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# MCQ in Geometry Part 5 | Mathematics Board Exam

This is the Multiple Choice Questions Part 5 of the Series in Geometry 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 Lines and Planes | MCQ in lane figures | MCQ in Application of Cavalier’s, Pappus and Prismodial Theorems | MCQ in Coordinate in Space | MCQ in Quadratic Surfaces | MCQ in Mensuration | MCQ in Plane Geometry | MCQ in Solid Geometry | MCQ in Spherical Geometry | MCQs in Analytical Geometry

#### Continue Practice Exam Test Questions Part 5 of the Series

Choose the letter of the best answer in each questions.

201. A sphere of radius 5 cm and a right circular cone of base radius 5 cm and a height 10 cm stand on a plane. Find the position of a plane that cuts the two solids in equal circular sections.

a. 2 cm

b. 2.5 cm

c. 1.5 cm

d. 3.2 cm

Solution:

202. A regular triangular pyramid has an altitude of 9 m and a volume of 187.06 cu. m. What is the base edge in meters?

a. 10

b. 11

c. 12

d. 13

Solution:

203. Two cylinders of equal radius 3 m have their axes at right angles. Find the volume of the common part.

a. 122 cu.cm.

b. 144 cu.cm.

c. 154 cu.cm.

d. 134 cu.cm.

Solution:

204. A solid has a circular base of radius 20 cm. find the volume of the solid if every plane section perpendicular to a certain diameter is an equilateral triangle.

a. 18,475.21 cm3

b. 20,475.31 cm3

c. 12,775.21 cm3

d. 21,475.21 cm3

Solution:

205. If the edge of a cube is increased by 30%, by how much is the surface increased?

a. 30%

b. 21%

c. 69%

d. 33%

Solution:

206. If the edge of a cube decreases by x%, its volume decrease by 48.8%. Find the value of x.

a. 10%

b. 20%

c. 16%

d. 25%

Solution:

207. Find the acute angles between the two planes 2x โ y + z = 8 and x + y + 2z โ 11 = 0.

a. 30ยฐ

b. 60ยฐ

c. 45ยฐ

d. 40ยฐ

Solution:

208. Find the volume of the solid bounded by the plane x + y + z = 1 and the coordinate planes.

a. 1/3

b. 1/4

c. 1/5

d. 1/6

Solution:

209. Compute the volume of a regular icosahedron with sides equal to 6 cm.

a. 470.88 cm3

b. 520.78 cm3

c. 340.89 cm3

d. 250.56 cm3

Solution:

210. Compute the volume (in cm3) of a sphere inscribe in an octahedron having sides equal to 18 cm.

a. 1622.33

b. 1875.45

c. 1663.22

d. 1892.63

Solution:

211. Find the volume of a spherical cone in a sphere of radius 17 cm if the radius of its zone is 8 cm.

a. 2120.35

b. 1426.34

c. 1210.56

d. 2316.75

Solution:

212. A spherical wooden ball 15 cm in diameter sinks to depth 12 cm in a certain liquid. Calculate the area exposed above the liquid in cm2.

a. 45 pi.

b. 20 pi.

c. 15 pi.

d. 10 pi.

Solution:

213. Given a solid right circular cone having a height of 8 cm. has a volume equal to 4 times the volume of the smaller cone that could be cut from the same cone having the same axis. Compute the height of the smaller cone.

a. 5.04 cm

b. 3.25 cm

c. 4.45 cm

d. 2.32 cm

Solution:

214. The diameter of a sphere and the base of a cone are equal. What percentage of that diameter must the cones height be so that both volumes are equal.

a. 100%

b. 200%

c. 50%

d. 400%

Solution:

215. The volume a regular pyramid whose base is a regular hexagon is 156 m3. If the altitude of the pyramid is 5 m., find the sides of the base.

a. 4 m

b. 8 m

c. 6 m

d. 3 m

Solution:

216. The base of a cylinder is a hexagon inscribed in a circle. If the difference in the circumference of the circle and the perimeter of the hexagon is 4 cm., find the volume of the prism if it has an altitude of 20 cm.

a. 10,367 cm3

b. 12,239 cm3

c. 10,123 cm3

d. 11,231 cm3

Solution:

217. The volume of a truncated prism with an equilateral triangle as its horizontal base is equal to 3600 cm3. The vertical edges at each corner are 4, 6, and 8 cm., respectively. Find one side of the base.

a. 22.37

b. 25.43

c. 37.22

d. 17.89

Solution:

218. Aluminum and lead have specific gravities of 2.5 and 16.48 respectively. If a cubical aluminum has edge of 0.30 m., find the edge of a cubical block of lead having the same weight as the aluminum.

a. 10 cm

b. 14 cm

c. 13 cm

d. 16 cm

Solution:

219. Find the area of a pentagonal spherical pyramid the angles of whose base are 105ยฐ, 126ยฐ, 134ยฐ, 146ยฐ and 158ยฐ on the sphere of radius 12 m.

a. 324.21

b. 343.56

c. 222.34

d. 433.67

Solution:

220. If the surface areas of two spheres are 24 cm2 and 96 cm2 respectively. Find the ratio of their volume.

a. 1/4

b. 5

c. 1/8

d. 3/5

Solution:

221. Considering the earth as a sphere of radius 6400 km, find the radius of the 60th parallel of latitude.

a. 3200 km

b. 1300 km

c. 2300 km

d. 3100 km

Solution:

222. A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume of its content.

a. 381.7 cm2

b. 281.6 cm2

c. 451.2 cm2

d. 367.4 cm2

Solution:

223. A sphere is dropped in a can partially filled with water. What is the rise in height of the water if they have equal diameters?

a. 0.75d

b. 0.67d

c. 1.33d

d. 1.5d

Solution:

224. A wooden cone is to be cut into two parts of equal volume by a plane parallel to its base. Find the ratio of the heights of the two parts.

a. 2.35

b. 3.85

c. 1.26

d. 1.86

Solution:

225. The ratio of the area of regular polygon circumscribed in a circle to the area of inscribed regular polygon of the same number of sides is 4:3. Find the number of sides.

a. 4

b. 6

c. 8

d. 10

Solution:

226. A rectangle ABCD which measures 18 by 24 cm is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

a. 18.5 cm

b. 22.5 cm

c. 21.5 cm

d. 19.5 cm

Solution:

227. If the straight lines ax + by +c = 0 and bx + cy + a = 0 are parallel, then which of the following is correct?

a. b2 = 4ac

b. b2 = ac

c. b2 + ac = 0

d. a2 = bc

Solution:

228. Find the equation of the perpendicular bisector of the segment joining the points (2, 6) and (-4, 3).

a. 2x – 4y + 5 = 0

b. 2x + 4y + 5 = 0

c. 4x + 2y โ 5 = 0

d. 5x โ 2y + 4 = 0

Solution:

229. The vertices of the base of an isosceles triangle are (-1, -2) and (1, 4). If the third vertex lies on the line 4x + 3y = 12, find the area of the triangle.

a. 8

b. 10

c. 9

d. 11

Solution:

230. The coordinates of the two vertices of a triangle are (6, -1) and (-3, 7). Find the coordinates of the third vertex so that the centroid of the triangle will be at the origin.

a. (-3, -6)

b. (-5, -5)

c. (4, -6)

d. (6, -4)

Solution:

231. Compute the angle between the line 2y – 9x – 18 = 0 and the x-axis.

a. 64.54ยฐ

b. 45ยฐ

c. 77.47ยฐ

d. 87.65ยฐ

Solution:

232. Find the value of k if the y-intercept of the line 3x – 4y – 8k = 0 is equal to 2.

a. 1

b. 2

c. -1

d. 3

Solution:

233. Find the area of the polygon whose vertices are (2, -6), (4, 0), (2, 4), (-3, 2), (-3, 3).

a. 32.5

b. 23.5

c. 47.5

d. 35.5

Solution:

234. In the triangle ABC having vertices at A(-2, 5), B(6, 1) and C(-2, -3), find the length of the median from vertex B to side AC.

a. 5

b. 7

c. 6

d. 8

Solution:

235. A line has an equation of 3x – ky – 8 = 0. Find the value of k if this line makes an angle of 45ยฐ with the line 2x + 5y – 17 = 0.

a. 5

b. 7

c. 8

d. 6

Solution:

236. The points (1, 3) and (5, 5) are two opposite vertices of a rectangle. The other two vertices lie on the line 2x – y + k = 0. Find the value of k.

a. -2

b. 2

c. -3

d. 4

Solution:

237. Let m1 and m2 be the respective slopes of two perpendicular lines. Then

a. m1 + m2 = -1

b. m1 x m2 = -1

c. m1 = m2

d. m1 x m2 = 0

Solution:

238. The abscissa of a point is 3. If its distance from a point (8, 7) is 13, find its ordinate.

a. -5 or 19

b. 3 or 5

c. 5 or 19

d. -3 or 7

Solution:

239. If the points (-3, -5), (p, q) and (3, 4) lie on a straight line, then which of the following is correct?

a. 2p โ 3q =1

b. p + q = -3

c. 3p โ 2q = 1

d. 2p โ q =3

Solution:

240. Find the equation of the line parallel to 7x + 2y โ 4 = 0 and passing through (-3, -5).

a. 7x + 2y + 31 = 0

b. 2x โ 4y -7 = 0

c. 3x โ 4y + 7 = 0

d. 2x โ 7y + 31 = 0

Solution:

241. Find the area of a triangle whose vertices are (1, 1), (3,-3), and (5,-3).

a. 4

b. 7

c. 10

d. 12

Solution:

242. Determine the x โ intercept of the line passing through (4, 1) and (1, 4).

a. 3

b. 5

c. 4

d. 6

Solution:

243. Find the slope of the line having a parametric equations of x = 2 + t and y = 5 – 3t.

a. 1

b. 1/3

c. -3

d. -1

Solution:

244. The midpoint of the line segment joining a moving point to (6, 0) is on the line y = x. Find the equation of its locus.

a. x โ y + 6 = 0

b. x โ 2y + 6 = 0

c. 2x โ y -3 = 0

d. 2x + 3y โ 5 = 0

Solution:

245. The base of an isosceles triangle is the line from (4, -3) to (-4, 5). Find the locus of the third vertex.

a. x โ y + 1 = 0

b. x + y + 1 = 0

c. x โ y โ 2 = 0

d. x + y โ 3 = 0

Solution:

246. What is the new equation of the line 5x + 4y + 3 = 0 if the origin is translated to the point (1, 2)?

a. 4xโ + 3yโ + 16 = 0

b. 5xโ + 4yโ + 16 = 0

c. 5xโ โ 4yโ โ 16 = 0

d. 6xโ + 6yโ โ 16 = 0

Solution:

247. One end of the diameter of the circle (x โ 4)2 + y2 = 25 is the point (1, 4). Find the coordinates of the other end of this diameter.

a. (7, -4)

b. (3, 4)

c. (-4, 7)

d. (-7, 4)

Solution:

248. Determine the area bounded by the curve x2 + y2 โ 6y = 0

a. 27.28 sq. units

b. 72.28 sq. units

c. 28.27 sq. units

d. 18.27 sq. units

Solution:

249. How far is the center of the circle x2 + y2 โ 10x โ 24y + 25 = 0 from the line y = 2?

a. 10

b. 14

c. 12

d. 16

Solution:

250. Find the equation of the circle tangent to the y-axis and the center is at (5, 3).

a. (x + 5)2 + (y โ 3)2 = 25

b. (x โ 5)2 + ( y + 3)2 = 25

c. (x โ 5)2 + (y โ 3)2 = 25

d. (x โ 5)2 + (y โ 3)2 = 50

Solution:

251. Find the shortest distance from (3, 8) to the curve x2+ y2 + 4x โ 6y = 12.

a. 1.21

b. 2.07

c. 4.09

d. 3.73

Solution:

252. The focus of the parabola y2 = 4x is at:

a. (4, 0)

b. (1, 0)

c. (0, 4)

d. (0, 1)

Solution:

253. An arc in the form of a parabola is 60 m across the bottom. The highest point is 16 m above the horizontal base. What is the length of the beam placed horizontally across the arc 3 m below the top.

a. 19.36

b. 24.86

c. 25.98

d. 27.34

Solution:

254. A curve has an equation of x2 = cy + d. the length of latus rectum is 4 and the vertex is at (0, 2). Compute the value of C and d.

a. 4, -8

b. 6, -2

c. 2, -5

d. 3, -7

Solution:

255. What conic section is 2x2 โ 8xy + 4x = 12?

a. Parabola

b. Ellipse

c. Hyperbola

d. Circle

Solution:

256. What conic section is described by the equation r = 6/(4 โ 3cosำจ)?

a. Circle

b. Ellipse

c. Hyperbola

d. Parabola

Solution:

257. An ellipse has its center at (0, 0) with its axis horizontal. The distance between the vertices is 8 and its eccentricity is 0.5. Compute the length of the longest focal radius from point (2, 3) on the curve.

a. 3

b. 5

c. 4

d. 6

Solution:

258. Determine the equation of the common tangents to the circles x2 + y2 + 2x + 4y โ 3 = 0 and x2 + y2 โ 8x โ 6y + 7 = 0.

a. x + y โ 1 = 0

b. 2x + y โ 1 = 0

c. x โ y โ 1 = 0

d. x -2x + 1 = 0

Solution:

259. An arc in the form of a parabolic curve is 40 m across the bottom. A flat horizontal beam 26 m long is placed 12 m above the base. Find the height of the arc.

a. 20.78 m

b. 18.67 m

c. 25.68 m

d. 15.87 m

Solution:

### Online Question and Answer in Geometry Series

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

MCQ in Geometry
PART 1: MCQ from Number 1 โ 50                                                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                                                           Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                                                         Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                                                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                                                         Answer key: PART 5

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