NCERT Solutions for Class 10 English First Flight

NCERT Solutions for Class 10 English First Flight

NCERT Solutions Class 10 English First Flight are the part of NCERT Solutions for Class 10 English. Here we have given NCERT Solutions for Class 10 English First Flight.

All Chapters NCERT Solutions for Class 10 English First Flight are provided on this page for free of cost. You can kick start your preparation taking the help of the Class 10th NCERT Solutions for English First Flight and score well in the exams. You can rely on the 10th Class NCERT Solutions of English First Flight as they are prepared by subject experts. Download the Chapterwise NCERT Solutions for Class 10 English First Flight and prepare from anywhere and anytime you want.

Free PDF Download of NCERT Solutions for Class 10 English First Flight

The Solutions of Class 10 English subject First Flight Textbook is written by the subject teachers in a simple language for easy understanding of the lessons to all students. All solutions are explained as per the latest CBSE English syllabus & marking scheme. So, preparing from the NCERT Class 10 English First Flight Solutions Textbook is most important to identify your subject learnings and preparation level.

Check Class 10th English (First Flight Textbook) Chapter-wise NCERT Solutions in Pdf by accessing the links provided below and download them offline for free.

NCERT Solutions for Class 10 English First Flight

NCERT Solutions for Class 10 English First Flight (Prose)

NCERT Solutions for Class 10 English First Flight (Poem)

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There are numerous benefits of using the NCERT Class 10 English First Flight Solutions. Some of them are listed below such as:

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  6. You can learn the question patterns and chapter-wise weightage of the actual exam question paper
  7. You can surely secure high marks in the exam.

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1. Can I find all lessons NCERT Solutions for Class 10 English First Flight online?

Yes, you can find all chapters NCERT Solutions for Class 10 English First Flight Online from several websites on the internet like Learninsta.com

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Yes, the available NCERT Class 10 English First Flight Solutions pdf is enough for the subject knowledge and it is created by subject experts in a simple manner to get a good grip on the subject.

3. How can I download Chapterwise NCERT Solutions for Class 10 English First Flight?

By tapping on the respective chapter link, you can download Chapterwise Class 10 English NCERT First Flight  Solutions in PDF format. Access them online & offline to read all concepts during preparation and revision time.

Wrapping Up

We wish the provided NCERT Solutions for Class 10 English First Flight PDF will help you when exam preparation. If you need any assistance on grade 10 CBSE Ncert English FF Solutions PDF share with us via comments and we will get back to you soon. Stay Connected with learninsta.com and discover more on NCERT 10th English Solutions PDF

NCERT Solutions for Class 10 Maths PDF Download | Free Chapter-wise NCERT Maths Solutions

NCERT Solutions for Class 10 Maths PDF Download | Free Chapter-wise NCERT Maths Solutions

NCERT Solutions for Class 10 Maths are the part of NCERT Solutions for Class 10. Here we have given CBSE Class 10 Maths NCERT Solutions.

Here you’ll find all chapters NCERT Solutions for Class 10 Maths in PDF format. Make use of these chapterwise NCERT Maths Solutions to ace up your CBSE class 10 board exam preparation & score high marks. Enough study materials and good practice can make students dream come true. Avail the PDF formatted CBSE NCERT Solutions for 10th Class Mathematics of all chapters via direct links available over here. You can download the NCERT Class 10 Maths Textbook Solutions PDF for free of cost from this page.

Download CBSE NCERT Solutions for Class 10 Maths in PDF

Solving all chapters important and unsolved questions provided in the NCERT Maths Textbooks is very important to score high marks in the final exams. To get a perfect knowledge of the subject and to answer all difficult and important questions easily at the time of board examination, practicing from the NCERT Solutions for class 10 maths is a must. Therefore, get chapter-wise NCERT class 10 maths solutions from the provided pdf links for free of cost & prepare on a daily basis.

Here is the list of Chapter-wise NCERT Solutions for Grade 10 Maths in PDF links. Access the respective chapter link from below and download pdf formatted NCERT Maths Solutions for Class 10 without any fail to kickstart your exam preparation.

Class 10 Maths NCERT Solutions

Chapter 1 Real Numbers

Chapter 2 Polynomials

Chapter 3 Pair of Linear Equations in Two Variables

Chapter 4 Quadratic Equations

Chapter 5 Arithmetic Progressions

Chapter 6 Triangles

Chapter 7 Coordinate Geometry

Chapter 8 Introduction to Trigonometry

Chapter 9 Some Applications of Trigonometry

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Areas Related to Circles

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

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Preparing candidates for class 10 board examinations are recommended to go ahead with the NCERT Solutions Book & practice well for the exams. 10th STD NCERT Maths Solutions acts as reference material at the time of your preparation and during revision time. Also, it is beneficial in many times for class 10 students of any boards. Check out the other benefits from here before planning to prepare with NCERT Solutions PDF:

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  • All solutions are prepared by subject experts in a simple language for easy understanding of the concepts.
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1. Where can I get NCERT Solutions Class 10 Maths PDF for all chapters?

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If you need any assistance to download NCERT Maths Solutions for grade 10 then reach us via comments below. We’ll get back to asap till then visit our site & get more updates on CBSE NCERT Textbook Solutions of all subjects.

NCERT Solutions for Class 10 Sanskrit Shemushi भाग 2 | शेमुषी संस्कृत Class 10 Solutions

NCERT Solutions for Class 10 Sanskrit Shemushi भाग 2 | शेमुषी संस्कृत Class 10 Solutions

NCERT Solutions for Class 10 Sanskrit Shemushi: Our subject experts prepared the NCERT Solutions for Class 10 Sanskrit Shemushi Bhag 2 शेमुषी संस्कृत बुक कक्षा 10 समाधान Text Book Questions and Answers Pdf free download covers solutions for all the topics prescribed in the NCERT Class 10th Sanskrit Text Book in accordance with the latest CBSE syllabus.

Sanskrit Class 10th NCERT Solutions | Shemushi Sanskrit Class 10 Solutions

Here, we have provided the links to the chapter-wise Sanskrit Class 10 NCERT Solutions of शेमुषी संस्कृत बुक भाग 2.

शेमुषी संस्कृत बुक Class 10 Solutions | Shemushi संस्कृत कक्षा 10 समाधान

  1. NCERT Solutions for Class 10 Sanskrit Chapter 1 शुचिपर्यावरणम्
  2. Shemushi Sanskrit Class 10 Solutions Chapter 2 बुद्धिर्बलवती सदा
  3. Sanskrit Class 10 NCERT Solutions Chapter 3 व्यायामः सर्वदा पथ्यः
  4. Class 10 Sanskrit Solutions Chapter 4 शिशुलालनम्
  5. Class 10th Sanskrit Book Solutions Chapter 5 जननी तुल्यवत्सला
  6. 10th Class Sanskrit Book Solution Chapter 6 सुभाषितानि
  7. Shemushi Sanskrit Class 10 Solutions Chapter 7 सौहार्दं प्रकृतेः शोभा
  8. NCERT Class 10 Sanskrit Solutions Chapter 8 विचित्रः साक्षी
  9. Shemushi Class 10 Solutions Chapter 9 सूक्तयः
  10. Shemushi संस्कृत कक्षा 10 समाधान Chapter 10 भूकंपविभीषिका
  11. शेमुषी संस्कृत बुक Class 10 Solutions Chapter 11 प्राणेभ्योऽपि प्रियः सुह्रद्
  12. शेमुषी भाग 2 Solutions Chapter 12 अनयोक्त्यः

Abhyasvan Bhav Sanskrit Class 10 Solutions

Abhyasvan Bhav Sanskrit Class 10 Solutions अभ्यासवान् भव भाग 2

NCERT Class 10 Sanskrit Grammar Book Solutions

Sanskrit Class 10 Grammar | Sanskrit Grammar Book for Class 10 CBSE Pdf

खण्डः ‘क’ (अपठित-अवबोधनम्)

खण्डः ‘ख’ (रचनात्मक कार्यम्)

खण्डः ‘ग’ (अनुप्रयुक्त-व्याकरणम्)

Sanskrit Syllabus Class 10 CBSE 2020-21 Pdf

संस्कृतम् (कोड नं. – 122)
कक्षा – दशमी

वार्षिकमूल्याङ्कनाय निर्मित प्रश्नपत्रे चत्वारः खण्डाः भविष्यन्ति-

  • ‘क’ खण्ड: अपठित-अवबोधनम् (10 अङ्काः)
  • ‘ख’ खण्डः रचनात्मक-कार्यम् (15 अङ्काः)
  • ‘ग’ खण्डः अनुप्रयुक्त-व्याकरणम् (25 अङ्काः)
  • ‘घ’ खण्डः पठित-अवबोधनम् (30 अङ्काः)

खण्डानुसारं विषयाः मूल्यभारः च

खण्डः विषयाः प्रश्नप्रकाराः मूल्यभारः
‘क’ अपठित-अवबोधनम्
1. एकः गद्यांशः
(80-100 शब्दपरिमितः)		 अति-लघूत्तरात्मकाः
पूर्णवाक्यात्मका:
लघूत्तरात्मका:
(भाषिककार्यम्)		 10
सम्पूर्णभारः 10
‘ख’ रचनात्मक-कार्यम्
2. औपचारिकम् अथवा अनौपचारिक पत्रम्
(मञ्जूषायाः सहायतया पूर्ण पत्रं लेखनीयम्)		 निबन्धात्मक: 5
3. चित्रवर्णनम् अथवा अनुच्छेदलेखनम् निबन्धात्मकः 5
4. हिन्दी/आङ्ग्लभाषातः संस्कृतेन अनुवादः पूर्णवाक्यात्मकः 5
सम्पूर्णभारः 15
‘ग’ अनुप्रयुक्त-व्याकरणम्
5. सन्धि लघूत्तरात्मकाः 4
6. समासः बहुविकल्पात्मका: 4
7. प्रत्ययाः बहुविकल्पात्मका: 4
8. वाच्यप्रकरणम् बहुविकल्पात्मका: 3
9. समयः लघूत्तरात्मकाः 4
10. अव्ययपदानि लघूत्तरात्मका: 3
11. संशोधनकार्यम् बहुविकल्पात्मकाः 3
सम्पूर्णभारः 25
‘घ’ पठित-अवबोधनम्
12. गद्यांश: अति-लघूत्तरात्मका:
पूर्णवाक्यात्मका:
लघूत्तरात्मकाः
(भाषिककार्यम्)		 5
13. पद्याशः अति-लघूत्तरात्मकाः
पूर्णवाक्यात्मका:
लघूत्तरात्मका
(भाषिककार्यम्)		 5
14. नाट्यांशः अति-लघूत्तरात्मकाः
पूर्णवाक्यात्मका:
लघूत्तरात्मका
(भाषिककार्यम्)		 5
15. प्रश्ननिर्माणम् पूर्णवाक्यात्मका: 4
16. अन्वयः अथवा भावार्थः पूर्णवाक्यात्मकाः 4
17. घटनाक्रमानुसारं वाक्यलेखनम् पूर्णवाक्यात्मका: 4
18. पर्यायमेलनम् / विशेष्य-विशेषण-मेलनम् लघूत्तरात्मका: 3
पूर्णभारः 30
सम्पूर्णभारः 80

Examination Structure
Sanskrit (Class – X)

Type of Questions No. of Questions No. of Division Marks per Question Total Marks
MCQ 1 Mark 3 + 4 + 4 + 3 + 3 = 17 5 1 17
VSA ½ Mark 6 + 2 + 2 + 2 = 12 4 ½ 6
VSA 1 Mark 2 = 2 1 1 2
LA ½ Mark
(Fill in the Blanks)		 10 + 4 + 4 = 18 3 ½ 9
LA ½ Mark 8 = 8 1 ½ 4
LA 1 Marks 5 + 5 + 1 + 1 + 1 + 4 = 17 6 1 17
LA 2 Marks 2 = 2 1 2 4
Title Q 1 Mark 1 = 1 1 1 1
SAQ 1 Mark 4 + 4 + 3 + 3 + 3 + 3 = 20 6 1 20
Total 80

CBSE Class 10 Sanskrit Question Paper Design

संस्कृतम् पाठ्यक्रम (कोड नं. 122)
कक्षा : दशमी

वार्षिकं मूल्याङ्कनम् (80 अंकाः)

‘क’ खण्डः
अपठित-अवबोधनम् (10 अंकाः)

एक: गद्यात्मकः खण्डः
80-100 शब्दपरिमितः गद्यांशः सरलकथा, वर्णन वा (2 + 4 + 1 अंकाः)

  • एकपदेन पूर्णवाक्येन च अवबोधनात्मक कार्यम
  • शीर्षकलेखनम्
  • अनुच्छेद-आधारितम्

भाषिकं कार्यम् भाषिककार्याय तत्वानि (3 अंकाः)

  • वाक्ये कर्तृ-क्रिया पदचयनम्
  • कर्तृ-क्रिया – अन्वितिः
  • विशेषण-विशेष्य चयनम्
  • पर्याय-विलोमपद-चयनम्

‘ख’ खण्डः
रचनात्मक कार्यम् (15 अकाः)

  1. संकेताधारितम् औपचारिक अथवा अनौपचारिकं पत्रलेखनम् (5 अकाः)
  2. चित्राधारितम् वर्णनम् अथवा अनुच्छेदलेखनम् (5 अकाः)
  3. हिन्दीभाषाथाम् आङ्ग्लभाषायां वा लिखितानां पञ्चसरलवाक्यानां संस्कृतभाषायाम् अनुवाद: (5 अकाः)

‘ग’ खण्डः
अनुप्रयुक्तव्याकरणम् (25 अंकाः)

शेमुषी-पुस्तक-आधारितम्
1. सन्धिकार्यम् (4 अंकाः)

  • व्यञ्जन सन्धिः- वर्गीयप्रथमवर्णस्य तृतीयवर्णे परिवर्तनम्, प्रथमवर्णस्य पञ्चमवणे परिवर्तनम्। (2 अंकाः)
  • विसर्गसन्धिः- विसर्गस्य उत्व, रत्वम्, विसर्गलोपः, विसर्गस्य स्थाने स्, श्, ष्। (2 अंकाः)

2. समासः वाक्येषु समस्तपदानां विग्रहः विग्रहपदानां च समासः (1 + 1 + 1 + 1 = 4 अंकाः)

  • तत्पुरुषः-विभक्तिः
  • बहुव्रीहिः
  • अव्ययीभावः (अनु, उप, सह (स), निर्, प्रति, यथा)
  • द्वन्द्वः

3. प्रत्ययाः (4 अंकाः)

  • तद्धिताः – मतुप, ठक्, त्व, तल् (3)
  • स्त्रीप्रत्ययौ – टाप्, ङीप् (1)

4. वाच्यपरिवर्तनम् केवलं लट्लकारे (कर्तृ-कर्म-क्रिया) (3 अंकाः)

5. समयः अंकाना स्थाने शब्देषु समयलेखनम् (सामान्य – सपाद – सार्ध – पादोन) (4 अंकाः)

6. अव्ययपदानि (3 अंकाः)
उच्चैः , च, श्वः, ह्यः, अद्य, अत्र-तत्र, यत्र-कुत्र, इदानीम्, (अधुना, सम्प्रति, साम्प्रतम्)
यदा, तदा, कदा, सहसा, वृथा, शनैः, अपि, कुतः, इतस्ततः, यदि-तर्हि, यावत्-तावत्

7. अशुद्धि-संशोधनम् (वचन-लिंग-पुरुष-लकार-विभक्तिदृष्ट्या संशोधनम्) (3 अंकाः)

‘घ’ खण्डः
पठित-अवबोधनम्
शेमुषी-पाठयपुस्तकम् अधिकृत्य) (30 अंकाः)

8. गद्यांशम् अधिकृत्य अवबोधनात्मक कार्यम् (5 अंकाः)
प्रश्नप्रकाराः – एकपदेन पूर्णवाक्येन च प्रश्नोत्तराणि, भाषिककार्य च।

9. पद्यांशम् अधिकृत्य अवबोधनात्मकं कार्यम् (5 अंकाः)
प्रश्नप्रकाराः – एकपदेन पूर्णवाक्येन च प्रश्नोत्तराणि, भाषिककार्य च।

10. नाट्यांशम् अधिकृत्य अवबोधनात्मक कार्यम् (5 अंकाः)
प्रश्नप्रकाराः – एकपदेन पूर्णवाक्येन च प्रश्नोत्तराणि, भाषिककार्य च।

11. वाक्येषु रेखाङ्कितपदानि अधिकृत्य चतुर्णा प्रश्नानां निर्माणम्। (4 अंकाः)

12. श्लोकान्वयः (द्वयोः श्लोकयोः) / एकस्य श्लोकस्य भावार्थः (4 अंकाः)

13. घटनाक्रमानुसारं कथालेखनम् (4 अंकाः)

14. पर्यायपदानां विशेष्य-विशेषण-पदानां वा मेलनम् अथवा वाक्येषु प्रयोगः (3 अंकाः)
(पठान् आधृत्य लघूत्तरात्मकाः प्रश्नाः)

पुस्तकम्-शेमुषी संस्कृत-पाठ्यपुस्तकम् द्वितीयः भागः (दशमश्रेण्यै)
परीक्षायै निर्धारिताः पाठाः

पाठ-संख्या पाठनाम
प्रथमः पाठः शुचिपर्यावरणम्
द्वितीयः पाठः बुद्धिर्बलवती सदा
तृतीयः पाठः व्यायामः सर्वदा पथ्यः
चतुर्थः पाठः शिशुलालनम्
पञ्चमः पाठः जननी तुल्यवत्सला
षष्ठः पाठः सुभाषितानि
सप्तमः पाठः सौह प्रकृतेः शोभा
अष्टमः पाठः विचित्रः साक्षी
नवमः पाठः सूक्तयः
दशमः पाठः भूकम्पविभीषिका (न परीक्षाकृते)
एकादशः पाठः प्राणेभ्योऽपि प्रियः सुहृद्

पाठ्यपुस्तकानि-

  1. ‘शेमुषी’ पात्यापुस्तकम भाग-2, संशोधितसंस्करणम् – प्रकाशनम् – रा.शै.प्र.अनु.परि.द्वारा
  2. ‘अभ्यसवान भव’ भाग-2 – प्रकाशनम् – रा.शै.प्र.अनु.परि.द्वारा
  3. व्याकरणवीथिः (अतिरिक्तपठनार्थम्) – प्रकाशनम् – रा.शै.प्र.अनु.परि.द्वारा
No. of Questions No. of Marks Per Question Total No. of Marks
Section A
Q. No. I. Apathita Gadyanshah 10 Marks
VSA (2Q) 1 × 2 = 2
LA (2Q) 2 × 2 = 4
Title (1Q) 1 × 1 = 1
MCQ (3Q) 1 × 3 = 3
Section B
Q. No. II Patra-Lekhanam
LA (10 Blanks)		 ½ × 10 = 5 15 Marks
Q. No. III Chitravarnam/Anuchchhed Lekhanam
LA (5 Sentences to write)		 1 × 5 = 5
Q. No. IV Hindi/English to Sanskrit Translation
LA (5 easy sentences to be translated from Hindi/English to Sanskrit)		 1 × 5 = 5
Section C
Q. No. V – Sandhih
SA 1 of 4		 1 × 4 = 4 25 Marks
Q. No. VI – Samasah
MCQ 1 of 4		 1 × 4 = 4
Q. No. VII – Pratyayah
MCQ 1 of 4		 1 × 4 = 4
Q. No. VIII – Vachya Parivartanam
MCQ 1 of 3		 1 × 3 = 3
Q. No. IX – Samayah
SA 1 of 4		 1 × 4 = 4
Q. No. X – Avyayaani
VSA 1 of 6		 ½ × 6 = 3
Q. No. XI – Ashuddhi-Samshodhanam
MCQ 1 of 3		 1 × 3 = 3
Section D
Q. No. XII. Gadyanshah 30 Marks
VSAQ (Ekapadena) ½ × 1 = 1
LAQ (Poorna Vakyena) 1 × 1 = 1
SA (Bhashikakaryam) 1 × 3 = 3
Q. No. XIII Padyanshah
VSAQ (Ekapadena) ½ × 1 = 1
LAQ (Poorna Vakyena) 1 × 1 = 1
SA (Bhashikakaryam) 1 × 3 = 3
Q. No. XIV Natyanshah
VSAQ (Ekapadena) ½ × 1 = 1
SAQ (Poorna Vakyena) 1 × 1 = 1
SA (Bhashikakaryam) 1 × 3 = 3
Q. No. XV Prashna Nirmanam
LAQ 1 of 4		 1 × 4 = 4
Q. No. XVI Shloka Anvayah
क. LAQ (4 Blanks) Q1 of ½ (4 Blanks) ½ × 4 = 2
ख. LAQ (4 Blanks) Q1 of ½ (4 Blanks) ½ × 4 = 2
or
Bhavartha-Lekhanam
LAQ Q 1 of 1 (4 Blanks)		 4 × 1 = 4
Q. No. XVII Ghatanakramanusar Vakyalekhanam
LA Q 1 of 8		 ½ × 8 = 4
Q. No. XVIII Melanam/chayanam (Paryaya/Visheshya-Visheshanam)
SAQ 1 of 3		 1 × 3 = 3

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NCERT Solutions for Class 10 English Footprints Without Feet

NCERT Solutions for Class 10 English Footprints Without Feet

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Download Chapterwise NCERT Solutions for Class 11 English Hornbill and Snapshots PDF

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NCERT Solutions for Class 11 Maths | NCERT Class 11 Maths Solutions

NCERT Solutions for Class 11 Maths | NCERT Class 11 Maths Solutions

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Maths 11 NCERT Solutions Chapter 1 Sets

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NCERT Solutions of Maths Class 11 Chapter 12 Introduction to three Dimensional Geometry

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NCERT Class 12 Physics Part 1 Book एन सी ई आर टी कक्षा १२ भौतिकी भाग 1
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NCERT Class 11 Physics Part 1 Book एन सी ई आर टी कक्षा ११ भौतिकी भाग 1
NCERT Class 11 Physics Part 2 Book एन सी ई आर टी कक्षा ११ भौतिकी भाग २
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NCERT Indian Economic Development एन सी ई आर टी कक्षा ११ भारतीय अर्थव्यवस्था का विकास
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NCERT Snapshots Supplementary Reader English
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NCERT Class 10 Science Book एन सी ई आर टी कक्षा १0 विज्ञान
NCERT Class 10 Maths Book एन सी ई आर टी कक्षा १0 गणित
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NCERT Contemporary India एन सी ई आर टी कक्षा १0 भारत और समकालीन विश्व भाग २
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NCERT Class 9 Science Book एन सी ई आर टी कक्षा ९ विज्ञान
NCERT Class 9 Maths Book एन सी ई आर टी कक्षा ९ गणित
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NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane

NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane

These Solutions are part of NCERT Solutions for Class 11 Physics. Here we have given NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane

Question 1.
State, for each of the following physical quantities, if it is a scalar or a vector :
Volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 1

Average Velocity Calculator – Calculate Average Velocity.

Question 2.
Pick out the two scalar quantities in the following list:
Force, Angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.
Answer:
Work and Current.

Question 3.
Pick out the only vector quantity in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
Answer:
Impulse.

Question 4.
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

  1. adding any two scalars,
  2. adding a scalar to a vector of the same dimensions,
  3. multiplying any vector by any scalar,
  4. multiplying any two scalars,
  5. adding any two vectors,
  6. adding a component of a vector to the same vector.

Answer:

  1. Not meaningful. Two scalars of different dimensions/units cannot be added.
  2. Not meaningful. A scalar and a vector cannot be added.
  3. Meaningful. A scalar and vector can be multiplied irrespective of their dimensions/units.
  4. Meaningful. Two scalars can be multiplied irrespective of their dimensions/units.
  5. eNot meaningful. Two vectors of different dimensions/units cannot be added.
  6. Not meaningful. A component of a vector cannot be added to it.

Question 5.
Read each statement below carefully and state with reasons, if it is true or false :
(a) The magnitude of a vector is always a scalar,
(b) each component of a vector is always a scalar,
(c) the total path length is always equal to the magnitude of the displacement vector of a particle
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,
(e) Three vectors not lying in a plane can never add up to give a null vector.
Answer:
(a) True, magnitude of the velocity of a body moving in a straight line may be equal to the speed of the body.
(b) False, each component of a vector is always a vector, not scalar.
(c) False, total path length can also be more than the magnitude of displacement vector of a particle. It is equal to the magnitude of displacement only if particle moves in one direction.
(d) True, average speed depends upon total path length which can be equal or more than the magnitude of displacement vector of the particle and average velocity depends upon the displacement vector. Thus average speed can be equal or greater than the magnitude of average velocity.
(e) True, three vectors not lying in a plane cannot form a closed triangle.

Question 6.
Establish the following vector inequalities geometrically or otherwise :
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 2
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 3

Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 4
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 5NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 6

Question 7.
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 7
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 8

Question 8.
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 9
Answer:
(1) PQ = diameter = 2r = 2 x 200 = 400 m
Since displacement vector does not depend upon the actual path length and it is the shortest distance between initial and final position, so in the case of each girl the displacement is 400 m.
(2) Actual path length in the case of girl B is least e., equal to the displacement vector.

Question 9.
A cyclist starts from the center O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the center along QO as shown in Fig. If the round trip takes 10 min, what is the
(a) net displacement,
(b) average velocity, and
(c) the average speed of the cyclist?
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 10
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 11

Question 10.
On open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
Answer:
(1) The path Followed by the motorist will be a closed hexagonal path.
Suppose the motorist starts his journey from point O. He takes the turn at point C.
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 12
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 13
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 14

(2) The motorist will take the sixth turn at O.
Displacement is zero Path length is 3000 m i.e., 3 km
Ratio of magnitude of displacement and path length is zero.

(3) The motorist will take the 8th turn at B
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 15
Question 11.
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is
(a) the average speed of the taxi,
(b) the magnitude of average velocity? Are the two equal?
Answer:
Magnitude of displacement = 10 km
Total path length = 23 km
Time taken=28 min=\( \cfrac { 28 }{ 60 } \)= \( \cfrac { 7 }{ 15 } \) h
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 16

Question 12.
Rain is falling vertically with a speed of 30 ms-1. A woman rides a bicycle with a speed of 10 ms-1 in the north to south direction. What is the direction in which she should hold her umbrella?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 17
In order to protect herself from rain, the woman should hold her umbrella

NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 18
So a woman should hold her umbrella at an angle of 18°26′ with the vertical, towards the south.

Question 13.
A man can swim at a speed of 4 km/h in still water. How long does he take to cross a river 1km wide if the river flows steadily at 3 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 19
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 20

Question 14.
In harbour, the wind is blowing at the speed of 72 km/h, and the flag on the mast of a boat anchored in the harbour along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 21
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 22
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 23

Question 15.
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 ms-1 can go without hitting the ceiling of the hall?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 24
Question 16.
A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 25

Question 17.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the
stone ?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 26

Question 18.
An aircraft executes a horizontal loop of radius 1 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
Answer:
Here r = 1 km = 103 m, υ= 900 km h_1 = 900 x \( \cfrac { 5 }{ 18 } \)= 250 ms_1.
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 27

Question 19.
Read each statement below carefully and state, with reasons, if it is true or false :
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the center.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
Answer:
(a) False, the net acceleration of a particle in circular motion is along the radius of the circle towards the center only in uniform circular motion.
(b) True
(c) True. (The direction of acceleration vector of a particle in uniform circular motion changes continuously. The sum of the vectors represented by a closed polygon taken in the same order is zero.)

Question 20.
The position of a particle is given by
\(\vec { r } \)=3.0 t \( \hat { i } \)-2.0 t2 \( \hat { i } \)+4.0\( \hat { k } \) m where t is in seconds and the coefficients have the proper units for r to be in meters.
(a) Find the v and a of the particle,
(b) What is the magnitude and direction of velocity of the particle at t = 3s?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 28

Question 21.
A particle starts from the origin at t = 0 with a velocity of 10.0 \( \hat { j } \) m/s and moves in the x-y plane with a constant acceleration of (8.0 \( \hat { i } \) +2.0  \( \hat { j } \))
ms-1
(a) At what time is the x-coordinate of the particle 16 m ? What is the y- coordinate of the particle at that time ?
(b) What is the speed of the particle at the time ?
Answer:
(a) The position of the particle is given by
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 29
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 30

Question 22.
\( \hat { i } \) and \( \hat { j } \) are unit vectors along x-and y-axis respectively. What is the magnitude and direction of the vectors. \( \hat { i }+ { j }\) and \( \hat { i }-{ j }\) ? What are the components of a vector \( \vec { A }= \) \( \hat { 2i }+ { 3j }\) along the directions of \( \hat { i }+ { j }\) and  \( \hat { i }-{ j }\)
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 31
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 32
Question 23.
For any arbitrary motion in space, which of the following relations are true:
(a) υaverage (1/2) (υ (t1+υ t2)
(b) υaverage = [r (t1) – r (t2)]-(t2-t1)
(c) υ(t) = υ(0) + at
(d) r(t) = r(0) + υ(0) t + (1/2) at2
(e) υaverage =υ(t2) – υ (t1)]/(t2 – t1)
(The ‘average’ stands for an average of the quantity over the time interval t1 to t2)
Answer:
(b) and (e) is true. For arbitrary motion, acceleration may not be constant. Hence, (a), (c) and (d) are not true.

Question 24.
Read each statement below carefully and state, with reasons and examples, if it is true or false :
A scalar quantity is one that

  1. is conserved in a process
  2. can never take a negative value
  3. must be dimensionless
  4. does not vary from one point to another in space
  5. has the same value for observers with different orientations of axes.

Answer:

  1. False, e.g. kinetic energy is a scalar quantity. In inelastic collisions, kinetic energy does not remain conserved.
  2. False, e.g. temperature is a scalar quantity. It can be positive as well as negative on the Celsius scale.
  3. False, e.g. mass is a scalar quantity but it is not dimensionless.
  4. False, e.g. gravitational potential is a scalar and it varies from one point to another in the space.
  5. True, A mass m kg will remain m kg for observers with different orientations of axes.

Question 25.
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10 s apart is 30°, what is the speed of the aircraft?
Answer:
Let A and B be the two positions of the aircraft separated by 10 s, then from the figure.
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 33
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 34

Question 26.
A vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors’ \( \vec { A } and { B }\) at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.
Answer:
A vector does not have any location in space. No, it can not vary with time provided its magnitude and direction are given. For Example, \( \vec { A }= \) \( \hat {2i }+{ 2j }+{ 5j }\) does not vary with time. Two equal vectors at different locations in space may have identical physical effects. For example, two bodies fall freely with the same acceleration at two positions if acceleration due to gravity at these two positions is equal.

Question 27.
A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?
Answer:
No. Anything that has magnitude and direction is a vector only if it obeys the laws of vector addition. The finite rotation of a body about an axis is not a vector because finite rotation does not obey the commutation law.

Question 28.
Can you associate vectors with

  1. the length of a wire bent into a loop
  2. a plane area
  3. a sphere? Explain.

Answer:

  1. Since direction at every point on the loop changes, so vector cannot be associated with the length of a wire bent in a loop.
  2. Vector can be associated with the plane area. Such a vector is called an area vector and its direction is taken as normal to the plane.
  3. Since the direction of a perpendicular drawn at every point on a sphere is different, so a vector cannot be associated with a sphere.

Question 29.
A bullet fired at an angle of 30° with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away? Assume the muzzle speed to the fixed, and neglect air resistance.
Answer:
Here R = 3 km = 3000 m, θ = 30°, g = 9.8 m s-2.
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 35
Maximum range of bullet =u2/g=3-46 m. Since the distance of the target (5 km) is greater than the maximum range of

Question 30.
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km h-1 passes directly overhead an anti-craft gun. At what angle from the vertical should the gun be fired for the shell muzzle speed 600 m s-1  to hit the plane? At what maximum altitude should the pilot fly the plane to avoid being hit? Take g = 10 m s-2
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 36
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 37
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 38

Question 31.
A cyclist is riding at a speed of 27 km/h. As he approaches a circular turn on the road of a radius of 80 m, he applies brakes and reduces his speed at the constant rate of 0.5 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Answer:
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 39
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 40

Question 32.
(a) Show that for a projectile, the angle between the velocity and the x-axis as a function of time is given by
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 41
(b) Show that the projection angle θo for a projectile launched from the origin is given by
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 42
where the symbols have their usual meaning.
Answer:
(a) Let a projectile fired at an angle θ with the x-axis.
As θ depends on t, θ(t), at any instant,
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 43
NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane 44

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