ITI Courses

Over the last few years, students who pass out 12th, prefer to join ITI. They find a good career through these courses. These courses provide more scope in technical fields like hardware support and similar jobs in Public Sector.

In this session, we will discuss the different aspects of ITI.

What is ITI?

ITI or the Industrial Training Institutes and Industrial Training Centres are the centres providing technical training, established under the Ministry of Labour, Union Government of India.

The ITIs are the organisations run by the government, while the ITCs are run by private organisations. Both provide technical training provided after your school education. In 2002, 1800 ITIs provided 373000 training locations and 2850 ITCs with 305000 locations.

You could choose the desired specialisation from the following:

  • Mechanical
  • Electronics
  • Computer
  • Fitter
  • Welder

ITI releases the application forms for different courses during the month of July. Candidates must clear the entrance exam to get the admission for the course. ITI courses are of two types- Engineering and Non-Engineering.

Candidates belonging to the age category of 14-40 years can apply for ITI courses. Let us discuss the ITI courses after class 12

ITI Courses after 12th

Aspirants looking for jobs after 12th could take up exclusive ITI courses. These courses help them upgrade the industry-set skills, thereby get the desired job in the specialised fields. ITI courses aim to encourage the aspirants to set small-scale businesses, creating more job opportunities.

There is another advantage of these courses for the class 12 students- these job oriented, industry-specific courses can be completed at affordable fees, which is a stepping stone to an early job in a student’s career.

Here is the tabular representation for the ITI courses after 12th:

Name of the Course Stream Duration
Computer Operator & Programming Assistant (COPA) Non-engineering 1 year
Instrument Mechanic Engineering 1 year
Stenography English Non-engineering 1 year
Radiology Technician Engineering 2 years
Stenography Hindi Non-engineering 1 year
Insurance Agent Non-engineering 1 year
Surveyor Non-engineering 2 years
Computer Hardware and Networking Engineering 2 years
Library and Information Science Non-engineering 1 year
Catering and Hospitality Assistant Non-engineering 1 year
Crèche Management Non-engineering 1 year
Gold Smith Non-engineering 2 years
Architectural Assistant Engineering 1 year
Interior Decoration and Designing Non-engineering 1 year
Desktop Publishing Operator Non-engineering 1 year
Plastic Processing Operator Non-engineering 1 year
Mechanic Lens or Prism Grinding Engineering 2 years
Mason Non-engineering 1 year
Dental Laboratory Equipment Technician Engineering 2 years
Architectural Draughtsmanship Engineering 2 years
Health and Sanitary Inspector Non-engineering 1 year
Computer Operator and Programming Assistant Engineering 2 years
Physiotherapy Technician Engineering 2 years
Craftsman Food Production Non-engineering 2 years
Travel and Tour Assistant Non-engineering 1 year
Marine Fitter Engineering 1 year
Human Resource Executive Non-engineering 1 year
Basic Cosmetology Non-engineering 1 year
Call Centre Assistant Non-engineering 1 year
Mechanic Agricultural Machinery Engineering 2 years
Old Age Care Assistant Non-engineering 1 year
Health Safety and Environment Non-engineering 1 year
Marketing Executive Non-engineering 1 year
Multimedia Animation and Special Effects Engineering 1 year

Each course have a duration of 6 months and would last up to 2 years, based on the syllabus set by ITI or the rules of DGET (Directorate General of Employment & Training). Duration of ITI courses under Engineering is more than those under non-engineering.

After the completion of the course and the training, candidates will have to take the AITT or the All India Trade Test, which includes practical as well as the theoretical exam. Candidates passing the exam would be awarded NTC (National Trade Certificate) and would be qualified to get a job in the desired field.

If you are interested in studying further, you could pursue Diploma courses in Engineering, Science, Arts & Commerce. Diploma courses with ITI certification could help you find better jobs.

ITI courses are not only for class 12 students but also for students of class 10. Let us look at the ITI courses suitable for class 10th students.

ITI Courses After 10th

Most students go through a tough time choosing the right subject for their career. ITI courses help them get a career with great job opportunities in the early stage.

Let us look at the top ITI courses for the students after completing 10th.

ITI in Instrument Mechanic

A 2-year course, comprising both practical and theory classes. On the completion, students get placed in the role of Machine mechanic, Assistant Mechanic, Instrument technician, and Instrumentation Technician

ITI in Sheet Metal Worker

Related to the industry of building development. There are many aspects covered in this course, such as cooling channel frameworks, siding, rooftops. Hence, you find jobs in construction companies

ITI in Tool & Die Making

One of the unique courses with a duration of 3 years, with aspects of metal working skills, hot-working of metals, surface grinding, cylindrical grinding, engineering drawing etc.

ITI in Radio & TV Mechanic

Many job opportunities open for students after completing this course, such as the television and radio manufacturing companies and upgrading firms apart from government endeavors. You could also consider self-employment.

ITI in Mechanic Medical Electronics

Specialising in this field could find a better career with B.E or a Diploma in Medical Electronics. After completion, you can find jobs as Biomedical equipment technician, Equipment Repairer, Network specialist etc.

ITI in Laboratory Assistant of Chemical Plant

A reputed position in chemical plants with a high salary. Duration of the course is 2 years, wherein you learn in both practical and theoretical ways. You could find high-profile jobs such as Research Associate, R&D Associate and Lab Analyst

ITI in Horticulture

Related to agriculture plant cultivation. Aspects of techniques in the fruit and vegetable cultivation. You will also learn about soil fertility and its management

ITI in Draughtsman (Mechanical)

A two-year course, wherein you get a good hold on the basic concepts of the draughtsman. You could get jobs as Junior Technical Assistant, Autocad Draughtsman, draughtsman piping and Structural Draughtsman

ITI in Building Maintenance

The course involves repairing and maintaining residential buildings with aspects such as painting, roofing, installation, and drywall. Job opportunities in commercial complexes as multi-skilled operative and maintenance assistant

ITI in Architectural Assistant

Equals the professional course, wherein most work revolves around drawing and engineering tasks, and the job nature comprises interior designing, site supervising and architectural technician

Conclusion

In this session, we discussed the various ITI courses for students of class 10 and 12 and the various job opportunities under each specialisation. Hope you find this session helpful. Choose the right career.

Courses After 10th

A few years ago, we had limited options to choose from, after completing the 10th standard exam. The main options certain Pre-University colleges were Science, Commerce, Arts in 11th and 12th standard (school level). And the Science stream has just two choices- Computer Science or Biology.

As years passed, the career choices after 10th standard increased drastically. These choices helped the students realise their real potential and found the career of their choice.

In this article, we will take a detailed look at the various courses available after 10th standard.

Diploma Courses After 10th

Apart from the regular choices such as Science, Commerce or Arts, there are certain Diploma courses that could improve their career graphs. Here are some of the best Diploma courses.

Commercial Art

Also known as Advertising Art yet differs from Fine Art. The course focuses on selling goods and services. Job opportunities in Advertising companies, publishing houses, art studios, and fashion houses. Great opportunities awaiting you!

Art Teaching

A 2-year programme, wherein the candidates would be trained on the basic rules of visual and design skills.

Beauty Culture & Hair Dressing

Course duration is 3 months or a year. The training is related to Body Care. Job opportunities in Beauty Salons

Industrial Training

Training organisations run by the government. Training provided in various fields and duration varying in each organisation. Opportunities in Public Sector

Garment Technology

A 3-year programme, providing training on utilisation of product and resources. Wide opportunities as Fashion Designer

Stenography

A course where candidates would be provided with shorthand dictations apart from the regular clerical work. Huge opportunities in both Public and Private sectors, as Stenographer, Clerk-cum-typist as well as a computer operator.

Laboratory Technician

Candidates trained in Clinical Laboratory, with duration depending on the course chosen; in corresponding laboratory technology. After completion, there are opportunities as Lab Technician, Assistant etc. Candidates can also choose self-employment

Hotel Management & Catering Technology

A 2-year programme, wherein the candidates learn the Hotel Management skills.

Engineering

A wide variety of choices. Certain technical diplomas rated below the undergraduate level, such as Mechanical, Civil, Automobile, Environmental, Fire Safety, Architecture, Computers, Electrical.

Best Courses After 10th

We discussed some of the top diploma courses helpful for students who passed out 10th standard. Students have become smarter in choosing their career. They start realising their talents and potential during their high school days. Hence, they start planning accordingly.

So, here are the top courses which help them get the job quickly. Let us look at the best courses:

Industrial Training

Vocational courses at Industrial Training Institutes are one of the best choices a student can choose from, after completing the 10th standard. ITI offers these courses with a job assurance:

  • Medical Technician
  • Mechanical Draftsman
  • Civil Draftsman
  • Chemical Plant Operator
  • Laboratory Technician
  • Quantity Surveyor
  • Airline Steward/ Stewardess
  • Hospitality Staff
  • Photography
  • Caregiver
  • Legal/ Para-Legal Assistant.
  • Automobile Mechanical Technician
  • Automobile Electrical Technician
  • Horticulture
  • Body & Beauty Care
  • Fireman and Disaster Relief
  • Dental Lab Technician
  • Denture Maker
  • Food Technician
  • Agricultural Farm Management
  • Dairy Management
  • Nutrition Assistant
  • Baking & Confectioning
  • Desktop Publishing
  • Corporate Housekeeping
  • Fashion Designing
  • Event Management
  • Facilities Management (old-age homes, hospitals etc)
  • IT and Electronics Maintenance
  • Welding Technician
  • Air Conditioning & Refrigeration Technician
  • Data Entry Operator
  • Floriculture & Commercial Landscaping
  • Food Processing
  • Logistics Assistant
  • Communications Equipment Technician

Students can take these courses easily as they are affordable and economical. These courses can help you find a job, anywhere in India as well as abroad.

Engineering

Apart from the regular graduate courses in Engineering stream, students can choose from a good set of Diploma courses after completing 10th. This could be an advantage if they wish to pursue Engineering as their career. Here are the specialisations from which they could choose the right career path:

  • Mechanical
  • Civil
  • Chemical
  • Electrical
  • Metallurgical

Medical Courses

It is understood that you cannot directly enter the Medical field soon after you complete 10th standard. However, if you are really interested in making a good career in Medical field, you could choose from these courses:

  • Diploma in Rural Healthcare
  • Diploma in Nursing Assistance
  • Certification in Nursing Assistance
  • Pathology Lab Technician
  • Diploma in Hospital Assitance
  • Diploma in Paramedic Nursing

Travel & Tourism

If you love travelling places, this could take you to greater heights. Find your right career path in Tourism through one of these Diploma courses:

  • Food & Beverage Management
  • Food & Beverage Production
  • Hospitality Management
  • Restaurant & Hotel Management
  • Food Technology
  • Nutrition
  • Catering & Catering Technology
  • Front Office & Reception Management
  • Hotel Stores Management

Tourism and Travel industry is in high demand. As per the World Trade Council, this is one of the fastest booming sectors across the globe.

IT & Computer

No students can avoid this booming career option of IT & Computer Technology. Find your career choice from these Certification courses. You could even choose a higher level such as Diploma courses for a better career in IT.

  • Search Engine Optimization (SEO)
  • Social Media Management
  • Search Engine Marketing (SEM)
  • Computer Technician
  • Hardware Maintenance

Indian Armed Forces

Serving your mother Nation is also very important. There are students who prefer to choose a career in Indian Army that would help them serve the country in a better way. Here are some courses by the Indian Armed Forces:

  • Soldier (General Duty)
  • Soldier (Tradesman)

Each course duration differs based on the rules set by the Armed Forces. The courses include training on arms and weapons. If you choose the Tradesman option, you would be trained on skills required during peacetime, disasters, and wars.

Conclusion

Our country is gradually developing and there are many career options being launched for young children to help them realise their skills and potentials. Students passing 10th standard can find their dream career at the very beginning, instead of waiting until they complete their 12th. Hope the article has been helpful to young children. May you achieve your goal in life.

Best Schools in India

Today’s children are tomorrow’s youth and hence ‘The Future’ of this nation, for whom the solid foundation of education is a prime focus. Directing their path in the best direction needs the best form of education, where school plays the pivotal role. So, here is the list of India’s top 20 schools:

The Doon School, Dehradun

Established in 1935, The Doon School, sprawled over an area of 72 acres is one of the finest schools in India. A boys-only independent boarding school located in Dehradun, Uttarakhand, Doon has been ranked the best among the residential schools in India by BBC, The Times of India and The New York Times. It is a school of various notable people like Rahul Gandhi – Congress Politician, Vikram Seth – writer and poet, Jyotiraditya Madhavrao Scindia – Politician etc.

Website: www.doonschool.com

Bishop Cotton Boy’s School, Bangalore

Established in 1865, Bishop Cotton Boy’s School is a boys-only school for boarders and day scholars in Bangalore, India. It is one of the top three schools in India. Sprawled over an area of 13 acres, it has excellent facilities to encourage overall personality development of the students. The school has alumni like Nandan Nilekani – Chairman of the Unique Identification Authority of India (UIDAI), Feroz Khan – actor, Dr. Raja Ramanna – Padma Vibhushan, etc.

Website: www.cottonboys.com

Mother’s International, Delhi

Positioned as one of the best 10 schools in India, and the best school in Delhi by Outlook’s “C-Fore Best School Survey, The Mother’s International School (MIS) is a co-educational institution which is a foundation of the Sri Aurobindo Education Society from 1956, which is an office of the Sri Aurobindo Ashram. The school provides sufficient facilities for various academic and sports events to be organized conveniently. No famous person has been recognized as alumni from this school yet.

Website: www.themis.in

Bombay Scottish School, Mumbai

A private, co-educational day school established in 1847 the Bombay Scottish School (BSS). It has been ranked one of the top ten schools in India for the past 80 years and one of the most reputed educational institutions in Mumbai. It is a school of various notable people from Bollywood and politics like Neerja Bhanot – Senior Flight Purser awarded the Ashoka Chakra posthumously; Aditya Thackeray – leader of Yuva Sena, Aamir Khan – actor, Ranbir Kapoor – actor, Ekta Kapoor – producer, etc.

Website: www.bombayscottish.in

Little Flower High School, Hyderabad

Established in July 1953, Outlook magazine ranked Little Flower High School as the best school in Hyderabad in the academic year 2009-10. It provides education in English and provides Telugu and Hindi as options for first and second languages. It also has NCC ( National Cadet Corps) and NIE ( National Institute of Engineering ) clubs. The school has alumni like Arshad Ayub – Speaker of the Telangana Legislative Assembly, Suresh Reddy – Speaker of the Legislative Assembly of Andhra Pradesh, etc.

Website: www.lfhshyd.org

St. Xavier’s Collegiate School, Kolkata

Often ranked as one of the best schools in India, St. Xavier’s Collegiate is a privately owned English-medium school for boys. Established in 1860, Xavier was ranked by Digital Learning as the top school in West Bengal in 2013. The school has alumni like Rabindranath Tagore – writer, 1913 Nobel Laureate, Jyoti Basu – longest serving Chief Minister of West Bengal, India, Sourav Ganguly – former Indian cricket captain, Shashi Tharoor – UN undersecretary, External Affairs Minister, Raj Kapoor – actor etc.

Website: www.sxcs.edu.in

Mallya Aditi International School, Bangalore

A prestigious private and a coed day school Mallya Aditi International School is one of the three schools that have been selected from all over the world by the Cambridge University as examples of schools that have science examinations for their students with an experimental approach. Over the past several years, Aditi has consistently ranked among India’s top 3 private schools. It has a well-architectured building, comprehensive laboratories, and various other sports and educational facilities for the students. No famous person has been recognized as alumni from this school yet.

Website: www.aditi.edu.in

La Martiniere, Kolkata

Established in 1836, today La Martiniere is one of the most well-known schools in India. It has two single-gender boys and girls schools. The school focuses on the all-round development of each student and works towards making them the best version of themselves. The school has alumni like Vijay Mallya – Chairman of the United Breweries (UB) Group and ex Rajya Sabha member, C. K. Birla – Hindustan Motors, Kiran Rao – film producer (“Dhobi Ghat”).

Website: www.lamartiniereforgirls.com

Emerald Heights International School, Indore

Established in 1982, Emerald Heights International School (EHIS) is located in Indore, Madhya Pradesh. It was ranked 1st in Madhya Pradesh (M.P.) and 2nd in India in the category of Day-cum-Boarding School, and 1st in Infrastructure by Education World. It has also received the honor of Best K-12 School by Business World Magazine. The school has two international level cricket grounds. It hosts Ranji Trophy matches every year. No famous person has been recognized as alumni from this school yet.

Website: www.emeraldheights.edu.in

The Scindia School, Gwalior

Founded in 1897, The Scindia School is a boarding school for boys and is considered to be one of the best schools in India. It and is situated in Gwalior Fort, in the city of Gwalior. Its campus is sprawled over an area of 110 acres. The school has alumni like Salman Khan – actor, K. Natwar Singh – politician, Pratap Chandra Lal – Air Chief Marshal, Rajendra S. Pawar – Chairman of NIIT, Anurag Kashyap – director, Vijay Kumar – Lieutenant General, Kalyan Banerjee – Chairman United Phosphorus Ltd etc.

Website: www.scindia.edu

St. John’s High School, Chandigarh

Founded in 1959, the beautiful and lush green St. John’s High School has been the best school in the tri-city ( Chandigarh, Mohali, and Panchkula ) for the years 2013, 2014, 2015. It was awarded the National Computer Literacy Award in the category of excellence in computer literacy and IT by the Ministry of Information and Technology. The school has alumni like Ayushmann Khurrana – actor, Sumrit Shahi – author, Kapil Sibal – former lawyer; politician, Jeev Milkha Singh – golfer, etc.

Website: www.stjohnschandigarh.com

The Valley School, Bangalore

One of the leading educational institutions in the country, The Valley School is a co-educational private day school founded in 1978. The school encourages its students to direct their learning based on Jiddu Krishnamurti’s philosophy that “Learning cannot happen when there is fear”.The school has a campus sprawled over 103 acres. No famous person has been recognized as alumni from this school yet.

Website: www.valleyschool.herokuapp.com

Modern School, Barakhamba Road, Delhi

A co-educational, day and boarding school in New Delhi, Modern School was founded in 1920 Modern School is consistently ranked among the best schools in India. It has a single campus covering 25 acres. The school has a long list of notable people as alumni like Gopal Krishna Gandhi – Governor of West Bengal, Khushwant Singh – author, Barkha Dutt – Consulting Editor of NDTV, Abhishek Bachchan – actor, Alok Nath – veteran actor, P.C. Lal – former Air Chief Marshals of the Indian Air Force, etc.

Website: www.modernschool.net

Loreto House, Kolkata

Established in 1842 in Kolkata, Loreto House has been renowned over the decades as one of the leading schools in India. The school’s aim is to provide education that involves the mind, body, and spirit of the child. The school has three well-stocked libraries, facilities such as basketball courts, audio-visual room, smart boards, playground and more. No famous person has been recognized as alumni from this school yet.

Website: www.loretohousekolkata.com

Maharani Gayatri Devi Girls School, Jaipur

First all-girls school to be established in Rajasthan in 1943, Maharani Gayatri Devi Girls School and was named after Her Highness Rajmata Gayatri Devi of Jaipur. It is located in the heart of the city and sprawls over 26 acres. The school has alumni like Sandhya Mridul – actress, Meira Kumar – Lok Sabha speaker, Apurvi Chandela – international shooter, etc.

Website: www.mgdschooljaipur.com

Dhirubhai Ambani International School, Mumbai

Built in 2003, Dhirubhai Ambani International School (DAIS) with Nita Ambani as the chairperson, is a private co-educational school in Mumbai which has been an IB World school since its establishment. Due to its world-class education and facilities, it is recognized as one of the top schools in India where almost every Bollywood star kid preferably goes to. Post-secondary school, DAIS offers the IB Diploma Programme. The school has not-so-famous but successful alumni like Abhinav Aggarwal – CEO of Fluid AI, Om Dhumatkar – Vice President at Deutsche Bank, Sukriti Yadava – Writer, etc.

Website: www.da-is.org

International School Of Hyderabad

Established in 1972, and spread over an area of 10-acre, The International School of Hyderabad (ISH) is a non-profit, English medium international school located in Hyderabad. The school provides education to students who plan to do their post-secondary education abroad and those from overseas as well. The school has been ranked as one of the top schools in India. No famous person has been recognized as alumni from this school yet.

Website: www.ishyd.org

D.A.V. Boys Senior Secondary School, Gopalapuram, Chennai

A senior secondary high school located in Gopalapuram, Chennai, D.A.V. Boys Senior Secondary School has been ranked among the top three schools in India for the past 2 years in the CBSE Class 12th Board Exam Results. It was rated as the best in Tamil Nadu by the magazines Outlook and Education World. The school has alumni like Siddharth Narayan – actor, Kutraleeswaran – swimmer, Rishikesha Krishnan – Director, IIM Indore, Nagarajan S – IIM-Ahmedabad Gold Medalist 1991, etc.

Website: www.davboysmogappair.com

SAI International School, Bhubaneswar

SAI International School is a co-educational day-cum boarding school in Bhubaneswar, Odisha. Although it has not been long since the school was established, the school and was ranked tied for 198th in the Education World India School Rankings 2018 and received the D. L. Shah National Quality wood Award by the Quality Council of India in the same year. SAI was also included by Fortune India in the list of “Future 50 Schools Shaping Success”. No famous person has been recognized as alumni from this school yet.

Website: www.saiinternationalschool.com

St. Mary’s School, Pune

Ranked as the fourth best school in India in 2013, St. Mary’s School, was established back in 1866. It has developed its programme to ensure a holistic balance between academics, mental and physical health. Education has been digitalized by providing iPads using the Apple educational tools to prep to class III students. For the higher classes, students can research and prepare projects and at three high-tech computer labs.

Website: www.smspune.com

MATHS CLASS 10TH QUESTION PAPER 2019 (RBSE)

 RAJASTHAN BOARD EXAMINATION, 2019

CLASS 10th

MATHEMATICS

समय: 3¼ घंटे                                                                                                                                                           अधिकतम अंक: 80


परीक्षाओं के लिए सामान्य निर्देश:-

1. सभी प्रश्न करने अनिवार्य हैं। 

2. सभी प्रश्नों के अंक प्रश्न के सामने अंकित हैं। 


भाग – अ 

PART-A

1) द्वन्द्व योग विधि से 62 का वर्ग ज्ञात कीजिए। 

Find the square of 62 by Dwandwa yoga method. 

 

2) हल कीजिए : (x+1) (x+2) = (x-5) (x-6) 

Solve : (x+l) (x+2) = (x-5) (x-6) 

 

3) 68 तथा 119 का महत्तम समापवर्तक ज्ञात कीजिए। 

Find the HCF of 68 and 119. 

 

4) tan260° ÷ 3cos230° का मान ज्ञात कीजिए। 

Find the value of tan260° + 3cos230° 

 

5) यदि sin2A = cos (A-18°) हो, तो A का मान ज्ञात कीजिए। 

If sin2A = cos (A-180), then find the value of A. 

 

6) समतल में लुढकने वाले वृत्त के केन्द्र का बिन्दु पथ लिखिए। 

Write the locus of the centre of the rolling circle in a plane. 

 

7) यदि ΔABC~ΔDER है जिनमें AB = 1.6 सेमी और DE = 2.4 सेमी हो तो ΔABC और ΔDEF क्षेत्रफलों का अनुपात ज्ञात कीजिए। 

If ΔABC~ΔDEF in which AB = 1.6cm and DE = 2.4cm. Find the ratio of the areas of ΔABC and ΔDEF. 

 

8) दो खिलाड़ी A और B शतरंज का एक मैच खेलते है यह ज्ञात हैं कि A द्वारा मैच जितने की प्रायिकताई ⅚ है। B के जीतने की प्रायिकता ज्ञात कीजिए। 

Two players A and B played a chess match. It is given that probability of winning the match by Aist. Find the probability of winning the match by B. 

 

9) यदि एक कार का किराया प्रथम किलोमीटर के लिए 20 रू. तथा इसके बाद प्रति किमी के लिये 11 रू. है तो 15 किमी चलने के लिये कुल किराया ज्ञात कीजिए। 

If the fare of a car for the first kilometer is ₹ 20 and for after 1 kilometer is ₹ 11, then find the total fare for 15 kilometers. 

 

10) एक पतंग भूमि से 75 मीटर की ऊँचाई पर उड़ रही है। जिसके धागे का भूमि के साथ झुकाव 60° है तो धागे की लम्बाई ज्ञात कीजिये। 

A kite is flying at a height of 75 metres from the level of ground attached to a string inclined at 60° to the horizontal. Find the length of the string. 

 

भाग -ब 

PART – B 

11) उपसूत्र आनुरूप्येण द्वारा 42 का घनफल ज्ञात कीजिए। 

Find the cube of 42 by using Upsutra Anurupyena. . 

 

12) सिद्ध कीजिए कि 7√5 एक अपरिमेय संख्या है। 

Prove that 7√5 is an irrational number. 

 

13) एक वृत्त की त्रिज्या 9 सेमी और त्रिज्य खण्ड का कोण 70° है वृत्त के लघु त्रिज्य खण्ड का क्षेत्रफल ज्ञात कीजिए।(π=22/7)

Radius of a circle is 9cm and the angle of the sector is 70°. Find the area of the minor sector of the circle. minor sector of the circle. (π=22/7)

 

 

14) एक बेलन की ऊँचाई 21 सेमी तथा उसका वक्र पृष्ठीय क्षेत्रफल 924 वर्ग सेमी है। बेलन की त्रिज्या ज्ञात कीजिए। 

The height of a cylinder is 21cm and its curved surface area is 924cm. Find the radius of the cylinder. 

 

15) A व B के मध्य की दूरी 125 किमी. है तथा इसके मध्य 8 यातायात सिग्नल मिलते हैं। यदि एक कार Sne प्रति घंटा की समान गति से सभी हरे सिग्नलों को पार करते हुए वह B बिंदु पर 2 घंटे 30 मिनट पर पहचान है। लेकिन अन्य दिन भारी यातायात के कारण निम्नानुसार रूकना पड़ता है। प्रथम यातायात सिग्नल 1 मिनट द्वितीय यातायात सिग्नल 2 मिनट ………8 वे सिग्नल तक …… 8 मिनट उसी कार द्वारा लिए गये कुल समय की गणना कीजिए। यदि वह सभी यातायात सिग्नलों की अनुपालना करती है। 

The distance between A and B is 125 km and there are Eight(8) traffic signals in between A and B. If a car by 50 km/h speed reaches point B crossing all greer signals in 2 hours and 30 minutes but on other days due to heavy traffic it happens to stop as follows. First Traffic Signal – 1 minute, Second Traffic Signal – 2 minutes and upto Eight(8th) signal – 8 minutes. Calculate the total time taken by that car if it follows the total traffic signals. 

 

भाग – स 

PART-C 

16) गुणन खण्ड विधि से समीकरण  1/x-2 +2/x-2 = 6/x जहाँ x ≠ 1, 2 को हल कीजिए। 

Solve the equation 1/x-2 +2/x-2 = 6/x  where x ≠ 1, 2 by factorisation method. 

 

17) 112 और 101 के मध्य 5 से विभाजित (भाज्य) होने वाली सभी प्राकृत संख्याओं का योग फल ज्ञात कीजिए।  

Find the sum of all the natural numbers divisible by 5 between 2 and 101. 

 

18) किसी अपूर्ण मीनार के आधार से 120 मीटर दूर किसी बिंदु से मीनार के शिखर का उन्नयन कोण 30° है। ज्ञात कीजिए कि मीनार को कितना ऊँचा बनाया जाये जिससे उसी स्थान पर उसका उन्नयन कोण 60° हो जाये? 

From a point on the ground which is 120m away from the foot of the unfinished tower, the angle of elevation of the top of the tower is found to be 30°. Find how much the height of the tower has to increase so that its angle of elevation at the same point becomes 60°? 

 

19) 5 सेमी भुजा वाले समबाहु त्रिभुज के अंतर्गत वृत्त की रचना कीजिए। 

Construct an incircle of an equilateral triangle with side 5 cm. 

 

23) त्रिज्या 10cm वाले एक वृत्त के अंतर्गत खींचे जा सकने वाले वर्ग का क्षेत्रफल ज्ञात कीजिए। 

Find the area of the square inscribed in a circle of radius 10cm. 

 

24) 6 सेमी व्यास का एक गोला 12 सेमी व्यास के बेलनाकार बर्तन में जिसमें पानी है डाला जाता है बर्तन में पानी कितना ऊपर चढ जायेगा? 

A sphere of 6cm diameter is dropped into a cylindrical vessel of diameter 12cm. Find the rise in water in the vessel. 

 

25) एक थैले में 15 कार्ड है जिन पर संख्याएँ 1, 2, 3, 4,…….., 15 अंकित है। थैले में से यादच्छिक एक कार्ड निकाला जाता है। प्रायिकता ज्ञात कीजिए कि इस पर 

i) एक अभाज्य संख्या है। 

ii) 2 से विभाजित होने वाली संख्या है। 

A bag contains 15 cards. The numbers 1,2,3,4,……..,15 are printed on them. A card is randomly drawn from the bag. Find the probability that the number on the card is 

i) a prime number women 

ii) a number is divisible by 2 

 

भाग – द 

PART – D 

26) निम्न रेखीक समीकरण युग्म को आलेखीय विधि द्वारा हल कीजिए

3x – 5y = -1

2x – y = -3

अतः इसकी सहायता से संबंध ………….. में ……….. का मान ज्ञात कीजिए।

Solve the following pair of linear equations by graphical method.

3x – 5y = -1

2x – y = -3

Thus find the value of A in the relation (x + y)2 = A

 

27) सिद्ध कीजिए।

Prove that:

i)(1+secA) /secA = sin2A /(1-cosA)

ii) cos2θ/1-tanθ + sin3θ /sinθ-cosθ = 1+sinθcosθ

अथवा

OR

सिद्ध कीजिए।

Prove that:

(i) sinθ/(1+cosθ) + (1+cosθ)/sinθ = 2cosecθ

(ii)(sinθ-2sin3θ) /(2cos3θ-cosθ) = tanθ

 

28) किसी समतल में चार बिंदु P(2, -1), Q(3, 4), R(-2, 3) और S(-3, -2) है तो सिद्ध कीजिए कि PQRS वर्ग नहीं एक समचतुर्भुज है।

If there are four points  P(2, -1), Q(3, 4), R(-2, 3) and S(-3, -2) in a plane, then prove that PQRS is not a square but a rhombus.

 

29) सिद्ध कीजिए कि चक्रीय चतुर्भुज के सम्मुख कोण यम्म सम्पूरक या उनका योग 1800 होता है।

Prove that the opposite angles of cyclic quadrilateral are supplementary or sum is 180°. 

अथवा OR

सिद्ध कीजिए कि यदि एक वृत्त की स्पर्शरेखासेक जीवा खींची जाए तो इस जीवा द्वारा दी गई स्पर्श रेखा से बनाये गए कोण क्रमश उसी जीवा द्वारा एकात्तर वृत्तखण्डों में बने कोणों के बराबर होते हैं। 

 

 

Prove that if a chord is drawn from a point of contact of the tangent or then angle made by this chord with the tangent are equal to the respective alternate angles made by segments with this chord. 

 

30) निम्न वारंवारता बंटन के माध्यक व बहुलक ज्ञात कीजिए। 

वर्ग  10-25 25-40 40-55 55-70 70-85 85-100
f1 6 20 44 26 3 1

Find the median and mode of the following frequency distribution. 

Class  10-25 25-40 40-55 55-70 70-85 85-100
f1 6 20 44 26 3 1

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