This is the Multiple Choice Questions Part 1 of the Series in Plane Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize yourself in each and every question 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 ME Board Exam Syllabi

- MCQ in Venn Diagram | MCQ in Definition of Plane Geometry | MCQ in Angles | MCQ in Circles | MCQ in Ellipse | MCQ in Polygons | MCQ in Triangles | MCQ in Quadrilaterals | MCQ in Trapezoids and Trapeziums | MCQ in Parallelograms | MCQ in Square and Rectangles | MCQ in Rhomboid and Rhombus

#### Start Practice Exam Test Questions Part 1 of the Series

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

**Problem 1: ECE Board November 1998**

Find the angle in mills subtended by a line 10 yards long at a distance of 5000 yards.

A. 1

B. 2

C. 2.5

D. 4

Answer: **Option B**

Solution: Review Solution for Number 1

**Problem 2: ECE Board April 1999**

Assuming that the earth is sphere whose radius is 6400 km. Find the distance along a 3 degree arc at the equator of the earth’s surface.

A. 335.10 km

B. 533.10 km

C. 353.10 km

D. 353.01 km

Answer: **Option A**

Solution: Review Solution for Number 2

**Problem 3: EE Board April 1992**

The angle subtended by an arc is 24o. If the radius of the circle is 45 cm, find the length of arc

A. 16.85 cm

B. 17.85 cm

C. 18.85 cm

D. 19.85 cm

Answer: **Option C**

Solution: Review Solution for Number 3

**Problem 4: ME Board April 1990**

A rat fell on a bucket of a water wheel with a diameter of 600 cm which travelled at an angle of 190° before it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell.

A. 950

B. 965

C. 985

D. 995

Answer: **Option D**

Solution: Review Solution for Number 4

**Problem 5: ECE Board November 1992**

Given the circle whose diameter AB equals 2 m. If two points C and D lie on the circle and angles ABC and BAD are 18o and 36o, respectively, find the length of the major arc CD.

A. 1.26 m

B. 1.36 m

C. 1.63 m

D. 1.45 m

Answer: **Option A**

Solution: Review Solution for Number 5

**Problem 6:**

A certain angle has as supplement 5 times its complement. What is the angle?

A. 67.5°

B. 58.5°

C. 30°

D. 27°

Answer: **Option A**

Solution: Review Solution for Number 6

**Problem 7: ECE Board November 1998**

Each angle of a regular dodecagon is equal to

A. 135°

B. 150°

C. 125°

D. 105°

Answer: **Option B**

Solution: Review Solution for Number 7

**Problem 8: CE Board May 1997**

How many sides has a polygon if the sum of the interior angles is 1080°?

A. 5

B. 6

C. 7

D. 8

Answer: **Option D**

Solution: Review Solution for Number 8

**Problem 9: ECE Board March 1996**

The sum of the interior angles of a polygon is 540o. Find the number of sides.

A. 3

B. 4

C. 5

D. 6

Answer: **Option C**

Solution: Review Solution for Number 9

**Problem 10: ECE Board April 1991**

Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle.

A. 150°

B. 160°

C. 170°

D. 180°

Answer: **Option D**

Solution: Review Solution for Number 10

**Problem 11: ME Board April 1999**

How many sides are in a polygon if each interior angle is 165 degrees.

A. 12

B. 24

C. 20

D. 48

Answer: **Option B**

Solution: Review Solution for Number 11

**Problem 12:**

How many diagonals are there in a polygon of 20 sides?

A. 200

B. 170

C. 100

D. 158

Answer: **Option B**

Solution: Review Solution for Number 12

**Problem 13: ME Board April 1999**

Find each interior angle of a hexagon.

A. 90°

B. 120°

C. 150°

D. 180°

Answer: **Option B**

Solution: Review Solution for Number 13

**Problem 14: EE Board April 1994**

Given a triangle, C = 100°, A = 15 m, B = 20 m. Find c.

A. 26 m

B. 27 m

C. 28 m

D. 29 m

Answer: **Option B**

Solution: Review Solution for Number 14

**Problem 15: CE Board November 1994**

In triangle ABC, angle A = 45° and C = 70°. The side opposite angle C is 40 m long. What is the length of the side opposite angle A?

A. 26.1 m

B. 27.1 m

C. 29.1 m

D. 30.1 m

Answer: **Option D**

Solution: Review Solution for Number 15

**Problem 16: CE Board May 1995**

In triangle ABC, angle C = 70°, A= 45°, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

A. 36.3 m

B. 36.6 m

C. 36.9 m

D. 37.2 m

Answer: **Option A**

Solution: Review Solution for Number 16

**Problem 17: EE Board April 1991**

From a point outside of an equilateral triangle, the distances to the vertices are 10 m, 18 m and 10 m, respectively. What is the length of one side of a triangle?

A. 17.75 m

B. 18.50 m

C. 19.95 m

D. 20.50 m

Answer: **Option C**

Solution: Review Solution for Number 17

**Problem 18: EE Board April 1991**

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed circle.

A. 2.25 cm

B. 2.35 cm

C. 2.45 cm

D. 2.55 cm

Answer: **Option C**

Solution: Review Solution for Number 18

**Problem 19: CE Board May 1996**

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm.?

A. 12.73 m

B. 13.52 m

C. 14.18 m

D. 15.55 m

Answer: **Option A**

Solution: Review Solution for Number 19

**Problem 20: EE Board April 1991**

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the circumscribing circle.

A. 7.14 cm

B. 7.34 cm

C. 7.54 cm

D. 7.74 cm

Answer: **Option A**

Solution: Review Solution for Number 20

**Problem 21: CE Board May 1996**

Two sides of a triangle are 50 m and 60 m long. The angle included between these sides is 30o. What is the interior angle opposite the longest side?

A. 93.74°

B. 92.74°

C. 90.74°

D. 86.38°

Answer: **Option D**

Solution: Review Solution for Number 21

**Problem 22: ECE Board March 1996**

A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border.

A. 1.76 cm

B. 1.35 cm

C. 1.98 cm

D. 2.03 cm

Answer: **Option A**

Solution: Review Solution for Number 22

**Problem 23: ME Board April 1996**

The area of a circle is 89.42 sq. inches. What is its circumference?

A. 32.25 in.

B. 33.52 in.

C. 35.33 in.

D. 35.55 in.

Answer: **Option B**

Solution: Review Solution for Number 23

**Problem 24: ECE Board April 1991**

A square section ABCD has one of its sides equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED.

A. 130°

B. 140°

C. 150°

D. 160°

Answer: **Option C**

Solution: Review Solution for Number 24

**Problem 25: CE Board November 1995**

The area of a circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m?

A. 100.25

B. 102.25

C. 104.25

D. 105.25

Answer: **Option D**

Solution: Review Solution for Number 25

**Problem 26: CE Board May 1995**

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side 10 cm long?

A. 104.7

B. 105.7

C. 106.7

D. 107.7

Answer: **Option A**

Solution: Review Solution for Number 26

**Problem 27: CE Board November 1992**

The area of a triangle inscribed in a circle is 39.19 cm^{2} and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

A. 11 cm

B. 12 cm

C. 13 cm

D. 14 cm

Answer: **Option D**

Solution: Review Solution for Number 27

**Problem 28: CE Board November 1994**

The area of a triangle is 8346 sq. m and two of its interior angles are 37o25’ and 56o17’. What is the length of the longest side?

A. 171.5 m

B. 181.5 m

C. 191.5 m

D. 200.5 m

Answer: **Option B**

Solution: Review Solution for Number 28

**Problem 29: ECE Board April 1998**

The angle of a sector is 30o and the radius is 15 cm. What is the area of the sector in cm^{2}?

A. 59.8

B. 89.5

C. 58.9

D. 85.9

Answer: **Option C**

Solution: Review Solution for Number 29

**Problem 30: EE Board April 1992**

Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part.

A. 30 cm^{2}

B. 31 cm^{2}

C. 32 cm^{2}

D. 33 cm^{2}

Answer: **Option B**

Solution: Review Solution for Number 30

**Problem 31: ECE Board April 1998**

The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. The area of the largest circle is?

A. 72 π

B. 23 π

C. 64 π

D. 16 π

Answer: **Option C**

Solution: Review Solution for Number 31

**Problem 32: ECE Board November 1993**

The arc of a sector is 9 unites and its radius is 3 units. What is the area of the sector in square units?

A. 12.5

B. 13.5

C. 14.5

D. 15.5

Answer: **Option B**

Solution: Review Solution for Number 32

**Problem 33: CE Board May 1998**

A circle having an area of 452 sq. m is cut into two segments by a chord which is 6 m from the center of the circle. Compute the area of the bigger segment.

A. 354. 89 sq. m

B. 363. 68 sq. m

C. 378. 42 sq. m

D. 383. 64 sq. m

Answer: **Option B**

Solution: Review Solution for Number 33

**Problem 34: ECE Board April 1992**

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 9 m and each circle passes through the center of the other. Find the area of the swimming pool.

A. 380 m^{2}

B. 390 m^{2}

C. 400 m^{2}

D. 410 m^{2}

Answer: **Option D**

Solution: Review Solution for Number 34

**Problem 35: ME Board April 1991**

Find the difference of the area of the square inscribe in a semi-circle having a radius of 15 ,. The base of the square lies on the diameter of the semi-circle.

A. 171.5 cm^{2}

B. 172.5 cm^{2}

C. 173.5 cm^{2}

D. 174.5 cm^{2}

Answer: **Option C**

Solution: Review Solution for Number 35

**Problem 36: ECE Board November 1995**

A rectangle ABCD which measures 18 cm. 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. 20.5 cm^{2}

B. 21.5 cm^{2}

C. 22.5 cm^{2}

D. 23.5 cm^{2}

Answer: **Option C**

Solution: Review Solution for Number 36

**Problem 37: ECE Board April 1998**

A trapezoid has an area of 36 m^{2} and an altitude of 2 m. Its two bases have the ration of 4:5. What are the lengths of the bases?

A. 12, 15

B. 7, 11

C. 8, 10

D. 16, 20

Answer: **Option D**

Solution: Review Solution for Number 37

**Problem 38: EE Board March 1998**

A rhombus has diagonals of 32 and 20 inches. Determine its area.

A. 360 in^{2}

B. 280 in^{2}

C. 320 in^{2}

D. 400 in^{2}

Answer: **Option C**

Solution: Review Solution for Number 38

**Problem 39: ECE Board April 1998**

If the sides of a parallelogram and an included angle are 6, 10 and 100o, respectively, find the length of the shorter diagonal.

A. 10.63

B. 10.37

C. 10.73

D. 10.23

Answer: **Option C**

Solution: Review Solution for Number 39

**Problem 40: CE Board November 1996**

Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225°.

A. 96 sq. m

B. 100 sq. m

C. 94 sq. m

D. 98 sq. m

Answer: **Option B**

Solution: Review Solution for Number 40

**Problem 41: EE Board October 1992**

Determine the area of the quadrilateral shown, OB = 80 cm, AO = 120 cm, OD = 150 cm and ϕ = 25o

A. 2721.66 cm^{2}

B. 2271.66 cm^{2}

C. 2172.66 cm^{2}

D. 2217.66 cm^{2}

Answer: **Option A**

Solution: Review Solution for Number 41

**Problem 42: CE Board October 1997**

A quadrilateral has sides 12 m, 20 m, 8 m and 16.97 m. If the sum of the opposite angles is equal to 225°, find the area of the quadrilateral.

A. 100 m^{2}

B. 124 m^{2}

C. 168 m^{2}

D. 158 m^{2}

Answer: **Option C**

Solution: Review Solution for Number 42

**Problem 43: ME Board October 1996, ME Board April 1997**

The area of a regular hexagon inscribed in a circle of radius 1 is?

A. 1.316

B. 2.945

C. 2.598

D. 3.816

Answer: **Option C**

Solution: Review Solution for Number 43

**Problem 44: EE Board April 1990**

Find the area (in cm^{2}) of a regular octagon inscribed in a circle of radius 10 cm?

A. 283

B. 289

C. 298

D. 238

Answer: **Option A**

Solution: Review Solution for Number 44

**Problem 45: GE Board February 1992**

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

A. 36. 45 sq. m

B. 63. 54 sq. m

C. 45. 63 sq. m

D. 54. 36 sq. m

Answer: **Option D**

Solution: Review Solution for Number 45

**Problem 46: EE Board April 1993**

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

A. 1075 m^{2}

B. 1085 m^{2}

C. 1080 m^{2}

D. 1095 m^{2}

Answer: **Option A**

Solution: Review Solution for Number 46

**Problem 47: ME Board October 1996**

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

A. 5.533 in.

B. 5.335 in.

C. 6.335 in.

D. 7.335 in.

Answer: **Option B**

Solution: Review Solution for Number 47

**Problem 48: EE Board April 1990**

In a circle of diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the area of that part not covered by the star?

A. 40.5 sq. m

B. 45.5 sq. m

C. 50.5 sq. m

D. 55.5 sq. m

Answer: **Option C**

Solution: Review Solution for Number 48

**Problem 49: EE Board March 1998**

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

A. 430.70 cm^{3}

B. 573.26 cm^{3}

C. 473.77 cm^{3}

D. 516.14 cm^{3}

Answer: **Option D**

Solution: Review Solution for Number 49

**Problem 50: EE Board March 1999**

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.

A. 441.66 cm^{2}

B. 467.64 cm^{2}

C. 519.60 cm^{2}

D. 493.62 cm^{2}

Answer: **Option C**

Solution: Review Solution for Number 50

### Online Question and Answer in Plane Geometry Series

Following is the list of practice exam test questions in this brand new series:

**MCQ in Plane Geometry**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

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

**PART 2**

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

**PART 3**

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