CBSE Class 10 Maths Question Paper 2016 with Solutions

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# CBSE Class 10 Maths Question Paper 2016 with Solutions

Edited By Safeer PP | Updated on Aug 21, 2023 01:49 PM IST | #CBSE Class 10th

CBSE Class 10 Maths Question Paper 2016 with Solutions - Are you looking for CBSE 10 maths question paper 2016, then you are at the right place. The board releases the question papers for the preparation of CBSE exams. Solving CBSE previous year question papers Class 10 Maths 2016 is an important part of the strategy for the board exam preparation. Students will get to know the exam pattern by referring to CBSE previous year papers and feel more confident to face the exam after solving CBSE class 10 maths question paper 2016. Here, you will get detailed analysis and solutions of CBSE previous year question papers Class 10 Maths 2016 for all the sets. Students should refer to CBSE class 10 maths question paper 2016 with solutions a one month before the exam.
Also, check CBSE previous year papers of Class 10 maths with solutions

CBSE class 10 maths 2016 question paper set-wise

Here, we have solved the maths board paper 2016 class 10 CBSE PDF, students looking for solutions must check this section. It is advised to solve CBSE class 10 math sample paper and question paper as much as possible for better practice. These CBSE 10th maths 2024 question paper set wise solution can be really helpful in knowing the mistakes and improving your performance.

### CBSE 10 Class 2016 Paper: 030 set 1 Maths

Question 1)

In fig .1 PQ is a tangent at a point C to a circle with center O . If AB is diameter and

$\angle CAB = 30 , find \: \: \angle PCA$

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Question 2)

For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of A.P ?

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Question 3)

A ladder leaning against a wall, makes an angle of 60 with the horizontal.

If the foot of the ladder is 2.5 m away from the wall , find the length of the ladder.

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Question 4)

A card is drawn at random from a well-shuffled pack of 52 playing cards.

Find the probability of getting neither a red card nor a queen .

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Question 5)

If -5 is a root of the quadratic equation $2x^2 + px -15 = 0$ and the quadratic equation $p ( x^2 + x )+ k = 0$ has equal roots, find the value of k.

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Question 6)

Let P and Q be the points of trisection of the line segment joining the point A(2,-2) and B (-7,4) such that P is nearer to A. Find the coordinates of P and Q

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Question 7)

In fig 2 a quadrilateral ABCD is drawn to circumscribe a circle, with center O, in such a way that the sides AB, BC, CD, and DA touch the circle at the points P, Q, R, and S respectively. Prove that AB + CD = BC + DA

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Question 8)

Prove that the points (3,0) (6,4) and (-1,3) are the vertices of a right-angled isosceles triangle

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Question 9)

The fourth term of an AP is Zero . Prove that the 25th term of the AP is three times its 11th term

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Question 10)

In fig 3 from an external point P , two tangents PT and PS are drawn to a circle with centre O and raidus r .

If OP = 2r , show that $\angle OTS = \angle OST = 30 \degree$

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Question 11)

In fig 4 , O is the center of circle such that diameter AB = 13 cm and AC = 12 cm . BC is joined . Find the area of the shaded region

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Question 12)

In fig 5 , a tent is in the shape of a cylinder surmounted by a conical top of the same diameter. If the height and diameter of the cylinder part are 2.1 m and 3 m respectively and the slant height of the conical part is 2.8, find the cost of canvas needed to make the tent if the canvas is available at the rate of 500/sq.meter

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Question 13)

If the point P(x,y) is equidistant from the point A (a-b, a +b ) and B (a-b, a +b ). Prove that bx = ay

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Question 14)

In fig , find the area of the shaded region , enclosed between two concentric circles of radii 7 cm and 14 cm where

$\angle AOC = 40 \degree$

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Question 15)

If the ratio of sum of first n terms of two A.P s is (7n+1):(4n+27), find the ratio of their $m ^{th }$ term

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Question 16)

solve for x : $\frac{1 }{( x-1)(x-2)} + \frac{1}{( x-2 )( x-3)}= 2/3 , x \neq 1,2,3\\\\$

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Question 17)

A sphere of diameter 12 cm, is dropped in a right circular cylinder vessel, partly filled with water.

If the sphere is completely submerged in water, the water level in the cylinder vessel rises by $3 \frac{5}{9}$ cm. Find the diameter of the cylindrical vessel.

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Question 18)

A man standing on the deck of a ship, which is 10 m above water level, observe the angle of elevation of the top of aa hell as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill from the ship and the height of the hill.

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Question 19)

Three different coins are tossed together. Find the probability of getting

3) at least 2 tails

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Question 20)

Due to heavy floods in a state, thousands were rendered homeless, 50 schools collectively offered to the state governments to provide the place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally The lower part of each tent is cylindrical of base radius 2.8m and height 3.5, with the conical upper part of the same base radius but of height 2.1m. If the canvas used to make the tents cost 120 per sq.m, find the amount shared by each school to set up the tents. what value is generated by the above problem?

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Question 21)

Prove that the lengths of the tangents drawn from an external point to a circle are equal

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Question 22)

Draw a circle of radius 4cm. Draw two tangents to the circle inclined at an angle of $60 \degree$ to each other

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Question 23)

In fig.7 two equal circles , with center O and O' , touch each other at X. OO' produce meets the circle with center O' at A . AC is tangent to the circle with center O , at the point C. O'D is perpendicular to AC. Find the value of $\frac{DO'}{CO}$

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Question 24)

Solve for x : $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4} , x \neq -1 ,-2,-4$

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Question 25)

The angle of elevation of the top Q of aa vertical tower PQ from a point X on the ground 60. From a point Y , 40m vertically above X, the angle of elevation of the top Q of the tower is 45. Find the height of the tower PQ and the distance PX

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Question 26)

The houses in a row are numbered consecutively from 1 to 49. show that there exists a value of X such that sum of numbers of horses proceeding the house numbered X is equal to sum of the numbers of houses following X

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Question 27)

In fig.8 , the vertices of $\Delta ABC$ are A (4,6), B(1,5) and C(7,2) . A line segment CE is drawn to intersect the sides AB and AC at

D and E respectively such that $\frac{AD}{AB} = \frac{AE }{AC} = \frac{1}{3}$ . Calculated the area of $\Delta ADE$ and compare it with area of $\Delta ABC$

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Question 28)

A number x is selected at random from the numbers 1,2,3 and 4 .Another number y is selected at random from the numbers 1,4,9 and 16. Find the probability that product of x and y is less than 16

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Question 29)

In fig.9 is shown a sector OAP of a circle with center O, containing $\angle \theta$. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of the shaded region is $r \left [ \tan \theta + \sec \theta + \frac{\pi \theta }{180}-1 \right ]$

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Question 30)

A motorboat whose speed is 24 Km/hr in still water takes 1 hour more go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

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Question 31)

A conical vessel, with base radius 5 cm and height 24cm, is full of water. This water is emptied into a cylinder vessel of base radius 10 cm. Find the height to which the water will rise in the cylinder vessel

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### CBSE 10 Class 2016 Paper: 030 set 2 Maths

Question 1)

Solve for x :

$\sqrt {2x+9} + x = 13$

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Question 2)

The digit of a positive of three digits are in AP and their sum is 15

The number obtained by reversing the digits is 594 less than the original number. Find the number.

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Question 3)

If the roots of the quadratic equation $( a-b)x^2 + ( b -c)x + ( c -a ) =0$ are equal , prove that $2a = b+c$

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Question 4)

From a pack of 52 playing cards, jacks, queens, and kings of red queen color are removed.

From the remaining, a card is drawn at random. Find the probability that the drawn card is :

1) a black king

2 ) a card of red color

3 ) a card of black colour

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Question 5)

Draw an isosceles $\Delta ABC$ in which BC = 5.5 cm and altitude AL = 3 cm .

Then construct another triangle whose sides are 3/4 of the corresponding sides of $\Delta ABC$

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Question 6)

Prove the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact

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Question 7)

As observed from the top of a lighthouse, 100 m high above sea level, the angles of depression of ship, sailing directly towards it , changes from $30 \degree$ to $60 \degree$ . Find the distance traveled by ship during the period of observation

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### CBSE 10 Class 2016 Paper: 030 set 3 Maths

Question 1)

solve for x : $\sqrt { 6x+7} - ( 2x-7) = 0$

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Question 2)

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out of the bag at random. Find the probability that the number on the selected cards (1) is divisible by 9 and is a perfect square (2) is a prime number greater than 80

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Question 3)

Three consecutive natural number are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers

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Question 4)

The sums of first n terms of three arithmetic progression are $S_1 , S_2 , S_3$ respectively. The first term of each A.P. is 1 and their common difference are 1,2,3 respectively. Prove that $S_1 +S_3 =2 S_2$

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Question 5)

Two pipes running together can fill in $11 \frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately

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Question 6)

Draw a triangle with sides 5cm, 6cm and 7cm . Then draw another triangle whose sides are 4/5 of the corresponding sides of first triangle

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Question 7)

From a point on the ground, the angle of elevation of the top of a tower is observed to be 60 degree. From a point 40m vertically above the first point of observation, the angle of elevation of the top of the tower is 30 degree. Find the height of the tower and its horizontal distance from the point of observation

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## How to Solve CBSE Class 10 Maths Question Paper 2016 with Solutions?

• First, try to solve CBSE previous year question papers Class 10 Maths 2016 on your own within the given time period.
• If you find difficulties while solving them, you can take help from these CBSE class 10 maths question paper 2016 with solutions provided in this article.
• Solutions of CBSE 10 maths question paper 2016 are prepared and explained in a detailed manner which can be understood easily.

After completing the entire syllabus of NCERT class 10 maths, you must practice the previous 5 years Class 10 CBSE question paper. It will also help you in the complete the final board paper on time and score well in the exam. In CBSE class 10 maths chapter 'Geometry' is considered to be the difficult chapter where most of the students feel trouble. Solving more problems from these chapters will help you to get command on these chapters.

## CBSE Class 10 Maths 2016 Question Paper Pattern

CBSE Class 10 Maths Question Paper 2016 consists of 31 questions divided into four sections A, B, C, D. All these questions are compulsory.

• CBSE 10 maths question paper 2016 contains four questions of one mark each where you need to answer in one word or one sentence as per the exact requirement of the question.

• Section B of CBSE class 10 maths question paper 2016 with solutions contains six short answer type questions of two marks each where you need to answer as per the exact requirement of the question.

• CBSE class 10 maths question paper 2016 section C contains 10 questions of three marks each where you need to provide complete solutions for each question.

• Section D of the CBSE previous year question papers Class 10 Maths 2016 contains 11 long answer type questions of four marks each where you need to write a step-by-step complete solution for each question.

Note:- There is no internal choice given in CBSE 10 maths question paper 2016.

CBSE Class 10 Maths Question Paper 2016 with Solutions - Section-wise Division

 Sl. No Sections Marks Number of questions Total marks 1 A 1 4 4 2 B 2 6 12 3 C 3 10 30 4 D 4 11 44

## CBSE class 10 maths 2016 question paper analysis

CBSE has conducted class 10 maths paper on the 19th March 2016 from 10.15 a.m. to 10.30 a.m. The starting 15 minute time has been allotted to read this question paper. This year's paper was considered to be tougher than the last year. Although most of the questions were directly taken from the NCERT or similar to the NCERT. Chater-wise marks distributions are tabulated below.

## CBSE Class 10 Maths Question Paper 2016 Analysis

 Sl.No Chapter Name Set 30/1/1 1 Real Numbers 0 2 Polynomials 0 3 Pair of Linear Equations in Two Variables 0 4 Quadratic Equations 2+4+4 5 Arithmetic Progressions 1+2+3+4 6 Triangles 2+3+4 7 Coordinate Geometry 2+3 8 Introduction to Trigonometry 0 9 Some Applications of Trigonometry 1+3+4 10 Circles 1+2+2+4+4 11 Constructions 4 12 Areas Related to Circles 3+3+4 13 Surface Areas and Volumes 3+3+3+4 14 Statistics 0 15 Probability 1+3+4

$\begin{array}{llll} \text { Difficulty Level } & \text { Count } & \text { Weightage } & \text { \% Weightage } \\ \text { Easy } & 13 & 32 & 35.6 \\ \text { Average } & 16 & 50 & 55.6 \\ \text { Difficult } & 2 & 8 & 8.9 \end{array}$

From the above analysis you can see that chapter 'Circles' has the highest weightage followed by the 'Surface area and volumes' in this paper. Only about 10% of the questions were difficult. Overall this paper was an average level but a little lengthier. Students who have conceptual clarity can score full marks also. Some students found it lengthy and weren't able to complete this paper on time. Students who have practiced well and solved some previous year's papers were able to complete this paper on time. An average student can score above 80 percent marks in this paper easily.

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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
##### 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
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Talent Director

Individuals who opt for a career as a talent director are professionals who work in the entertainment industry. He or she is responsible for finding out the right talent through auditions for films, theatre productions, or shows. A talented director possesses strong knowledge of computer software used in filmmaking, CGI and animation. A talent acquisition director keeps himself or herself updated on various technical aspects such as lighting, camera angles and shots.

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.

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##### 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
##### 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
##### Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 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
##### SEO Analyst

An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.

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##### 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.

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##### 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.

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##### 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
##### 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
##### IT Consultant

An IT Consultant is a professional who is also known as a technology consultant. He or she is required to provide consultation to industrial and commercial clients to resolve business and IT problems and acquire optimum growth. An IT consultant can find work by signing up with an IT consultancy firm, or he or she can work on their own as independent contractors and select the projects he or she wants to work on.

2 Jobs Available
##### Data Architect

A Data Architect role involves formulating the organisational data strategy. It involves data quality, flow of data within the organisation and security of data. The vision of Data Architect provides support to convert business requirements into technical requirements.

2 Jobs Available
##### Security Engineer

The Security Engineer is responsible for overseeing and controlling the various aspects of a company's computer security. Individuals in the security engineer jobs include developing and implementing policies and procedures to protect the data and information of the organisation. In this article, we will discuss the security engineer job description, security engineer skills, security engineer course, and security engineer career path.

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##### UX Architect

A UX Architect is someone who influences the design processes and its outcomes. He or she possesses a solid understanding of user research, information architecture, interaction design and content strategy.

2 Jobs Available