- a. sin wt
- b. w
- c. (e exponent wt)
- d. cos st

435. The laplace transform of cos wt is:

- a. s/[(square) + (w square)]
- b. w/[(square) + (w square)]
- c. w/s + w
- d. s/s + w

436. K divided by [(s square) + (k square)] is inverse laplace transform of:

- a. cos kt
- b. sin kt
- c. (e exponent Ky)
- d. 1.0

437. Find the inverse transform of [2/(s + 1)] – [(4/(s + 3)] is equal to:

- a. [2 e (exp – t) – 4e (exp – 3t)]
- b. [e (exp – 2t) + e (exp – 3t)]
- c. [e (exp – 2t) – e (exp - 3t)]
- d. [2e (exp – t) – 2e (exp - 2t)]

438. What is the laplace transform of e^(-4t)

- a. 1/ (s + 1)
- b. 1/ (s + 4)
- c. 1/ (s – 4)
- d. 1/ (s + t)

439. Determine the laplace transform of I(S) = 200 / [(s^2) + 50s + 10625]

- a. I(S) = 2e^(-25t) sin100t
- b. I(S) = 2te^(-25t) sin100t
- c. I(S) = 2e^(-25t) cos100t
- d. I(S) = 2te^(-25t) cos100t

440. Determine the inverse laplace transform of (s + a) / [(s + a) ^2 + w^2]

- a. e^(-at) cos wt
- b. te^(-at) cos wt
- c. t sin wt
- d. e^(-at) sin wt

441. Determine the inverse laplace transform of 100/ [(S + 10) (S + 20)]

- a. 10e^(-10t) + 20e^(-20t)
- b. 10e^(-10t) – 20e^(-20t)
- c. 10e^(-10t) – 10e^(-20t)
- d. 20e^(-10t) + 10e^(-20t)

442. A thin heavy uniform iron rod 16 m long is bent at the 10 m mark forming a right angle L – shaped piece 6 m by 10 m of bend. What angle does the 10 m side make with the vertical when the system is in equilibrium?

- a. 28° 12’
- b. 19° 48’
- c. 24° 36’
- d. 26° 14’

443. Three men carry a uniform timber. One takes hold at one end and the other two carry by means of a crossbar placed underneath. At what point of timber must the bar be placed so that each man may carry one third of the weight of the weight of the timber? The timber has a length of 12 m.

- a. 4m
- b. 5m
- c. 2.5 m
- d. 3m

444. A painters scaffold 30 m long and a mass of 300 kg, is supported in a horizontal position by a vertical ropes attached at equal distances from the ends of the scaffold. Find the greatest distance from the ends that the ropes may be attached so as to permit a 200 kg man to stand safely at one end of scaffold.

- a. 8m
- b. 7m
- c. 6m
- d. 9m

445. A cylindrical tank having a diameter of 16 cm weighing 100 kN is resting on a horizontal floor. A block having a height of 4 cm is placed on the side of the cylindrical tank to prevent it from rolling. What horizontal force must be applied at the top of the cylindrical tank so that it will start to roll over the block? Assume the block will not slide and is firmly attached to the horizontal floor.

- a. 57.74 kN
- b. 58.36 kN
- c. 68.36 kN
- d. 75.42 kN

446. Two identical sphere weighing 100 kN are each place in a container such that the lower sphere will be resting on a vertical wall and a horizontal wall and the other sphere will be resting on the lower sphere and a wall making an angle of 60 degrees with the horizontal. The line connecting the two centers of the spheres makes an angle of 30 degrees with the horizontal surface. Determine the reaction between the contact of the two spheres. Assume the walls to be frictionless.

- a. 150
- b. 120
- c. 180
- d. 100

447. The 5 m uniform steel beam has a mass of 600 kg and is to be lifted from the ring B with two chains, AB of length 3 m, and CB of length 4 m. Determine the tension T in chain AB when the beam is clear of the platform.

- a. 2.47 kN
- b. 3.68 kN
- c. 5.42 kN
- d. 4.52 kN

448. A man attempts to support a stack of books horizontally by applying a compressive force of F = 120 N to the ends of the stack with his hands, determine the number of books that can be supported in the stack if the coefficient of friction between any two books is 0.40.

- a. 15 books
- b. 20 books
- c. 10 books
- d. 12 books

449. Two men are just to lift a 300 kg weight of crowbar when the fulcrum for this lever is 0.3m from the weight and the man exerts their strengths at 0.9 m and 1.5 m respectively from the fulcrum. If the men interchange positions, they can raise a 340 kg weight. What force does each man exert?

- a. 25 kg, 40 kg
- b. 30 kg, 50 kg
- c. 35 kg, 45 kg
- d. 40 kg, 50 kg

450. A man exert a maximum pull of 1000 N but wishes to lift a new stone door for his cave weighing 20 000 N. if he uses lever how much closer must the fulcrum be to the stone than to his hand?

- a. 10 times nearer
- b. 20 times farther
- c. 10 times farther
- d. 20 times nearer

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