NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

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# NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

Edited By Ramraj Saini | Updated on Nov 30, 2023 10:46 AM IST

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry are discussed in this article. These NCERT solutions are created by the expert team at careers360 considering the latest CBSE syllabus 2023. Constructions of figures or sketches are mandatory for the design of different types of equipment, instruments, buildings, etc. In CBSE NCERT solutions for Class 6 Maths chapter 14 practical geometry, you will get questions related to constructions of figures using rulers and compass.

As per the NCERT syllabus for Class 6 Maths, the important topics of this chapter are the construction of the circle of a given radius using a compass, the construction of line segments and angles, etc. In the last exercise of this chapter as mentioned in the NCERT Books for Class 6 Maths, you will get questions related to measuring of angle using a compass and ruler. In some questions in NCERT, you will be drawing lines using the compass. There are many other constructions explained in 6 exercises of NCERT solutions for practical geometry class 6. You will get NCERT Solutions from Class 6 to 12 for Science and Math by clicking on the above link.

## NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry - Important Points

Geometrical shapes: This class 6th maths chapter 14 focuses on the methods used to draw various geometrical shapes. The shapes are constructed using mathematical instruments such as a graduated ruler, compasses, divider, set-squares, and a protractor.

Constructions using ruler and compasses:

(i) Circle: A circle can be drawn when the length of its radius is known. The compasses are used to measure and draw the circle.

(ii) Line segment: With the ruler and compasses, a line segment can be constructed when its length is given.

(iii) Copy of a line segment: The compasses are used to create an exact copy of a given line segment.

For more, Download Ebook - NCERT Class 6 Maths: Chapterwise Important Formulas And Points

(iv) Perpendicular to a line through a point:

• (a) On the line: A perpendicular line can be drawn through a point that lies on the given line.
• (b) Not on the line: A perpendicular line can be drawn through a point that does not lie on the given line.

(v) Perpendicular bisector: The perpendicular bisector of a line segment, which divides it into two equal halves, can be constructed.

(vi) Angle of a given measure: An angle with a specific measure can be constructed using the ruler and compasses.

(vii) Copy of an angle: With the ruler and compasses, an exact copy of a given angle can be drawn.

(viii) Bisector of an angle: The bisector of a given angle, which divides it into two equal angles, can be constructed.

(ix) Special angles: The class 6 maths chapter 14 chapter also covers the construction of angles with special measures such as 90 degrees, 45 degrees, 60 degrees, 30 degrees, 120 degrees, and 135 degrees. These angles are constructed using the ruler and compasses

Free Download NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry For CBSE Exam

## NCERT Class 6 Maths Chapter 14 Practical Geometry Exercise 14.1

Question: 1 Draw a circle of radius 3.2 cm.

(i) Take compasses for the required radius of 3.2 cm.

(ii) Mark point O where you want the centre of the circle.

(iii) After placing the compass on O, rotate the compasses slowly to make the circle.

(i) First, Set the compass for radius 4 cm

(ii) Mark point O which will be the centre for the circles.

(iiI) Place the pointer of compasses on O.

(iv) Turn the compasses slowly to draw the circle.

Repeat above 4 steps with the compass set at 2.5 cm

Answer: By joining the ends of the two diameters, we get a rectangle.

Therefore, by measuring, we find that $AB=CD$ and $BC=AD$ , i.e, pairs of opposite sides are equal and also $\angle A = \angle B = \angle C = \angle D = 90^{\circ}$ .

and each angle is fo $90^{\circ}.$

Hence, it is a rectangle:

If the diameters are perpendicular to each other, then by joining the ends of two diameters, we get a square.

Then, by measuring the length of the side we find that $AB=BC=CD=DA$ . that is all sides are of the same length also, $\angle A = \angle B = \angle C = \angle D = 90^{\circ}$ , that is each angle is $90^{\circ}.$

Hence, it is a square:

(a) A is on the circle. (b) B is in the interior of the circle.
(c) C is in the exterior of the circle.

Answer: To draw the circle with the given conditions:

First, mark point 'O' as the centre and place the pointer of the compasses at 'O' then turn the compasses slowly to complete the circle.

Now, mark point A on the circle, mark the point 'B' in the interior of the circle, also point 'C' exterior to the circle.

Answer: First, draw two circles of equal radii taking A and B as their centre and they intersect at C and D. Then, join AB and CD.

From the figure, AB and CD intersect at right angle with

## NCERT Class 6 Maths Chapter 14 Practical Geometry Exercise 14.2

Answer: Let the line segment be 'AB':

Then, follows these steps:

(i) Place the zero mark of the ruler at a point A.

(ii) Mark point B at a distance of 7.3cm from A.

(iii) Now, join AB.

Then, AB is the required line segment of the length of 7.3 cm.

(i) Draw a line ′l′. Mark a point A on this line.

(ii) Place the compasses pointer on the zero mark of the ruler. Open it to place the pencil point up to 5.6 cm mark.

(iii) Without changing the opening of the compasses. Place the pointer on A and cut an arc at B on line l.

$\bar{AB}$ is the required line segment of length 5.6 cm.

(i) Place the zero mark of the ruler at A.

(ii) Mark a point B at a distance 7.8 cm from A.

(iii) Again, mark a point C at a distance 4.7 from A.

By measuring $\bar{BC}$ , we find that BC = 3.1 cm

( Hint : Construct $\overline{PX}$ such that length of $\overline{PX}$ = length of $\overline{AB}$ ; then cut off $\overline{XQ}$ such that $\overline{XQ}$ also has the length of $\overline{AB}$ .)

Answer: The steps of constructions are following:

(i) Draw a line ′l′.

(ii) Construct $\bar{PX}$ such that length of $\bar{PX}$ = length of $\bar{AB}$

(iii) Then cut of $\bar{XQ}$ such that $\bar{XQ}$ also has the length of $\bar{AB}$ .

(iv) Thus the length of $\bar{PX}$ and the length of $\bar{XQ}$ added together make twice the length of $\bar{AB}$ .

Verification :

By measurement we find that PQ = 7.8 cm

= 3.9 cm + 3.9 cm = $\bar{AB} + \bar{AB}$ = $2\times\bar{AB} .$

Answer: The steps of construction are as follows:

(i) Draw a line ′l′ and take a point X on it.

(ii) Construct $\bar{XZ}$ such that length $\bar{XZ}$ = length of $\bar{AB}$ = 7.3 cm

(iii) Then cut off $\bar{ZY}$ = length of $\bar{CD}$ = 3.4 cm

(iv) Thus the length of $\bar{XY}$ = length of $\bar{AB}$ – length of $\bar{CD}$

Verification :

By measurement we find that length of $\bar{XY}$ = 3.9 cm

$= 7.3 cm - 3.4cm = \bar{AB} - \bar{CD}$

## NCERT Class 6 Maths Chapter 14 Practical Geometry Exercise 14.3

Answer: The steps of constructions are the following:

(i) Given $\bar{PQ}$ whose length is not known.

(ii) Fix the compasses pointer on P and the pencil end on Q. The opening of the instrument now gives the length of $\bar{PQ}$ .

(iii) Draw any line $'l'$ . Choose a point A on $'l'$ . Without changing the compasses setting, place the pointer on A.

Draw an arc that cuts at $'l'$ a point, say B. Now $\bar{AB}$ is a copy of $\bar{PQ}$ .

Answer: The steps of construction are followings:

(i) Given $\bar{AB}$ whose length is not known.

(ii) Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of $\bar{AB}$ .

(iii) Draw any line $'l'$ . Choose a point P on $'l'$ . Without changing the compasses setting, place the pointer on Q.

(iv) Draw an arc that cuts $'l'$ at a point R.

(v) Now place the pointer on R and without changing the compasses setting, draw another arc that cuts $'l'$ at a point Q.

Thus $\bar{PQ}$ is the required line segment whose length is twice that of AB.

## NCERT Class 6 Maths Chapter 14 Practical Geometry Exercise 14.4

Answer: The steps of constructions are the following:

(i) With M as the centre and a convenient radius, draw an arc intersecting the line AB at two points C and B.

(ii) With C and D as centres and a radius greater than MC, draw two arcs, which cut each other at P.

(iii) Join PM. Then PM is perpendicular to AB through point M.

Answer: The steps of constructions are:

(i) Place a set-square on $PQ$ such that one arm of its right angle aligns along $PQ$ .

(ii) Place a ruler along the edge opposite to the right angle of the set-square.

(iii) Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.

(iv) Join RM along the edge through R meeting $PQ$ at M. Then RM ⊥ PQ.

Answer: The steps of construction are as follows:

(i) Draw a line $'l'$ and take point X on it.

(ii) With X as the centre and a convenient radius, draw an arc intersecting the line $'l'$ at two points A and B.

(iii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.

(iv) Join AC and produce it to Y. Then XY is perpendicular to $'l'$ .

(v) With Y as the centre and a convenient radius, draw an arc intersecting XY at two points C and D.

(vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.

(vii) Join YF, then YF is perpendicular to XY at Y.

## NCERT Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

Answer: The axis of symmetry of the line segment $\bar{AB }$ will be the perpendicular bisector of $\bar{AB }$ . So, draw the perpendicular bisector of AB.

The steps of constructions are as follows:

(i) Draw a line segment $\bar{AB }$ = 7.3 cm

(ii) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.

(iii) Join CD. Then CD is the axis of symmetry of the line segment AB.

Answer: The steps of constructions are:

(i) Draw a line segment $\bar{AB}$ = 9.5 cm

(ii) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.

(iii) Join CD. Then CD is the perpendicular bisector of $\bar{AB}$ .

Answer: Follow the steps to draw the perpendicular bisector of a line XY.

a) PX= PY

b)MX=MY

Answer: The steps of constructions are:

(i) Draw a line segment AB = 12.8 cm

(ii) Draw the perpendicular bisector of $\bar{AB}$ which cuts it at C. Thus, C is the mid-point of $\bar{AB}$ .

(iii) Draw the perpendicular bisector of $\bar{AC}$ which cuts it at D. Thus D is the mid-point of .

(iv) Again, draw the perpendicular bisector of $\bar{CB}$ which cuts it at E. Thus, E is the mid-point of $\bar{CB}$ .

(v) Now, point C, D, and E divide the line segment $\bar{AB}$ in the four equal parts.

(vi) By actual measurement, we find that

$\bar{AD} = \bar{DC} = \bar{CE} = \bar{EB} = 3.2cm$

Answer: The steps of constructions are:

(i) Draw a line segment $\bar{PQ}$ = 6.1 cm.

(ii) Draw the perpendicular bisector of PQ which cuts, it at O. Thus O is the mid-point of $\bar{PQ}$ .

Taking O as the centre and OP or OQ as radius draw a circle where the diameter is the line segment $\bar{PQ}$ .

Answer: The steps of constructions are:

(i) Draw a circle with centre C and radius 3.4 cm.

(ii) Draw any chord $\bar{AB}$ .

(iii) Taking A and B as centres and radius more than half of $\bar{AB}$ , draw two arcs which cut each other at P and Q.

(iv) Join PQ. Then PQ is the perpendicular bisector of $\bar{AB}$ .

This perpendicular bisector of $\bar{AB}$ passes through the centre C of the circle.

Answer: The steps of constructions are:

(i) Draw a circle with centre C and radius 3.4 cm.

(ii) Draw its diameter $\bar{AB}$

(iii) Taking A and B as centres and radius more than half of it, draw two arcs which intersect each other at P and Q.

(iv) Join PQ. Then PQ is the perpendicular bisector of $\bar{AB}$

We observe that this perpendicular bisector of $\bar{AB}$ passes through the centre C of the circle.

Answer: The steps of constructions are:

(i) Draw the circle with O and radius 4 cm.

(ii) Draw any two chords $\bar{AB}$ and $\bar{CD }$ in this circle.

(iii) Taking A and B as centres and radius more than half AB, draw two arcs which intersect each other at E and F.

(iv) Join EF. Thus EF is the perpendicular bisector of chord $\bar{CD }$ .

(v) Similarly draw GH the perpendicular bisector of chord $\bar{CD }$ .

These two perpendicular bisectors meet at O, the centre of the circle.

Answer: The steps of constructions are:

(i) Draw any angle with vertex O.

(ii) Take a point A on one of its arms and B on another such that

(iii) Draw perpendicular bisector of $\bar{OA}$ and $\bar{OB}$ .

(iv) Let them meet at P. Join PA and PB.

With the help of divider, we obtained that $\bar{PA} = \bar{PB}.$

## NCERT Class 6 Maths Chapter 14 Practical Geometry Topic 14.5.4 Angles of Special Measures

Question: How will you construct a 15° angle?

Answer: First, we make $30^{\circ},$ and then its bisector.

The steps of constructions are:

1. Draw a ray OA.

2. Taking O as the center and any radius of your own choice, draw an arc cutting OA at B.

3. Now, taking B as center and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.

4. Draw the ray OD passing through the C.

Thus, $\angle AOD = 60^{\circ}$

Now, we draw bisector of $\angle AOD$

5. Taking C and D as the center, with radius more than $\frac{1}{2}CD$ , draw arcs intersecting at E.

6. Join OE.

Thus, $\angle AOE = 30^{\circ}$

Now, we draw the bisector of $\angle AOD$

7. Mark point P where the ray OE intersects the arc.

8. Taking P and B as center, with having the radius more than $\frac{1}{2}PB$ , draw arcs intersecting at F.

9. Join OF

Thus, $\angle AOF = 15^{\circ}.$

Question: How will you construct a 150° angle?

Answer: Take a line segment, say, AB.

Choose a point C on it.

With center C, and radius BC, draw an arc.

With center B and radius BC, cut the previous arc at say DD.

$(\angle DCB=60^{\circ}\ because\ we\ just\ made\ CD=BC=BD )$

With center D, and radius BC draw an arc.

With center B and radius BC, cut this arc at, say, EE.

Then EC is the bisector of ∠BCD, and

Hence, $\angle BCE=30^{\circ}$

Then, $\angle ACE=180^{\circ} - \angle BCE=150^{\circ}$

Question: How will you construct a 45° angle?

1. Draw a ray OA.

2. Taking O as center and any radius, draw an arc cutting OA at B.

3. Now, taking B as center and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.

4. With C as the center and the same radius, draw an arc cutting the arc at D.

\

5. With C and D as centers and radius more than , draw two arcs intersecting at P.

6. Join OP.

Thus,

Now, we draw the bisector of

7. Let OP intersects the original arc at point Q.

8. Now, taking B and Q as centers, and radius greater than draw two arcs intersecting at R.

9. Join OR.

Thus,

## Question: 1 Draw $\angle$ POQ of measure 75° and find its line of symmetry.

1. Draw a ray OA.

2. Place the centre of the protractor on point O, and coincide line OA and Protractor line

3. Mark point B on 75 degrees.

4. Join OB

Therefore

Now, we need to find its line of symmetry

that is, we need to find its bisector.

1. Mark points C and D where the arc intersects OA and OB

2. Now, taking C and D as centres and with the radius more than , draw arcs to intersects each other.

3. Let them intersects at point E.

4. Join O and E.

Therefore OE is the line of symmetry of

Answer: The steps of constructions are:

1. Draw a line OA.
2. Using protractor and centre 'O draw an angle AOB =147°.
3. Now taking 'O' as the centre and any radius draws an arc that intersects 'OA' and 'OB' at p and q.
4. Now take p and q as centres and radius more than half of PQ, draw arcs.
5. Both the arcs intersect at 'R'
6. Join 'OR' and produce it.
7. 'OR' is the required bisector of angle AOB.

(a) Draw a line PQ and take a point O on it.

(b) Taking O as the centre and convenient radius, draw an arc that intersects PQ at A and B.

(c) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.

(d) Join OC. Thus, ∠COQ is the required right angle.

(e) Taking B and E as centre and radius more than half of BE, draw two arcs that intersect each other at point D.

(f) Join OD. Thus, the OD bar is the required bisector of ∠COQ.

Answer: The steps of constructions are:

(a) Draw a ray OA.

(b) At O, with the help of a protractor, construct ∠AOB = 153 degrees.

(c) Draw OC as the bisector of ∠AOB.

(d) Again, draw OD as bisector of ∠AOC.

(e) Again, draw OE as bisector of,∠BOC.

(f) Thus, OC, OD, and OE divide ∠AOB into four equal parts.

Answer: The steps of constructions are:

1. Draw a ray OA

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.

3. Taking P as the centre and the same radius, cut the previous arc at Q. Join OQ. Thus,∠BOA is the required angle of 60°

30 o

Answer: The steps of constructions are:

1. Draw a ray OA.

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.

3. Taking P as the centre and the same radius, cut the previous arc at Q. Join OQ. Thus, ∠BOA is the required angle of 60°.

4. Put the pointer on P and mark an arc.

5. Put the pointer on Q and with the same radius, cut the previous arc at C. Thus, ∠COA is required angle of 30°

90 o

Answer: The steps of constructions are:

1. Draw a ray OA

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at X.

3. Taking X as the centre and the same radius, cut the previous arc at Y. Taking Y as the centre and the same radius, draw another arc intersecting the same arc at Z. 4. Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at S.

5. Join the OS. Thus, ∠SOA is a required angle of 90°

120 o

Answer: The steps of constructions are:

1. Draw a ray OA

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.

3. Taking P as the centre and same radius, cut the previous arc at Q. Taking Q as the centre and the same radius cut the arc at S. Join OS. Thus, ∠AOS is the required angle of 120°.

45 o

Answer: The steps of constructions are:

1. Draw a ray OA

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at X.

3. Taking X as the centre and the same radius, cut the previous arc at Y. Taking Y as the centre and the same radius, draw another arc intersecting the same arc at Z.

4. Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at S. Join OS. Thus, ∠SOA is a required angle of 90°.

5. Draw the bisector of SOA. Hence, ∠MOA = 45°

135 o

Answer: The steps of constructions are:

1. Draw a line PQ and take a point O on it.

2. Taking O as the centre and convenient radius, mark an arc, which intersects PQ at A and B.

3. Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R. Join OR. Thus, ∠QOR = ∠POR = 90°.

4. Draw OD the bisector of ∠POR. Thus, ∠QOD is required angle of 135°

Answer: The steps of constructions are:

1. Draw a ray OA

2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at X.

3. Taking X as a centre and the same radius, cut the previous arc at Y. Taking Y as the centre and the same radius, draw another arc intersecting the same arc at Z.

4. Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at S. Join OS. Thus, ∠SOA is a required angle of 90°.

5. Draw the bisector of ∠SOA. Hence, ∠MOA = 45°

6. Draw the bisector of ∠MOA. Hence, ∠NOA= 22.5 0

Answer: The steps of constructions are:

(a) Draw a line PQ and take a point O on it.

(b) Taking O as the centre and convenient radius, mark an arc, which intersects PQ at A and B.

(c) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.

(d) Join OR. Thus, ∠QOR = ∠POQ = 90 .

(e) Draw OD the bisector of ∠POR. Thus, ∠QOD is the required angle of 135.

(f) Now, draw OE as the bisector of ∠QOD=1/2 of 135=67.5

Answer: The steps of constructions are:

(a) Draw an angle 70 degrees with a protractor, i.e., ∠POQ = 70 degrees

(b) Draw a ray AB.

(c) Place the compasses at O and draw an arc to cut the rays of ∠POQ at L and M.

(d) Use the same compasses, setting to draw an arc with A as the centre, cutting AB at X.

(e) Set your compasses setting to the length LM with the same radius.

(f) Place the compasses pointer at X and draw the arc to cut the arc drawn earlier at Y.

(g) Join AY. Thus, ∠YAX = 70 degree

The steps of constructions are:

(a) Draw an angle of 40 degrees with the help of a protractor, naming ∠ AOB.

(b) Draw a line PQ.

(c) Take any point M on PQ.

(d) Place the compasses at O and draw an arc to cut the rays of ∠AOB at L and N.

(e) Use the same compasses setting to draw an arc O as the centre, cutting MQ at X.

(g) Place the compasses at X and draw the arc to cut the arc drawn earlier Y.

(h) Join MY.

(i) Thus, < QMY = 40 degree and < PMY is supplementary of it.

## Main Topics of NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

• The Circle
• Construction of a circle when its radius is known
• A-Line Segment
• Construction of a line segment of a given length
• Constructing a copy of a given line segment
• Perpendiculars
• Perpendicular to a line through a point on it
• Perpendicular to a line through a point not on it
• The perpendicular bisector of a line segment
• Angles
• Constructing an angle of a given measure
• Constructing a copy of an angle of an unknown measure
• Bisector of an angle
• Angles of special measures

Also Check

NCERT Books and NCERT Syllabus

## NCERT Solutions for Class 6 Mathematics Chapter Wise

 Chapters No. Chapters Name Chapter - 1 Chapter - 2 Chapter - 3 Chapter - 4 Chapter - 5 Chapter - 6 Chapter - 7 Chapter - 8 Chapter - 9 Chapter -10 Chapter -11 Chapter -12 Chapter -13 Symmetry Chapter -14 Practical Geometry

## Key Features of NCERT Solutions for Class 6 Maths Chapter 14

Expertly Crafted Solutions: The NCERT Solutions for Chapter 14 are meticulously developed to offer clear and precise explanations for all the problems and concepts discussed in the chapter.

Conceptual Clarity: The solutions aim to improve students' conceptual understanding by simplifying complex topics and presenting them in a more comprehensible manner.

Comprehensive Coverage: The solutions cover all the essential topics and subtopics of Chapter 14, ensuring that students gain a thorough understanding of the entire chapter.

## NCERT Solutions for Class 6 Subject Wise

### Benefits of NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry-

• You will get NCERT Solutions for Class 6 very easily.
• You will get some different ways to construct geometrical in this solution article.
• There are some figures and images given in these solutions. It will help you in drawing geometrical figures easily.
• In CBSE NCERT solutions for Class 6 Maths chapter 14 Practical Geometry, you will find that questions are explained with step-by-step to construct lines and geometrical figures with the help of compass and rulers. So you can understand easily

Happy learning!!!

1. How to draw geometrical shapes in accurate sizes and accurate angle

We need some instruments to draw geometrical shapes in accurate size and accurate angle here are some given below;

• The compasses
• The Ruler
• The Divider
• Scale
• Protractor
2. What is line segment?

The line segment is the least possible distance between the two given points. above in this article we have discussed some problems based on this concept. Practice them to get in-depth understanding the concepts. These concepts also gives drawing ideas for class 6 which are useful for upcoming classes.

3. What is a circle?

In a circle the points on its boundary is at an equal distance to its center such a geometrical shape is called a circle. practice problems based on the circle given with detailed and comprehensive solution to get command in the concepts. these concepts are comprehensively covered in class 6 chapter 14 maths.

4. What are the topics are covered in NCERT solution Class 6 Chapter Practical Geometry?

The following are covered in NCERT solution for class 6 maths chapter 14:

• The Circle
• Construction of a circle when its radius is known
• A-Line Segment
• Construction of a line segment of a given length
• Constructing a copy of a given line segment
• Perpendiculars
• Perpendicular to a line through a point on it
• Perpendicular to a line through a point not on it
• The perpendicular bisector of a line segment
• Angles
• Constructing an angle of a given measure
• Constructing a copy of an angle of an unknown measure
• Bisector of an angle
• Angles of special measures

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 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9
##### Bio Medical Engineer

The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.

4 Jobs Available

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

4 Jobs Available
##### Database Architect

If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi

3 Jobs Available
##### Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Geothermal Engineer

Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

3 Jobs Available
##### Geotechnical engineer

The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction.

The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions.

3 Jobs Available
##### Cartographer

How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.

3 Jobs Available
##### Bank Probationary Officer (PO)

A career as Bank Probationary Officer (PO) is seen as a promising career opportunity and a white-collar career. Each year aspirants take the Bank PO exam. This career provides plenty of career development and opportunities for a successful banking future. If you have more questions about a career as  Bank Probationary Officer (PO), what is probationary officer or how to become a Bank Probationary Officer (PO) then you can read the article and clear all your doubts.

3 Jobs Available
##### Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Finance Executive

A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.

3 Jobs Available
##### Investment Banker

An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

3 Jobs Available
##### Bank Branch Manager

Bank Branch Managers work in a specific section of banking related to the invention and generation of capital for other organisations, governments, and other entities. Bank Branch Managers work for the organisations and underwrite new debts and equity securities for all type of companies, aid in the sale of securities, as well as help to facilitate mergers and acquisitions, reorganisations, and broker trades for both institutions and private investors.

3 Jobs Available
##### Treasurer

Treasury analyst career path is often regarded as certified treasury specialist in some business situations, is a finance expert who specifically manages a company or organisation's long-term and short-term financial targets. Treasurer synonym could be a financial officer, which is one of the reputed positions in the corporate world. In a large company, the corporate treasury jobs hold power over the financial decision-making of the total investment and development strategy of the organisation.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
##### Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
##### Carpenter

Carpenters are typically construction workers. They stay involved in performing many types of construction activities. It includes cutting, fitting and assembling wood.  Carpenters may help in building constructions, bridges, big ships and boats. Here, in the article, we will discuss carpenter career path, carpenter salary, how to become a carpenter, carpenter job outlook.

2 Jobs Available
##### Welder

An individual who opts for a career as a welder is a professional tradesman who is skilled in creating a fusion between two metal pieces to join it together with the use of a manual or fully automatic welding machine in their welder career path. It is joined by intense heat and gas released between the metal pieces through the welding machine to permanently fix it.

2 Jobs Available
##### Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.

2 Jobs Available
##### Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

2 Jobs Available
##### Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.

2 Jobs Available
##### Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
##### Veterinary Doctor

A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

5 Jobs Available
##### Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
##### Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

4 Jobs Available
##### Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
##### Surgical Technologist

When it comes to an operation theatre, there are several tasks that are to be carried out before as well as after the operation or surgery has taken place. Such tasks are not possible without surgical tech and surgical tech tools. A single surgeon cannot do it all alone. It’s like for a footballer he needs his team’s support to score a goal the same goes for a surgeon. It is here, when a surgical technologist comes into the picture. It is the job of a surgical technologist to prepare the operation theatre with all the required equipment before the surgery. Not only that, once an operation is done it is the job of the surgical technologist to clean all the equipment. One has to fulfil the minimum requirements of surgical tech qualifications.

3 Jobs Available
##### Maxillofacial Surgeon

A Maxillofacial Surgeon is a medical professional who performs facial surgeries that include tooth implant, neck, head or other surgeries such as removal of tumours, cosmetic surgeries and treatment of injuries on the face.

2 Jobs Available
##### Surgical Assistant

Surgical assistants are professionals in the service of saving others’ lives. They perform various medical procedures. In a career as a surgical assistant, one works in a team and contributes to the success of operations. Surgical assistants learn new procedures and update their knowledge of new medical technology and equipment. Surgical assistants clean and sterilize the tools used in surgery. In a career as a surgical assistant, individuals perform all the basic duties that allow surgeons to keep their focus on essential technical functions.

2 Jobs Available
##### Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.

4 Jobs Available
##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Visual Communication Designer

Individuals who want to opt for a career as a Visual Communication Designer will work in the graphic design and arts industry. Every sector in the modern age is using visuals to connect with people, clients, or customers. This career involves art and technology and candidates who want to pursue their career as visual communication designer has a great scope of career opportunity.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available

Advertising managers consult with the financial department to plan a marketing strategy schedule and cost estimates. We often see advertisements that attract us a lot, not every advertisement is just to promote a business but some of them provide a social message as well. There was an advertisement for a washing machine brand that implies a story that even a man can do household activities. And of course, how could we even forget those jingles which we often sing while working?

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

3 Jobs Available

A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

2 Jobs Available
##### Quality Systems Manager

A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party.

2 Jobs Available
##### Merchandiser

A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying.

2 Jobs Available
##### Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.

2 Jobs Available
##### Production Planner

Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner.

2 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### .NET Developer

.NET Developer Job Description: A .NET Developer is a professional responsible for producing code using .NET languages. He or she is a software developer who uses the .NET technologies platform to create various applications. Dot NET Developer job comes with the responsibility of  creating, designing and developing applications using .NET languages such as VB and C#.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### DevOps Architect

A DevOps Architect is responsible for defining a systematic solution that fits the best across technical, operational and and management standards. He or she generates an organised solution by examining a large system environment and selects appropriate application frameworks in order to deal with the system’s difficulties.

2 Jobs Available
##### Cloud Solution Architect

Individuals who are interested in working as a Cloud Administration should have the necessary technical skills to handle various tasks related to computing. These include the design and implementation of cloud computing services, as well as the maintenance of their own. Aside from being able to program multiple programming languages, such as Ruby, Python, and Java, individuals also need a degree in computer science.

2 Jobs Available