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Below are the answers key for the Multiple Choice Questions in Calculus – MCQs Part 6.

251. c. 17/3

252. d. 40pi

253. c. 50√3

254. a. 46.83

255. c. 72

256. c. 5/21

257. d. 37/12

258. a. 268.1

259. b. 1.05

260. a. 1/90 rad/sec

261. c. the intersection of Df and Dg without the zeros of function g

262. d. the closed interval [a + 3 , b + 3]

263. a. the interval (a - 4 , +infinity)

264. b. (f / g)(x) is also continuous everywhere except at the zeros of g(x).

265. b. -10

266. c. lim [ f(x) . g(x) ] as x --> a may be +infinity or -infinity

267. c. (A) or (B) above

268. d. None of the above

269. d. (A) and (C) only

270. b. (-infinity , -3] U [3 , +infinity)

271. b. 1 / 10

272. b. f '(x) = g '(x)

273. b. f '(x) = g '(u) . u '(x)

274. a. 1

275. d. 4

276. a. 5

277. A. [ 2 e( exp –t ) – 4 e( exp – 3t ) ]

278. A. I(s) = 2 e^(-25t) sin 100t

279. D. cos wt

280. B. 2 cos 3x – 6 sin 3x

281. A. (1/4) e^t sinht

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Below are the answers key for the Multiple Choice Questions in Calculus – MCQs Part 5.

201. c. 27

202. a. xsinx + cosx + C

203. c. 2/3

204. a. 0.159 ft/min

205. c. 402.12 cm²/s

206. b. infinity

207. b. 1.64 m/s

208. c. -0.75 m/s

209. c. 1

210. c. -8.08 m/s

211. a. (1, 1)

212. a. 625 ft²

213. a. x + 4y = 9

214. b. 32

215. a. 4.08 units

216. c. 2 inches

217. a. (5^(2x + 1))ln25

218. a. 30°

219. a. 1.333 square units

220. c. 20.11 cu. units

221. d. 2200 copies/month

222. c. third order, first degree

223. a. dy / dx = 2x + 2y

224. b. –tanx

225. b. N/e

226. a. 2/3

227. c. 210 ft.

228. a. 2x³ – 15x – 3y + 2 = 0

229. c. (3/4, 3/10)

230. d. 1, 4

231. d. 12, 24

232. c. 5.66

233. b. 8,000

234. a. 30.26 m/s²

235. c. 16

236. a. 5.595

237. b. 10.67

238. c. 473.74

239. a. 225 x 10⁶ cm⁴

240. c. 4/3

241. a. 6 ft.

242. b. Negative

243. a. -0.0442

244. d. 0.178

245. c. 290 m

246. d. 7.07 m/s

247. c. 4.583 km

248. d. 1024 ft

249. b. 2 slugs/ft

250. b. $ 2

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Below are the answers key for the Multiple Choice Questions in Geometry – MCQs Part 5.

201. a. 2 cm

202. c. 12

203. b. 144 cu.cm.

204. a. 18,475.21 cm³

205. c. 69%

206. b. 20%

207. b. 60°

208. d. 1/6

209. a. 470.88 cm³

210. c. 1663.22

211. c. 1210.56

212. a. 45 pi.

213. a. 5.04 cm

214. b. 200%

215. c. 6 m

216. a. 10,367 cm³

217. c. 37.22

218. d. 16 cm

219. a. 324.21

220. c. 1/8

221. a. 3200 km

222. a. 381.7 cm²

223. b. 0.67d

224. b. 3.85

225. b. 6

226. b. 22.5 cm

227. b. b² = ac

228. c. 4x + 2y – 5 = 0

229. b. 10

230. a. (-3, -6)

231. c. 77.47°

232. c. -1

233. a. 32.5

234. d. 8

235. b. 7

236. a. -2

237. b. m₁ x m₂ = -1

238. a. -5 or 19

239. c. 3p – 2q = 1

240. a. 7x + 2y + 31 = 0

241. a. 4

242. b. 5

243. c. -3

244. a. x – y + 6 = 0

245. a. x – y + 1 = 0

246. b. 5x’ + 4y’ + 16 = 0

247. a. (7, -4)

248. c. 28.27 sq. units

249. b. 14

250. c. (x – 5)² + (y – 3)² = 25

251. b. 2.07

252. b. (1, 0)

253. c. 25.98

254. a. 4, –8

255. c. Hyperbola

256. b. Ellipse

257. b. 5

258. a. x + y – 1 = 0

259. a. 20.78 m

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Below are the answers key for the Multiple Choice Questions in Algebra and General Mathematics – MCQs Part 11.

501. b. 0 , √3 , - √3

502. b. Pi/6

503. c. 1500Pi

504. c. 2

505. a. 216

506. d. 7/(4√2)

507. a. (√45 - 2√24)/35

508. d. -1/2

509. b. 19.806

510. d. 57.67

511. b. 130 deg.

512. c. 1

513. b. 2488 mi.

514. c. 20.9, 69.1

515. c. x + 2y = 30

516. c. 30°

517. a. 21.7°, 321.86 mph

518. d. 137°56’

519. b. 216

520. a. 168.18

521. d. 1.71 cm

522. c. 54

523. a. 1075

524. c. 486.29

525. d. decreases then increases

526. b. 8a + 4b + 2c + d

527. a. 140/429

528. b. y ≤ –3

529. c. Pi/2

530. a. 1/15

531. b. 280

532. c. –9

533. a. 1 hour 12 minutes

534. a. a circle

535. d. –1

536. c. (3 , 1)

537. c. 18

538. d. 50.47

539. a. 124.71 sq. cm.

540. c. 12

541. b. 9.8 m

542. c. 3

543. a. 10 cm

544. a. 323.75 cm²

545. b. 75.4 m

546. a. 24 cm²

547. b. 119.3 cm²

548. a. 937.5 cm²

549. c. 7.5 kg

550. c. 7.94 cm

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Below are the answers key for the Multiple Choice Questions in Algebra and General Mathematics – MCQs Part 10.

451. b. 2

452. d. 20,000

453. a. 35,350

454. a. 1200

455. b. 10,912

456. a. 27.89 m

457. a. 3 & 5

458. d. x = 1, y = 2

459. c. -27

460. b. 480 ways

461. b. 560

462. a. 2,520

463. a. 0.01

464. a. 1/420

465. d. 25

466. a. 4000

467. b. 5

468. d. Pi / 6 + n*Pi , 11 Pi / 6 + n*Pi

469. c. II

470. a. 14.57°

471. d. 5

472. c. 2Pi / 3 + 2n*Pi , 4Pi / 3 + 2n*Pi

473. b. 1.25

474. c. 800 mils

475. a. 10^-3

476. a. 0°

477. a. px = qy

478. a. 7Pi / 6 + 2n*Pi , 11Pi / 6 + 2n*Pi

479. a. N40° E

480. c. 9.17 in

481. a. 90 m

482. a. 3,200 km

483. a. Pi / 6 + n*Pi , 5Pi / 6 + 2n*Pi , Pi / 3 + n*Pi , 2Pi / 3 + n*Pi

484. d. 358.49 m

485. b. 81.6 ft.

486. a. 42.54 m

487. a. 10.2

488. c. 2/3

489. a. Pi / 3 , 5Pi / 3 , Pi

490. a. 0 , Pi , 3Pi / 4 , 7Pi / 4

491. a. 35,415.56 ft

492. c. 85°

493. a. 55 ft

494. c. 4 ft

495. c. 0.5

496. a. 72

497. b. 0 , Pi / 3 , Pi , 5Pi / 3

498. c. 120 deg.

499. a. 30 deg.

500. a. 90.6 m

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Below are the answers key for the Multiple Choice Questions in Algebra and General Mathematics – MCQs Part 9.

401. d. 5/36

402. a. 28

403. c. 420

404. a. 24

405. c. 3¹⁰³

406. d. 36

407. a. 64Pi

408. a. 31.25

409. b. 40,800

410. d. y*w*n / (x*c)

411. b. 7

412. c. -2

413. b. 9

414. a. 25 kg

415. c. 5.5 mins

416. d. 250

417. c. 2

418. c. 290,000

419. c. 11/12

420. c. 15/2

421. b. - 2 - 2√2

422. a. (3 + √3/2 , 5/2)

423. c. 2√5

424. a. 3

425. c. - 1

426. b. 2/3

427. a. |x - 1|

428. d. (-2 , -1) U (1 , 2)

429. b. 64Pi

430. c. 55,000

431. c. 17

432. b. 370

433. d. √5 + √3

434. a. 31.25

435. d. (a + 1) / (b + 1)

436. a. 19

437. c. -11/3

438. c. a = 5 , b = 6

439. a. 28.8

440. c. 1 + √6

441. a. 1050

442. a. 200 & 180

443. a. 20 days

444. a. 34

445. c. -8

446. d. 27

447. b. 4 km/hr

448. c. 27

449. c. 36

450. a. 6

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Below are the answers key for the Multiple Choice Questions in Algebra and General Mathematics – MCQs Part 8.

351. c. 4

352. c. -6

353. d. 13/16

354. b. 5

355. c. 24√2

356. a. 20√3

357. b. 2 / (x - 2)

358. c. -1/3

359. d. -3

360. b. An irrational number

361. a. -2, 60

362. a. 28

363. d. 112

364. c. 50,800

365. a. y = x³

366. a. 4/3

367. c. 40 mins.

368. d. 0.00004

369. a. 0.198

370. a. 3/13

371. b. x⁶

372. c. 0.05

373. a. 2:43.64

374. b. 1092

375. d. 8 km/hr

376. a. x³ – 12x² + 44x – 48 = 0

377. c. 2,520

378. a. 3

379. c. 970

380. c. 22

381. b. 247

382. a. 10

383. c. 29/56

384. a. 3:4:5

385. b. -8, 6, -4

386. c. 240

387. c. 6

388. a. 160L

389. a. 12 MPH

390. c. 128

391. a. 844

392. d. 2.03 days

393. c. 21%

394. a. 1%

395. d. 11, 11, 11

396. b. 8/15

397. b. 1

398. d. 100

399. a. 5

400. a. 1.5

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Below are the answers key for the Multiple Choice Questions in Algebra and General Mathematics – MCQs Part 7.

301. b. 24/35

302. c. Associative Law

303. a. 8

304. c. 30

305. c. 27

306. a. 4

307. b. 22 hrs.

308. d. 75

309. a. 2(x + 3)

310. b. 5 √3

311. d. 8π

312. b. 2

313. a. 4

314. b. 5√3 / 14

315. c. a < 0 and b ≠ –4

316. b. 1/49

317. b. 510056

318. b. 5

319. c. 40°

320. c. 4√3

321. c. –4

322. d. (8y + 11)/3

323. d. (-2, 3)

324. a. 8

325. b. 108.9

326. a. x < (xy)/2 < y

327. c. 3/5

328. b. 157°

329. a. 6

330. a. 10√3

331. c. -4/3

332. c. 3√5

333. d. –3

334. c. 6

335. d. n(100 - r) / 100

336. a. 75°

337. b. 6

338. b. –1

339. b. 255

340. a. 35

341. b. 21 / 5

342. a. 312,500

343. b. –4

344. a. 1/2

345. a. 17

346. b. 25Pi

347. a. 90°

348. a. 1/√3

349. c. 3x + y = 7

350. d. -0.5

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Below are the answers key for the Multiple Choice Questions in Calculus – MCQs Part 4.

151. C. 30.45

152. B. 19.53 kg.

153. A. 171.24 lbs

154. B. P6,750

155. D. P13,498.60

156. A. 0

157. A. 3i

158. C. 2i - 1

159. D. 7

160. C. 5 cis 53.1°

161. B. –sqrt(70)

162. D. – (3 – i)

163. C. 30.8 cis 45°

164. B. 8i

165. A. 12.5 + j21.65

166. B. -4(1 + i)

167. A. 1.9 + j1.1

168. C. -8 + 4i

169. B. (-18 - i)/25

170. A. 1 + 2i

171. C. (-7 + 17i)/13

172. B. 1.12 – j0.66

173. C. square root of 3 + i

174. A. 6.47 cis 3°

175. B. -10 + j10

176. A. 0.707

177. C. j1.732

178. D. 1.28 + j0.98

179. C. 4

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

181. D. 10 e^(j40πt)

182. C. 5

183. B. -101

184. C. 326

185. B. -28

186. C. 3

187. C. (1, 2, -1)

188. B

189. D.

190. A.

191. C. 0

192. A. -4, 6

193. D. 0

194. A.

195. D.

196. A.

197. B.

198. A.

199. B. sin kt

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

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Below are the answers key for the Multiple Choice Questions in Calculus – MCQs Part 3.

101. C. 32/3

102. A. 88/3

103. B. 64/3 square units

104. A. 21.33

105. A. 75

106. A. 5.33

107. D. 10.67 sq. units

108. A. 4.25

109. D. 5.595

110. D. 10.7

111. A. 8

112. D. 32/3

113. C. a^2

114. A. 0.4 from the x-axis and 0.5 from the y-axis

115. B. (0,1.6)

116. B. (3/5, 3/4)

117. B. 4.6 units

118. A. 5.33

119. A. 355.3

120. B. 2228.83

121. B. 181

122. D. 26.81

123. C. 59.22

124. D. 50.26

125. B. 2.13

126. A. Fourth order, first degree

127. C. 2xy dx + (2 + x^2) dy = 0

128. C. 2y dx = (x^2 + 1) dy

129. C. y’ = y/(2x)

130. C. 1.55

131. B. x^3 – 3y + 2 = 0

132. C. y = y^2 + C

133. B. sin x cos y = ln (c sin x)

134. C. x^2 – 2y – 1 = 0

135. B. y(k) = 20 + 5k

136. A. sqrt(x^2 + y^2) + y = C

137. A. (x – 1) y” – xy’ + y = 0

138. A. y = C (sec x + tan x)

139. D. ln (xy) = x + 2y) + C

140. C. x^2 - 2xy - y^2 = C

141. B. ydx=(x+1)dy

142. B. xdy – ydx = 0

143. A. 2xdx – ydy = 0

144. C. (x – h)dx – (y – k)dy = 0

145. C. x + yy’ = 0

146. C. 92.16

147. B. 116 years

148. A. 6.70%

149. A. y = Ce^(-x)

150. A. 33.59 min.

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Below are the answers key for the Multiple Choice Questions in Calculus – MCQs Part 2.

51. C. 2000

52. B. 2m x 2m x 2.5m

53. B. 200,000

54. B. 3.0 km

55. B. 100

56. D. 12 kph

57. A. 44%

58. C. 1.50 m

59. B. 2.24

60. D. 2 and 1

61. C. 3.71 m

62. C. 8.33 fps

63. A. 3.64 m/s

64. A. 0.64 m/min

65. C. 6.28 m^3/sec

66. A. 7/6 gph

67. C. 10.32 m/s

68. D. 1.49 m/sec

69. C. 12 ft./s

70. D. 45 kph

71. B. 51

72. A. 67.08

73. C. 4

74. C. 0.0025

75. C. -0.001 amp/sec

76. A. (1/12)(3t - 1)^4 + C

77. D. ln 2

78. A. (1/4) sin(2x^2 + 7) + C

79. C. (7x^4)/4 + (4x^3)/3 + C

80. C. 0.0417

81. D. 0.533

82. A. 0.2

83. D. 5π/32

84. A. 0.456

85. B. 0.022

86. B. 35π/768

87. D. 0.305

88. A. y/2 + (sin 2y)/4 + C

89. A. -2*sqrt(2) cos(x/2) + C

90. B. 0.293

91. B. 1

92. A. 2.0

93. A. (e^(sin 2x))/2 + C

94. A. sin x + C

95. D. ln (e exp x + 1) square - x + C

96. D. 1/3

97. D. 40

98. A. 2/3

99. B. 1.33 sq. units

100. B. 4 sq. units

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