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MCQ in Calculus Part 4 | Mathematics Board Exam

MCQs in Calculus Part 4

This is the Multiple Choice Questions Part 4 of the Series in Calculus topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

  • MCQ in Complex Variables | MCQ in Derivatives and Applications | MCQ in Integration and Applications | MCQ in Transcendental Functions | MCQ in Partial Derivatives | MCQ in Indeterminate forms | MCQ in Multiple Integrals | MCQ in Differential Equations | MCQ in Maxima/Minima and Time Rates

Continue Practice Exam Test Questions Part 4 of the Series

MCQ in Calculus Part 3 | Mathematics Board Exam

Choose the letter of the best answer in each questions.

151. An object falls from rest in a medium offering a resistance. The velocity of the object before the object reaches the ground is given by the differential equation dV/dt + V/10 = 32 ft/sec. What is the velocity of the object one second after it falls?

A. 40.54

B. 38.65

C. 30.45

D. 34.12

View Answer:

Answer: Option C

Solution:

152. 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 a minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour?

A. 15.45 kg.

B. 19.53 kg.

C. 12.62 kg.

D. 20.62 kg.

View Answer:

Answer: Option B

Solution:

153. A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2 gpm. Find the amount of salt in the tank at the end of 30 minutes.

A. 171.24 lbs

B. 124.11 lbs

C. 143.25 lbs

D. 105.12 lbs

View Answer:

Answer: Option A

Solution:

154. If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuously compounded account?

A. P5,750

B. P6,750

C. P7,500

D. P6,350

View Answer:

Answer: Option B

Solution:

155. A nominal interest of 3% compounded continuously is given on the account. What is the accumulated amount of P10,000 after 10 years?

A. P13,620.10

B. P13,500.10

C. P13,650.20

D. P13,498.60

View Answer:

Answer: Option D

Solution:

156. Simplify the expression i1997 + i1999, where i is an imaginary number.

A. 0

B. –i

C. 1 + i

D. 1 – i

View Answer:

Answer: Option A

Solution:

157. Simplify: i^29 + i^21 + i

A. 3i

B. 1 – i

C. 1 + i

D. 2i

View Answer:

Answer: Option A

Solution:

158. Write in the form a + bi the expression i3217 – i427 + i18

A. 2i +1

B. –i +1

C. 2i – 1

D. 1 + i

View Answer:

Answer: Option C

Solution:

159. The expression 3 + 4i is a complex number. Compute its absolute value.

A. 4

B. 5

C. 6

D. 7

View Answer:

Answer: Option D

Solution:

160. Write the polar form of the vector 3 + j4.

A. 6 cis 53.1°

B. 10 cis 53.1°

C. 5 cis 53.1°

D. 8 cis 53.1°

View Answer:

Answer: Option C

Solution:

161. Evaluate the value of sqrt(-10) x sqrt(-7).

A. i

B. –sqrt(70)

C. sqrt(70)

D. sqrt(17)

View Answer:

Answer: Option B

Solution:

162. Simplify (3 – i)2 – 7(3 – i) + 10

A. – (3 + i)

B. 3 + i

C. 3 – i

D. – (3 – i)

View Answer:

Answer: Option D

Solution:

163. If A = 40 e(j120°), B = 2 cis -40°, C = 26.46 + j0, solve for A + B + C.

A. 27.7 cis 45°

B. 35.1 cis 45°

C. 30.8 cis 45°

D. 33.4 cis 45°

View Answer:

Answer: Option C

Solution:

164. What is 4i cube times 2i square?

A. -8i

B. 8i

C. -8

D. -8i2

View Answer:

Answer: Option B

Solution:

165. What is the simplified complex expression of (4.33 + j2.5) square?

A. 12.5 + j21.65

B. 20 + j20

C. 15 + j20

D. 21.65 + j12.5

View Answer:

Answer: Option A

Solution:

166. Find the value of (1 + i)5, where I is an imaginary number.

A. 1 – i

B. -4(1 + i)

C. 1 + i

D. 4(1 + i)

View Answer:

Answer: Option B

Solution:

167. Find the principal 5th root of [ 50(cos 150° + jsin 150°) ].

A. 1.9 + j1.1

B. 3.26 – j2.1

C. 2.87 + j2.1

D. 2.25 – j1.2

View Answer:

Answer: Option A

Solution:

168. What is the quotient when 4 + 8i is divided by i3?

A. 8 – 4i

B. 8 + 4i

C. -8 + 4i

D. -8 – 4i

View Answer:

Answer: Option C

Solution:

169. If A = -2 – 3i, and B = 3 + 4i, what is A/B?

A. (18 – i)/25

B. (-18 – i)/25

C. (-18 + i)/25

D. (18 + i)/25

View Answer:

Answer: Option B

Solution:

170. Rationalize (4 + 3i) / (2 – i).

A. 1 + 2i

B. (11 + 10i)/5

C. (5 + 2i)/5

D. 2 + 2i

View Answer:

Answer: Option A

Solution:

171. Simplify [(2 + 3i)(5 – i)] / [(3 – 2i)2].

A. (221 – 91i)/169

B. (21 + 52i)/13

C. (-7 + 17i)/13

D. (-90 + 220i)/169

View Answer:

Answer: Option C

Solution:

172. What is the simplified expression of the complex number (6 + j2.5)/(3 + j4)?

A. – 0.32 + j0.66

B. 1.12 – j0.66

C. 0.32 – j0.66

D. – 1.75 + j1.03

View Answer:

Answer: Option B

Solution:

173. Perform the operation: 4 (cos 60° + i sin 60°) divided by 2(cos 30° + i sin 30°) in rectangular coordinates.

A. square root of 3 – 2i

B. square root of 3 – i

C. square root of 3 + i

D. square root of 3 + 2i

View Answer:

Answer: Option C

Solution:

174. Find the quotient of (50 + j35)/(8 + j5).

A. 6.47 cis 3°

B. 4.47 cis 3°

C. 7.47 cis 30°

D. 2.47 cis 53°

View Answer:

Answer: Option A

Solution:

175. Three vectors A, B and C are related as follows: A/B = 2 at 180°, A + C = -5 + j15, C = conjugate of B. Find A.

A. 5 – j5

B. -10 + j10

C. 10 – j10

D. 15 + j15

View Answer:

Answer: Option B

Solution:

176. Evaluate cosh(jπ/4).

A. 0.707

B. 1.41 + j0.866

C. 0.5 + j0.707

D. j0.707

View Answer:

Answer: Option A

Solution:

177. Evaluate tanh(jπ/3).

A. 0.5 + j1.732

B. j0.866

C. j1.732

D. 0.5 + j0.866

View Answer:

Answer: Option C

Solution:

178. Evaluate in (2 + j3).

A. 1.34 + j0.32

B. 2.54 + j0.866

C. 2.23 + j0.21

D. 1.28 + j0.98

View Answer:

Answer: Option D

Solution:

179. Evaluate the terms of a Fourier series 2 e(j10πt) + e(- j10πt) at t = 1.

A. 2 + j

B. 2

C. 4

D. 2 + j2

View Answer:

Answer: Option C

Solution:

180. Given the following series:

sin x = x – x3/3! + x5/5! + …

cos x 1 – x2/2! + x4/4! + …

e^x = 1 + x + x2/2! + x3/3! + …

What relation can you draw from these series?

A. ex = cos x + sin x

B. e(ix) = cos x + i sin x

C. e(ix) = I cos x + sin x

D. iex = i cos x + i sin x

View Answer:

Answer: Option B

Solution:

181. One term of a Fourier series in cosine form is 10 cos 40πt. Write it in exponential form.

A. 5 e(j40πt)

B. 5 e(j40πt) + 5 e(-j40πt)

C. 10 e(-j40πt)

D. 10 e(j40πt)

View Answer:

Answer: Option D

Solution:

182. Evaluate the determinant:

MCQ in Calculus Part 4 | Mathematics Board Exam

A. 4

B. 2

C. 5

D. 0

View Answer:

Answer: Option C

Solution:

183. Evaluate the determinant:

MCQ in Calculus Part 4 | Mathematics Board Exam

A. 110

B. -101

C. 101

D. -110

View Answer:

Answer: Option B

Solution:

184. Evaluate the determinant:

MCQ in Calculus Part 4 | Mathematics Board Exam

A. 489

B. 389

C. 326

D. 452

View Answer:

Answer: Option C

Solution:

185. Compute the value of x by determinant.

MCQ in Calculus Part 4 | Mathematics Board Exam

A. -32

B. -28

C. 16

D. 52

View Answer:

Answer: Option B

Solution:

186. Given the equations:

x + y + z = 2

3x – y – 2z = 4

5x – 2y + 3z = -7

Solve for y by determinants.

A. 1

B. -2

C. 3

D. 0

View Answer:

Answer: Option C

Solution:

187. Solve the equations by Cramer’s Rule:

2x – y + 3z = -3

3x + 3y – z = 10

-x – y + z = -4

A. (2, 1, -1)

B. (2, -1, -1)

C. (1, 2, -1)

D. (-1, -2, 1)

View Answer:

Answer: Option C

Solution:

188. If,

MCQ in Calculus Part 4 | Mathematics Board Exam

What is the cofactor of the second row, third column element?

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option B

Solution:

189. If,

MCQ in Calculus Part 4 | Mathematics Board Exam

What is the cofactor with the first row, second column element?

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option D

Solution:

190. If a 3 x 3 matrix and its inverse are multiplied together, write the product.

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option A

Solution:

191. If matrix

MCQ in Calculus Part 4 | Mathematics Board Exam

A. 3

B. 1

C. 0

D. -2

View Answer:

Answer: Option C

Solution:

192. Given the matrix equation, solve for x and y.

MCQ in Calculus Part 4 | Mathematics Board Exam

A. -4, 6

B. -4, 2

C. -41 -2

D. -4, -6

View Answer:

Answer: Option A

Solution:

193. If matrix

MCQ in Calculus Part 4 | Mathematics Board Exam

A. 8

B. 1

C. -4

D. 0

View Answer:

Answer: Option D

Solution:

194. If

MCQ in Calculus Part 4 | Mathematics Board Exam

What is A times B equal to?

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option A

Solution:

195. Matrix

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option D

Solution:

196. Elements of matrix

MCQ in Calculus Part 4 | Mathematics Board Exam

Find the elements of the product of the two matrices, matrix BC.

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option A

Solution:

197. Transpose the matrix

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option B

Solution:

198. Determine the inverse matrix of

MCQ in Calculus Part 4 | Mathematics Board Exam

View Answer:

Answer: Option A

Solution:

199. k divided by [ (s square) + (k square) ] is the inverse Laplace transform of:

A. cos kt

B. sin kt

C. (e exponent kt)

D. 1.0

View Answer:

Answer: Option B

Solution:

200. The Laplace transform of cos wt is

A. s / [(s square) + (w square) ]

B. w / [ (s square) + (w square) ]

C. w / (s + w)

D. s / (s + w)

View Answer:

Answer: Option A

Solution:

Online Questions and Answers in Calculus Series

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

MCQ in Calculus
PART 1: MCQ from Number 1 – 50                               Answer key: PART 1
PART 2: MCQ from Number 51 – 100                          Answer key: PART 2
PART 3: MCQ from Number 101 – 150                        Answer key: PART 3
PART 4: MCQ from Number 151 – 200                        Answer key: PART 4
PART 5: MCQ from Number 201 – 250                        Answer key: PART 5
PART 6: MCQ from Number 251 – 300                        Answer key: PART 6
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