Class 10

Punjab State Board PSEB 10th Class English Book Solutions English Notice Writing Exercise Questions and Answers, Notes.

PSEB 10th Class English Notice Writing

A notice is a written or printed news, announcement or information. It is usually displayed publicly as on a school / college notice-board. A notice can also be given for insertion in a newspaper like an advertisement. But there is one main difference between an advertisement and a notice. An advertisement is chiefly commercial (or matrimonial) in nature; but a notice is a general piece of information for a particular group. A notice should be in complete sentences or even in the form of a short paragraph, whereas an advertisement can be in the form of merely catchy phrases and slogans.

Question 1.
A notice is to be prepared for putting up on the students’ noticeboard, informing them about the school inspection to be held on 16th May, 2018. It is from Reema Sharma, The Principal, Government High School, Mohali.
Answer:

Govt. High School, Mohali Notice 10 May, 2018 This is to inform all the students and the school staff that the school inspection will be held on 16 May, 2018 by the District Education Officer. Therefore, all the students, teachers and the school staff are requested to maintain discipline, cleanliness and punctuality to keep up the good reputation of the school during the inspection. Reema Sharma (Principal)

Question 2.
You are Manav Shukla, the Secretary, the Help All Club of the Navodaya Vidyalaya, Kashmiri Gate, Delhi. Prepare a notice for the school students to help the earthquake victims with money, medicine, food and clothes.
Answer:

Navodaya Vidyalaya 16 October 20_ _ Kashmiri Gate, Delhi NOTICE The recent earthquake in the hilly areas has caused heavy loss of life and property. The affected people are having a horrible time. They are without food, clothes, money and medicine. The Help All Club of the school appeals to all students to help the victims with money, medicine, food and clothes. For your donations, contact the undersigned. Manav Shukla Secretary

Question 3.
As the Secretary of Sai Baba Society, Somesh Vihar, Delhi, prepare a notice for the residents of the colony, giving hints for protection against Dengue fever. Your name is Sheetal Jain.
Answer:

SAI BABA SOCIETY 10 August 20_ _ Somesh Somesh Vihar, Delhi NOTICE Hints for Protection against Dengue Many cases of dengue have been reported in the city. The escape from this disease lies more in prevention than in cure. All residents of the colony are advised to take the following steps to protect themselves against this dangerous disease. Disinfect all places where mosquitoes can breed. Use mosquito repellents. Do not let water stagnate around your houses. Wear clothes that cover arms and legs. In case of fever, contact your doctor or the nearest hospital. Sheetal Jain Secretary

Question 4.
Draft a notice on behalf of the Principal, Delhi Public School, Ludhiana, announcing elections for the posts of President and Secretary of English Literarary Society of the school.
Answer:

DELHI PUBLIC SCHOOL LUDHIANA NOTICE 20 October 20– The school is going to hold elections for the posts of President and Secretary of the English Literary Society of the school. Those who want to give their nominations for the same posts should give their names to the undersigned by the 13th of this month. Sanjeev Jain (Principal)

Question 5.
You are Mohan Kumar, Sports Secretary, Govt High School, Jalandhar. Some old sports goods have to be put on sale to collect money for donation to the poor cancer patients. Draft a notice, inviting students to help by buying these goods.
Answer:

GOVT. HIGH SCHOOL, JALANDHAR NOTICE 10 March 20 – – The school has decided to sell some of the old sports goods. The sale will be organized in the school hall on 15 March, 20 _ _. These goods include cricket bats, balls, hockey sticks, footballs, volleyballs and basketballs. All the goods are in a fairly good condition. The amount collected from the sale will be donated for the treatment of poor cancer patients. Please come, buy and help in the good cause. Mohan Kumar (Sports Secretary)

Question 6.
You are Nimisha, Student Editor, School Magazine, Radha Vatika School, Khanna. Draft a notice, inviting entries for the magazine from students. The last date is 10th of October.
Answer:

RADHA VATIKA SCHOOL, KHANNA NOTICE Contributions For The School Magazine 1 October 20 – – We are going to bring out the annual issue of our school magazine next month. Those who want to have their articles, stories, poems, etc. published in this issue should hand over their articles to the undersigned by the 10th of this month. The articles should be original and written neatly on one side of the paper only. Nimisha Paul (Student Editor)

Question 7.
You wish to arrange a charity show in your school. Write a notice in this regard, specifying the purpose, date and time of the show.
Answer:

P.S.N. PUBLIC SCHOOL, LUDHIANA 10 December 20_ _ The Cultural Committee of the school has decided to arrange a charity show to extend help to the victims of recent earthquake in Uttarakhand. Funds f collected from this charity show will be spent for purchasing clothes, food, blankets, etc. for the earthquake victims. Skits, folk dances, songs and a lot of fun is included in this charity show. So, all students are invited to this show on 15 December, 2017 at 11.00 a.m. at the school auditorium. Tamanna Bhatia (Cultural President)

Question 8.
You are Sonal, Cultural Secretary of the City Public School, Lucknow. Write a notice, inviting students to give their names for the Fancy Dress Competition being held in the School.
Answer:

CITY PUBLIC SCHOOL, LUCKNOW NOTICE FANCY DRESS COMPETITION 1 October 20 – – A Fancy Dress Competition is going to be held at our school on 10 October, 2017. The competition will be open to the students from Nursery to Class-V only. Famous dress designer, Ritu Beri, has consented to be the judge for this competition. So those desirous of taking part in this event, should give their names to the undersigned by 5 October, 20 Sonal (Cultural Secretary)

Question 9.
You are Munish, the Head Boy of Kamal Public School, Kamal. Write a notice ‘ for the school notice-board, inviting the students to participate in the Annual Sports Day.
Answer:

KARNAL PUBLIC SCHOOL, KARNAL NOTICE 10 March 20_ _ The school is holding its Annual Sports Day on 21st March. Those who want to participate in the various events should give their names to the undersigned by the 13th of this month. The list of various events is available with the undersigned. No student can take part in more than three events, excluding the relay. Munish Lai (Head Boy)

Question 10.
You are Nikhil Kumar, the Head Boy of Govt. Sr. Sec. School, Ambala. Draft a notice regarding a book that has been found in the school compound.
Answer:

GOVT. SR. SEC. SCHOOL, AMBALA NOTICE LOST AND FOUND 22 March 20_ _ A book on English Grammar was found lying in the school compound last evening. It is of brown colour with a name written on it. The owner is requested to collect it from the school office after showing his / her identity card. Nikhil Kumar (Head Boy)

Question 11.
Rakesh Sharma is a student of class X-A in Govt. Sen. Sec. School, Amritsar. He has lost his English Reader Book during the lunch .break. Draft a notice on his behalf for the school notice-board.
Answer:

GOVT. SEN. SEC. SCHOOL, AMRITSAR NOTICE LOST ! LOST! LOST! 15 October 20 I have lost my English Reader Book somewhere in the school. The book bears my name and class roll number. I have put in it some notes and hints in my own hand. The finder is requested to return the book to me or deposit it with the school office. It will be an act of great favour. Rakesh Sharma Roll No. 5

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 2 Polynomials Ex 2.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.1

Question 1.
The graphs of y = p (x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p (x), in each case.

Solution:
The graphs of y = p (x) are given in figure above, for some polynomials p (x). The number of zeroes of p (x) in each case are given below:
(i) From the graph, it is clear that it does not meet x-axis at any point.
Therefore, it has NIL; no. of zeroes.

(ii) From the graph, it is clear that it meets x- axis at only one point.
Therefore, it has only one no. of zeroes.

(iii) From the graph, it is clear that it meets x-axis at three points.
Therefore, it has three no. of zeroes.

(iv) From the graph, it is clear that it meets x- axis at two points.
Therefore, it has two no. of zeroes.

(v) From the graph, it is clear that it meets x- axis at four points.
Therefore, it has four no. of zeroes.

(vi) From the graph, it is clear that it meets pr-axis at three points.
Therefore, it has three no. of zeroes.

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 1 Real Numbers Ex 1.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

Question 1.
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion :
(i) \(\frac{13}{3125}\)

(ii) \(\frac{17}{8}\)

(iii) \(\frac{64}{455}\)

(iv) \(\frac{15}{1600}\)

(v) \(\frac{29}{343}\)

(vi) \(\frac{23}{2^{3} 5^{2}}\)

(vii) \(\frac{129}{2^{5} 5^{7} 7^{5}}\)

(viii) \(\frac{6}{15}\)

(ix) \(\frac{35}{50}\)

(x) \(\frac{77}{210}\)
Solution:
(i)Let x = \(\frac{13}{3125}\) ………..(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 13 and q = 3125
Prime factors of q = 3125 = 5 × 5 × 5 × 5 × 5 = 5⁵ × 2⁰
which are of the form 2ⁿ × 5^m here n = 0, m = 5
which are non negative integers.
∴ x = \(\frac{13}{3125}\) have a terminating decimal expansion.

(ii) Let x = \(\frac{17}{8}\) …………………(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 17 and q = 8
Prime factors of q = 8 = 2 × 2 × 2 = 2³ = 2³ × 5⁰

which are of the form 2ⁿ × 5^m here n = 3, m = 0
and these are non negative integers.
∴ x = \(\frac{17}{8}\) have a terminating decimal expansion.

(iii) Let x = \(\frac{64}{455}\) …………(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 64, q = 455
Prime factors of q = 455 = 5 × 7 × 13 which are not of the form 2ⁿ × 5^m
∴ x = \(\frac{64}{455}\) has a non – terminating decimal expansion.

(iv) Let x = \(\frac{15}{1600}\) ……….(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 15 and q = 1600
Prime factors of q = 1600
= 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 = 2⁶ × 5²
which are of the form 2ⁿ × 5^m, here n = 6, m = 2 and these are non negative integers.
∴ x = having terminating decimal expansion.

(v) Let x = \(\frac{29}{343}\) ………… (1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 29 and q = 343
prime factors of q = 343
= 7 × 7 × 7 = 7³
which are not of the form 2ⁿ × 5^m, here n = 0, m = 0
∴ x = \(\frac{29}{343}\) will have a non – terminating decimal expansion.

(vi) Let x = \(\frac{23}{2^{3} 5^{2}}\) ……….(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 23, q = 2³5²
Prime factors of q = 2³5²
which are of the form 2ⁿ × 5^m, here n = 3, m = 2 and these are non negative integers.
∴ x = \(\frac{23}{2^{3} 5^{2}}\) will have a terminating decimal expansion.

(vii) Let x = \(\frac{129}{2^{5} 5^{7} 7^{5}}\) ……………….(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 129 and q = 2⁵ 5⁷ 7⁵
Prime factors of q = 2⁵ 5⁷ 7⁵
which are not of the form 2ⁿ × 5^m,
∴ x = \(\frac{129}{2^{5} 5^{7} 7^{5}}\) have a non – terminating decimal expansion.

(ix) Let x = \(\frac{35}{50}=\frac{7}{10}\) …………. (1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 7, q = 10
Prime factors of q = 10 = 2 × 5 = 21 × 51
Which is of the form 2ⁿ × 5^m here n = 1, m = 1
both n and m are non negative integer.
∴ x = \(\frac{35}{50}\) have a terminating decimal expansion.

(x) Let x = \(\frac{77}{210}=\frac{11}{30}\) ……………..(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 11, q = 30
Prime factors of q = 30 = 2 × 5 × 3
which are not of the form 2ⁿ × 5^m,
∴ x = \(\frac{77}{210}\) have a non – terminating decimal expansion.

Question 2.
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solution:
(i) Let x = \(\frac{13}{3125}\)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 13,q = 3125
Prime factors of q = 3125 = 5 × 5 × 5 × 5 × 5 = 5⁵ × 2⁰
Which are of the form 2ⁿ × 5^m, where n = 0, m = 5 and these are non negative integers
∴ x = have a terminating decimal expansion.
To Express in Decimal form
x = \(\frac{13}{3125}=\frac{13}{5^{5} \times 2^{0}}\)

x = \(\frac{13 \times 2^{5}}{5^{5} \times 2^{5}}\)
[∵ we are to make 10 in the denominator so multiply and divide by 2⁵]

x = \(\frac{13 \times 32}{(2 \times 5)^{5}}\)

x = \(\frac{416}{(10)^{5}}=\frac{416}{100000}\)

x = 0.00416

(ii) Let x = \(\frac{17}{8}\) ………………..(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 17, q = 8
Prime factors of q = 8 = 2 × 2 × 2 = 2³ × 5⁰
Which are of the form 2ⁿ × 5^m, where n = 3, m = 0 and these are non negative integers
∴ x = \(\frac{17}{8}\) can be expressed as a terminating decimal expansion.
To Express in Decimal form

x = \(\frac{17}{8}=\frac{17}{2^{3} \times 5^{0}}\)

x = \(\frac{17 \times 5^{3}}{2^{3} \times 5^{3}}\)
[Multiply and divide with 5³ to make the denominator 10]

x = \(\frac{17 \times 125}{(2 \times 5)^{3}}\)

x = \(\frac{2125}{(10)^{3}}=\frac{2125}{1000}\)

x = 2.125

⇒ \(\frac{17}{8}\) = 2.125

(iii) Let x = \(\frac{15}{1600}\) …………….(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 15, q = 1600
Prime factors of q = 1600
= 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
= 2⁶ × 5²
Which are of the form 2ⁿ × 5^m, where n = 6, m = 2 and these are non negative integers
∴ x = \(\frac{15}{1600}\) can be expressed as a terminating decimal expansion.
To Express in Decimal form

x = \(\frac{15}{1600}\)

x = \(\frac{15 \times 5^{4}}{2^{6} \times 5^{2} \times 5^{4}}\)
[To make denominator a power of 10 multiply and divide by 5⁴]

x = \(\frac{15 \times 625}{2^{6} \times 5^{6}}\)

x = \(\frac{9375}{(2 \times 5)^{6}}\)

x = \(\frac{9375}{(10)^{6}}=\frac{9375}{1000000}\) = 0.009375

In Decimal form, x = \(\frac{15}{1600}\) = 0.009375

(iv) Let x = \(\frac{23}{2^{3} 5^{2}}\) …………….(1)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 15, q = 2³ 5²
Prime factors of q = 2³ 5²
Which are of the form 2ⁿ × 5^m, where n = 3, m = 2 and these are non negative integers
∴ x = \(\frac{23}{2^{3} 5^{2}}\) have a terminating decimal expansion.
To Express in Decimal form

x = \(\frac{23}{2^{3} 5^{2}}=\frac{23 \times 5}{2^{3} \times 5^{2} \times 5}=\frac{115}{2^{3} \times 5^{3}}\)

x = \(\frac{115}{(2 \times 5)^{3}}=\frac{115}{1000}\) = 0.115

In Decimal form,
x = \(\frac{23}{2^{3} 5^{2}}\) = 0.115

(v) Let x = \(\frac{6}{15}=\frac{2}{5}\)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 2, q = 5
Prime factors of q = 5 = 2⁰ × 5¹
Which are of the form 2ⁿ × 5^m, where n = 0, m = 1 and these are non negative integers
∴ x = \(\frac{6}{15}\) have a terminating decimal expansion.
To Express in Decimal form

x = \(\frac{6}{15}=\frac{2}{5}\)

x = \(\frac{2 \times 2^{1}}{2^{1} \times 5^{1}}=\frac{4}{10}\) = 0.4

In Decimal form,
x = \(\frac{6}{15}\) = 0.4

(vi) Let x = \(\frac{35}{50}=\frac{7}{10}\)
Compare (1) with x = \(\frac{p}{q}\)
Here p = 7, q = 10
Prime factors of q = 5 = 2¹ × 5¹
Which are of the form 2ⁿ × 5^m, where n = 1, m = 1 and these are non negative integers
∴ x = \(\frac{7}{10}\) have a terminating decimal expansion.
To Express in Decimal form

x = \(\frac{35}{50}\)

x = \(\frac{7}{10}\)

x = \(\frac{7}{2^{1} \times 5^{1}}\)

x = \(\frac{7}{(2 \times 5)^{1}}=\frac{7}{(10)^{1}}\) = 0.7
Hence in decimal form, x = 0.7

Question 3.
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form f, what can you say about the prime factors of q?
(i) 43.123456789
(ii) O.120120012000120000……
(iii) 4.3.123456789
Solution:
(i) Let x= 43.123456789 ……….. (1)
It is clear from the number that x is rational number.
Now remove the decimal from the number

∴ x = \(\frac{43123456789}{1000000000}\)

= \(\frac{43123456789}{10^{9}}\) …………….(2)
From (2) x is a rational number and of the \(\frac{p}{q}\).

Where p = 43123456789 and q = 10⁹
Now, Prime factors of q = 10⁰ = (2 × 5)⁹
⇒ Prime factors of q are 2⁹ × 5⁹

(ii) Let x = 0.120120012000120000
It is clear from the number that it is an irrational number.

(iii) Let x = 43.123456789 …. (1)
It is clear that the given number is a rational number because it is non-terminating and repeating decimal.
To show that (i) is of the form \(\frac{p}{q}\)
Multiply (1) with 10⁹ on both sides,
10⁹ x = 43123456789.123456789 …………….(2)
Subtract (1) from (2), we get:

which is rational number of the form \(\frac{p}{q}\)
x = \(\frac{4791495194}{111111111}\)
Here p = 4791495194, q = 111111111
x = \(\frac{4791495194}{3^{2}(12345679)}\)
Hence, prime factors of q are 3² (123456789)

Punjab State Board PSEB 10th Class English Book Solutions English Letter Writing Exercise Questions and Answers, Notes.

PSEB 10th Class English Letter Writing

परीक्षा-पत्र में निम्नलिखित प्रकार के पत्र पूछे जा सकते हैं
1. Personal letters to friends and relatives.
2. Letters of complaint, enquiry, request; applications.
3. Letters to Editor.
पत्र-लेखन के सम्बन्ध में कुछ आवश्यक जानकारी
1. आजकल पत्र-लेखन के सम्बन्ध में एक नई विधि को अपनाना शुरू कर दिया गया है, यद्यपि भाषा-विज्ञान की दृष्टि से इसका कोई आधार नहीं है।

2. नई विधि के अनुसार पत्र-प्रेषक का पता तथा पत्र लिखने की तिथि कई बार ऊपरी दाएं कोने में लिखने की बजाए बाएं कोने में लिख दिए जाते हैं, और प्राप्तकर्ता का नाम, पता तथा सम्बोधन करने के शब्द, आदि भी इसी के साथ नीचे लिख दिए जाते हैं तथा इनके लिखने में विराम-चिन्हों का प्रयोग भी लुप्त कर दिया जाता है। पत्र के अन्त में पत्र-प्रेषक अपना नाम या हस्ताक्षर भी बाईं तरफ़ ही डालता है। यह विधि यद्यपि कुछ अटपटी सी प्रतीत होती है, फिर भी बहुधा लोग इसे अपनाना बेहतर मानते हैं।

3. परम्परागत पुरानी विधि के अनुसार पत्र-प्रेषक का पता तथा पत्र लिखने की तिथि दोनों ही दाईं तरफ़ के ऊपरी कोने में लिखे जाते हैं और प्राप्तकर्ता को सम्बोधित करने सम्बन्धी शब्द बाईं तरफ़ नीचे को हटा कर लिखे जाते हैं। पत्र-प्रेषक अपना नाम या हस्ताक्षर, आदि भी पत्र के अन्त में दाईं सरफ़ हटा कर डालता है। तथा इन सब के लिखने में विराम-चिन्हों का विशेष ध्यान रखा जाता है।

4. विद्यार्थी को पत्र लिखते समय इस बात का विशेष ध्यान रखना चाहिए कि वह नई या पुरानी, किसा भा वाध का प्रयोग कर सकता है। किन्तु इन दोनों को किसी भी हालत में एक-दूसरी से मिला कर न लिखे। ऐसा करने से अंक काटे जा सकते हैं।

5. इस पृष्ठ पर ऊपर दिए गए उदाहरणों में पुरानी विधि के अनुसार विराम-चिन्हों का प्रयोग किया गया है, किन्तु . आजकल अधिकतर पत्र नई विधि के अनुसार ही लिखे जाते हैं, जैसा कि अगले पृष्ठों में दिखाया गया है।

Important Personal Letters

Advising Brother To Improve His Health

Question 1.
You are Rohit Verma, living at 27, Gandhi Nagar, Delhi. Your younger brother is a bookworm. He is good at studies but weak in health. Write him a letter, advising him to take part in games.
Answer:
27 Gandhi Nagar
Delhi
12 April 20… …
Dear Kapil
Your friend, Ashok, met me a few days ago. He told me that you have become a bookworm. You do not care at all about your health. You do not take part in games. It is not good on your part. Games are a part and parcel of education. Health is wealth. You can’t have a sound mind without a sound body. No doubt, you are good at studies, but you have a very poor health.
I advise you to be careful about your health. You should go out for a walk daily. Take part in games also. You must improve your health. One can’t enjoy one’s life without good health. If health is lost, everything is lost. Be a good boy. I hope you will act upon my advice.
With love
Yours affectionately
Rohit

Permission To Join An Educational Tour

Question 2.
You are Rahul Duggal, studying in class X at Govt. Sr. Secondary School, Maud Kalan, Bathinda. Write a letter to your father, requesting him to allow you to join an educational tour conducted by your school.
Answer:
Queen’s Hostel
Govt. Sr. Secondary School
Maud Kalan
Bathinda
10 December 20– —
My dear Father
Our school is breaking up for Christmas holidays on the 24th of this month. Some students of our school are going on an educational tour. The tour has been organised by our Principal. It will be a seven-day tour, from December 25 to December 31. The students shall visit Bengaluru, Mysore, Chennai and Madurai. I request you to allow me to go on this tour. Each student has to deposit ₹5000/ for this tour. I shall do with ₹ 1000/- only for my pocket expenses. Kindly send me ₹ 6000/- as soon as possible. I hope you will not disappoint me.
With regards
Yours affectionately
Rahul Duggal

Inviting Cousin To Spend Winter Break With You

Question 3.
Write a letter to your cousin Pulkit, inviting him to spend his winter break with you. You are Rohan and you live at 24, Mall Road, Shimla.
Answer:
24 Mall Road Shimla
16 December 20– —
Dear Pulkit
I invite you to come to Shimla in your winter vacation. We will have a nice time together. Snowfall in Shimla is a beautiful sight. Many tourists come to see it. We will also visit all the beauty spots near Shimla. I hope you will definitely come. Pay my deep regards to dear uncle and aunt.
Yours affectionately
Rohan

To Father About Home News

Question 4.
You are Monu and you live at 51, Central Town, Nangal. Write a letter to your father, who is away on a long tour, giving him home news.
Answer:
51 Central Town Nangal
6 September 20
Dear Father
Many things have happened since I wrote you last. Bittoo fell down the stairs and broke her leg. She became senseless. She was moved to hospital. She is quite fit now. You need not worry about her. Mohan’s result Was out yesterday. He got 700 marks. He is sure to get a scholarship. He is very happy. Uncle Kartar Singh also visited us last week. He stayed with us for two days. We all miss you badly. Please come back home soon.
Yours affectionately
Monu.

Giving details of a medical camp

Question 5.
Write a letter to your sister, Mohini, giving her the details of a free medical camp that your grandmother arranged recently. You are Sudhir Singh and live at 111, Chandigarh Road, Rajpura.
Answer:
111 Chandigarh Road Rajpura
20 November 20– —
Dear Mohini
You know our grandmother is a social activist. Last week, she organized a free medical camp for poor patients in the local Town Hall. Eleven eminent doctors provided their services. Patients were given free consultation and medicines. More than 1000 patients benefited from this camp. Such camps are really a true service towards mankind.
Yours affectionately
Sudhir Singh.

A Letter Of Condolence

Question 6.
You are Tanbir Singh, living at G-312, Adarsh Colony, Moga. Write a letter of condolence to your friend Amrit on the death of her mother.
Answer:
G-312 Adarsh Colony Moga
5th January 20
Dear Amrit
I was shocked to learn about the untimely death of your mother. She was quite healthy. I met her the other day. I never thought that her end was so near.
She was a very noble lady. She was kind to all. She was a lovable mother. She took keen interest in your studies. She looked upon me as her own daughter.
Dear Amrit your loss is great. But it was God’s will. His ways are strange. We must bow before Him. May God grant peace to the departed soul !
With deep sympathies …
Yours sincerely
Tanbir Singh

Thanking For Gift

Question 7.
Write a letter to your uncle, thanking him for the birthday gift he has sent you. You are Bhushan, living at 37, Civil Lines, Ludhiana.
Answer:
37 Civil Lines Ludhiana
5 August 20_ _
My dear Uncle
Thank you for the lovely gift you have sent me on my birthday. Your gift is truly after my heart. The wristwatch sent by you looks very beautiful. All my friends have liked it very much.
Dear uncle, I was badly in need of a watch. I was often late for school. I had to pay some fine every month. This watch will now prove useful for me. It will help me during the examinations. It will also help me to regulate my daily work. It is a token of your love for me. I shall keep it with great care. I once again thank you for this nice present.
Yours affectionately
Bhushan

Describing A Visit To A Historical Place

Question 8.
Write a letter to your younger brother Hitesh, describing your visit to some historical building. You are Naresh, living at Pratibha Hostel, Bal Bharti, Delhi.
Answer:
Pratibha Hostel
Bal Bharti
Delhi
10 October 20_ _
Dear Hitesh
You will be glad to know that I went to Agra during the last Christmas holidays. Our history teacher arranged this tour. There we visited the Taj. It has a majestic look. It is a large and beautiful building. It stands on a raised platform. In the middle of the platform, there is a splendid white dome. At its four corners, there are four stately towers. Underneath the white dome are the marble tombs of Mumtaz Mahal and Shah Jahan. The Taj was built by Shah Jahan in the sweet memory of his beloved wife. It is made of pure white marble. The beauty of the Taj beggars description. It looks like a fairy dressed in white. We stayed there for about two hours. I left the place most unwillingly. Its memory is still fresh in my mind.
With love
Yours affectionately
Naresh

About Your Stay With Your Uncle And Aunt

Question 9.
Write a letter to your mother, telling her about your stay with your uncle and aunt. You are Rajni and you live at Mansarovar Hostel, Vanketeshwara College, Karnal.
Answer:
Mansarovar Hostel
Vanketeshwara College
Karnal
20 June 20 _ _
Dear Mother
During my last holidays, I visited Uncle Rajan in Delhi. I spent there a couple of days. Aunt Neeru was very happy to have me there. She took me daily for shopping. We visited a number of historical places also. I came back on the fourth day with lots of gifts. How nice these people are !
With love
Rajni

Congratulating Friend On Success In Examination

Question 10.
You are Vishal and you live at New Janta Nagar, Jalandhar. Write a letter to your friend, Tanuj, congratulating him on his grand success in the Matriculation Examination.
Answer:
415 New Janta Nagar
Jalandhar 20 March
20- –
My dear Tanuj
The result of the Matriculation Examination was declared today. I looked up your roll number in the gazette. You are getting a high first division. It has given me great pleasure. Please accept my heartiest congratulations on your grand success. It is really a big achievement for you. And it is all the result of your hard work.
All of us are full of joy at your success. Please convey my congratulations to your dear parents also. They must be proud of your success. I hope you will be giving a party to celebrate your success. Don’t forget to keep my share. What are your future plans ? Write to me.
Your loving friend
Vishal

Scolding Brother For Neglecting Studies

Question 11.
You are Deepak Gupta. You live with your parents at 61, G.T., Road, Rajpura. Write a letter to your younger brother, Keshav, scolding him for neglecting his studies.
Answer:
61 G.T. Road
Rajpura
20 March 20_ _
My dear Keshav
I received your result card yesterday. Your result is very poor. You fail in all the subjects. This is a matter of shame for us. Manav, you should mend your ways. You should work very hard. Engage some tutor. Leave bad company. Make friends with good boys. Stop seeing movies. Start playing games in the evening. All this will pay you in the long run.
If you do not mend your ways now, you will repent later on.
I hope you will act upon my advice.
Yours affectionately
Deepak

Important Bussiness Letters

Wrong Supply Of Books

Question 1.
Write a letter to a bookseller, complaining about the wrong supply of a books. You are Jatinder Singh, living at 21, Model Town, Nakodar.
Answer:
21 Model Town
Nakodar
26 March 20 _ _
Messrs India Book Depot Mai Heera Gate Jalandhar
Subject : Wrong Supply of Books Dear Sirs
On 15th March, I ordered 10 copies each of books, ‘Background of Music’ by H.S. Narang and ‘History of Punjab’, by A.C. Arora, remitting ₹ 2000/-, the entire amount of their price, in advance.
On opening the parcel, received this morning, I found that it contained copies of the different titles by the same authors. I regret to say that I did not place the order for these titles. I am, therefore, returning them by parcel and requesting the replacement.  I hope the replacement will be despatched at the earliest date. I also hope that I shall not be charged any additional packing or postal expenses.
Yours faithfully
Jatinder Singh

Ordering Sports Goods

Question 2.
Write a letter ordering some sports goods to the firm, Messrs Avtar Singh and Sons at Jalandhar. You are Prabhjot, studying at Government High School, Nawan Shehar.
Answer:
Govt. High School Nawan Shehar
28 November 20_ _
Messrs Avtar Singh and Sons ’ Sports Goods Suppliers
Nakodar Road Jalandhar
Subject : Order for sports goods Dear Sirs
Kindly send the following sports goods at your earliest.
Footballs  Cosmo                      6 pcs.
Cricket      Bats English Willow One dozen
Cricket      Pads Antel               One dozen
Please check the above goods before packing. Send these goods through Satluj Transport Company. An a/c payee cheque for ₹2500/- is enclosed as advance payment.
Yours faithfully
Prabhjot Kaur

Complaint About A Tv Set

Question 3.
Ravi Sundaram of 28, Civil Lines, Ludhiana, bought a colour TV set from Messrs Ram Electronics, 14, Bazaar Marg, Ludhiana, a month ago. Now he finds that the sound is not clear and the picture changes to black and white from time to time. He writes a letter to the dealer, complaining about the same and requesting him to attend to it at the earliest. Write the letter.
Answer:
28 Civil Lines Ludhiana
28 March 20_ _
Messrs Ram Electronics
14 Bazaar Marg
Ludhiana
Subject: A recently purchased colour TV Set Dear Sirs
I bought a Venus Colour TV set from your shop against cash memo no. 1786 dated 17.3.20 and I regret to inform you that the set is not working properly, to the great dismay of each one in the house. The sound is not clear and the volume keeps fluctuating automatically. The picture also changes to black and white from time to time. The set is still under warranty, and I request you to attend to it at your earliest.
I hope you’ll enable us to watch on our TV the one-day Singer Cup cricket matches going to commence next Monday.
Thanking you
Yours faithfully
Ravi Sundram.

Cancelling An Order

Question 4.
You placed an order with Messrs Readymade Woollens, Ludhiana, for the supply of ladies cardigans, but they have delayed the execution of the order. Write a letter to them, cancelling the order. You are Nirmal Jain, Proprietor, Messrs Nirmal and Sons, Sangrur.
Answer:
Messrs Nirmal and Sons
Sangrur
5 October 20_ _
Messrs Readymade Woollens Ludhiana
Subject : Cancelling the order Sirs
We placed an order with you on 5th September for 200 pieces of ladies cardigans to be delivered by 20th September. But till now, we have received neither the goods nor any letter from you. The time of delivery has long expired and we are compelled to cancel the order, and should the goods arrive, they will now be refused.
Yours faithfully
Nirmal Jain
Proprietor

Placing An Order For Books

Question 6.
Imagine you are Rahul. You live at Muktsar. You live in Gandhi Nagar. Your house number is 765. You want to buy same books. Write a letter to Manager, Layal Book Depot, Ludhiana, ordering books of your choice.
Answer:
765, Gandhi Nagar
Muktsar
21 August 20_ _
The Manager
Layai Book Depot
Ludhiana
Subject: Placing an order for books
Dear Sir
Kindly send me one copy each of the following books by V.P.P. AU the books should be of the latest edition. I need them very urgently. Please send them at your earliest.
1. Modern English Grammar by Prof. Dharam Pal Bhanot (B.A. I)
2. History of Punjab by M.S. Mann (B.A.I)
3. Indian Political System by R.N. Duggal (B.A.I)
4. Essentials of Macro Economics by V.K. Srivastava (B.A.I)
Yours truly
Rahul Kushwaha

Complaint About A Beauty Product

Question 7.
You are Simran, living at Old Court Road, Sunam. Write a letter to Rama Herbal Cosmetics, Bengaluru, complaining about the body lotion they sent you.
36 Old Court Road Sunam
20 June 20_ _
Messrs Rama Herbal Cosmetics Bengaluru
Subject : Complaint about the body lotion sent by you Dear Sirs
Taken in by your much advertised body lotion, I had ordered three vials of it, the supply of which was received last Monday. But now I find that the lotion is very sticky and gives a very bad smell. Since this lotion is of no use to me, I want my money back. Please arrange to take back the vials and make good all the costs that have been borne by me.
Yours faithfully Simran
(Prop. Shiva Cosmetics)

Complaint Against The Postman

Question 7.
The postman of your street is rude and irregular. Write a letter to the postmaster complaining against the conduct of the postman. You are Gurpreet Singh, living at 11, Sector 25, Model Town, Jalandhar.
11, Sector 25
Model Town ‘
Jalandhar 19 April 20 _ _
The Postmaster General Post Office Jalandhar Sir
I am very sorry to report that my letters are not properly delivered to me. Ram Lai, the postman of our area, is very careless. Often he comes very late. He does not do his duty honestly. On the outer wall of my house, I have put up a letter box. It bears my name. But the postman never cares to put my letters into this box. He often throws them in at the gate. Sometimes, he hands them to the children playing in the street. Many important letters are thus lost. Kindly look into the matter and take suitable action.
Yours faithfully
Gurpreet Singh

Important Official Letters

Suggesting New Programmes For Children

Question 1.
During summer vacation, children stick to the television most of the time. Write a letter to the Director, Doordarshan, suggesting some new programmes you would like to have for children. You are Nikhil Gupta, living at 12, Patiala Road, Nabha.
Answer:
12 Patiala Road Nabha
28 May 20- –
The Director
Doordarshan
New Delhi
Subject : Request for showing certain programmes for children
Sir
As you know, these are the leisurely days of summer vacation. The school-going children can’t play outdoors due to scorching heat. They spend most of the time in front of the television. Therefore, I request you to telecast programmes on cartoons, general knowledge and new discoveries. It would help to increase their knowledge and also use their time in a constructive manner.
I hope you will do the needful.
Thanking you in anticipation
Yours faithfully
Nikhil Gupta.

Request For Installation Of Traffic Lights

Question 2.
Write a letter to the Superintendent of Police (Traffic), Chandigarh, requesting him to install traffic lights at the crossing near your school. You are Raj an Sethi, a student of class Xllth, DA.V. School, Chandigarh.
Answer:
D.A.V. School Chandigarh
28 September 20
The Superintendent of Police (Traffic)
Chandigarh
Subject : Installation of traffic lights at the crossing Sir .
There are no traffic lights at the crossing near our school. The traffic is very fast there. There is a grave danger to the life and limb of the students.
I, therefore, request you to kindly arrange traffic lights at the crossing.
Hoping for an immediate action
Yours faithfully
Rajan Sethi
Class XII

Request For A Study Loan

Question 3.
Write a letter to the manager of a bank, requesting for a loan for higher studies. You are Nikhil, living at 34, Krishna Nagar, Patiala.
Answer:
34 Krishna Nagar Patiala
28 November 20
The Manager Punjab National Bank Patiala
Subject : Request for a study loan Dear Sir
I read your advertisement in Hindustan Times yesterday. I have cleared the CAT examination and’have been selected for IIM, Ahmedabad. My father is a government teacher. The entire family banks upon him alone. So it is quite impossible for him to pay the fees for my course which is about ₹5 lac. I request you to sanction me a plan of this much amount. I undertake you to return the amount as per the conditions given in the advertisement.
Yours faithfully
Nikhil

Complaint About Insanitation

Question 4.
Imagine you are Raman. You live in Gali Ram Nath, Malerkotla. Write a letter to the Health Officer of your town complaining about the insanitary condition of your street.
Answer:
Gali Ram Nath
Malerkotla
16 March 20 _ _
The Health Officer Malerkotla
Subject : Insanitary condition of our street Sir
I beg to draw your attention to the insanitary condition of Gali Ram Nath in this city. Mainly poor people live in this area. Perhaps that is why no Sanitary Inspector
has ever visited it. There are very few proper drains here. The drains are not cleaned regularly. These are never flushed with water. No dustbins have been provided. People throw all their refuse here and there. Flies and mosquitoes buzz about. All this gives this area a very dirty look.
I hope you will take suitable measures to improve the sanitary condition of this area.
Yours faithfully
Raman

About Environmental Pollution

Question 5.
You are Raghu, staying at 12, Balmik Colony, Gurdaspur. Write a letter to the Editor of a newspaper to create awareness among the masses about pollution hazards.
Answer:
Balmik Colony Gurdaspur
March 20- –
The Editor The Tribune
Chandigarh
Subject : Environmental pollution
Sir
Environmental pollution is the biggest problem facing the modern man. Only recently has our government become aware of the gravity of this situation. More attention is being paid to afforestation. The unauthorised felling of trees is being checked. Scientists are developing methods to minimise the effect of smoke let out by our autos and chimneys. In fact, environmental awareness is a social necessity. It is not only the duty of the government, but also a social responsibility of the masses to keep the environment free from pollution.
Yours truly
Raghu

About The Problem Of Begging

Question 6.
You are Ramesh, living at 86, Sunam Road, Mansa. Write a letter to the Editor of a newspaper suggesting how the problem of begging can be solved.
Answer:
Adarsh Vihar Dwarka 27 April 20-
The Editor
The Indian Express
Delhi
Subject : The problem of begging Sir
The problem of beggars has assumed an alarming proportion in the city. Some beggars, no doubt, deserve our sympathy. They are handicapped. But the pity is that most of the beggars are able-bodied. Begging has become a profession for them. Some of them are criminals. They beg only to hide their crimes.
Begging should be abolished by law. Able-bodied beggars should be forced to work. If they go without work, they must also go without food. We should not encourage them by giving alms. People can thus play a big role in ending this evil.
Yours truly
Ramesh

Application For The Job Of A Computer Operator

Question 7.
Write an application for employment in Hindustan Limited, New Delhi, as a computer operator. You are Manu Gupta, living at 811, Sector 15, Rohini, New Delhi.
Answer:
811 Sector 15
Rohini New Delhi
25 July 20_ _
The General Manager Hindustan Limited
New Delhi
Subject : Application for the job of a computer operator
Sir
With reference to your advertisement in The Times of India, dated 20 July 20
I want to apply for the job of a computer operator in your company. As regards my qualifications, I have done Diploma in Computer Applications (DCA) after doing 10+2 from the CBSE. I have served for three years with a travel agency and am fairly good at all basic operations related to computer. If given a chance, I am sure you will feel satisfied with my services.
Yours faithfully
Manu Gupta

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7

Question 1.
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Am and Biju Is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Solution:
Let Ani’s age = x years
and Biju’s age = y years
Dharam’s age = 2x years
Cathy’s age = years
According to 1st condition,
(Ani’s age) (Biju’s age) = 3
x – y = 3 ……………(1)
According to 2nd condition,
(Dharam’ age) – (Cathy’s age) = 30
2x – \(\frac{y}{2}\) = 30
or \(\frac{4 x-y}{2}\) = 30
or 4x – y = 60 ………….(2)
Now (2) – (1) gives,

Substitute this value of x in (1), we get:
19 – y = 3
or -y = 3 – 19
or -y = -16
or y = 16
Hence, Ani’s age = 19 years
Biju’s age =16 years.

Question 2.
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “if you give me ten, I shall be six times as rich as you.” Tell me what is the amount of their (respective) capital ? [From the Bijaganita of Bhaskara II] [Hint: x + 100 = 2(y – 100), y + 10 = 6 (x – 10)].
Solution:
Let Capital of one friend = ₹ x
and capital of 2nd friend = ₹ y
According to 1st condition
x + 100 = 2(y – 100)
or x + 100 = 2y – 200
or x – 2y = -200 – 100
or x – 2y = -300 …………..(1)
According to 2nd condition
y + 10 = 6(x – 10)
or v-f 10 = 6x – 60
or 6x – y = 10 + 60
or 6x – y = 70 ……………(2)
Multiplying (1) by 6, we get
6x – 12y = – 1800 …………….(3)
Now, (3) – (2) gives

Substitute this value of y in (2), we get:
6x – 170 = 70
or 6x = 70 + 170
or 6x = 240
or x = \(\frac{240}{6}\) = 40
Hence, amount of their capital are 40 and 170 respectively.

Question 3.
A train covered a certain distance at a uniform speed. If the train would have been 10 km/b faster, It would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Solution:
Let speed of train =x km/hour
and time taken by train =y hour
∴ Distance covered by train = (Speed) (Time) = (xy) km
According to 1st condition,
(x + 10)(y – 2) = xy
or xy – 2x + 10y – 20 = y
or -2x + 10y – 20 = 0
or x – 5y + 10 = 0
According to 2nd condition,
(x – 10) (y + 3) = xy
or xy + 3x – 10y – 30 = xy
or 3x – 10y – 30 = 0
Multiplying (1) by 3, we get:
3x – 15y + 30 = 0
Now, (3) – (2) gives

Substitute this value of y in (1), we get:
x – 5 × 12 + 10 = 0
or x – 60 + 10 = 0
or x – 50 = 0
or x = 50
Speed of train = 50 km/hour
Time taken by train = 12 hour
Hence, distance covered by train = (50 × 12) km = 600 km.

Question 4.
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Solution:
Let number of students in each row = x
and number of rows = y
Total number of students in the class = xy
According to 1st condition,
(x + 3) (y – 1) = xy
or xy – x + 3y – 3 = xy
or -x + 3y – 3 = 0
or x – 3y + 3 = 0
According to 2nd condition,
(x -3) (y + 2) = xy
or xy + 2x – 3y – 6= xy
or 2x – 3y – 6 = 0
Now, (2) – (1) gives

x = 9
Substitute this value of x in (1), we get:
9 – 3y + 3 = 0
or -3y + 12 = 0
or -3y = -12
or y = \(\frac{12}{3}\) = 4
∴ Number of students in each row = 9 and number of rows = 4
Hence, total number of students in the class = 9 × 4 = 36.

Question 5.
In a ∆ABC, ∠C = 3 ∠B = 2(∠A +∠B) find the three angles.
Solution:
In ∆ABC,
Given that, ∠C = 3∠B = 2(∠A + ∠B)
I II III
From II and III, we get:
3∠B =2(∠A+∠B)
or 3∠B = 2∠A + 2∠B
or 3∠B – 2∠B = 2∠A
or ∠B = 2∠A ……………..(1)
From I and II, we get:
∠C = 3∠B
or ∠C = 3(2∠A) [using (1)]
or ∠C = 6∠A …………….(2)
Sum of three angles of a triangle is 180°
∠A + ∠B + ∠C = 180°
or ∠A + 2∠A + 6∠A = 180°
or 9∠A = 180°
∠A = \(\frac{180^{\circ}}{9}\) = 20°
Hence, ∠A = 20°: ∠B =2 x 20° = 40°; ∠C = 6 x 20° = 120°.

Question 6.
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle
formed by these lines and the y axis.
Solution:
Given pair of linear equation are 5x – y = 5 and 3x – y = 3
Consider,
5x – y = 5
or 5x = 5 + y
Putting y = 0 in (1), we get:
x = \(\frac{5+0}{5}=\frac{5}{5}\)
Putting y = – 5 in (1), we get:
x = \(\frac{5-5}{5}=\frac{0}{5}\) = 0
Putting y = 5 in (1), we get:
x = \(\frac{5+5}{5}=\frac{10}{5}\) = 2

Plotting A (1, 0); B (0, — 5); C (2, 5) on the graph, we get the equation of line 5x — y = 5
and 3x – y = 3
or 3x = 3 + y
or x = \(\frac{3+y}{3}\) ……………(2)
Putting y = 0 in (2), we get:
x = \(\frac{3+0}{3}=\frac{3}{3}\) = 1
Putting y = 3 in (2), we get:
x = \(\frac{3-3}{3}=\frac{0}{3}\) = 0
Putting y = 3 in (2), we get:
x = \(\frac{3+3}{3}=\frac{6}{3}\) = 2
Table:

Plotting A (1, 0); D (0, -3); E (2, 3) on the graph. we get the equation of line 3x – y = 3. From the graph, it is clear that given lines intersect at A (1, 0). Triangle formed by these lines and y axis are shaded in the graph i.e. ∆ABD. Coordinates of the vertices of ∆ABD are A(1, 0); B(0, -5) and D(0, -3).

Question 7.
Solve the following pair of linear equations:
(i) px + qy = p – q
qx – py = p + q

(ii) ax + by = c
bx + ay = 1 + c

(iii) \(\frac{x}{a}-\frac{y}{b}\) = 0
ax + by = a² + b²

(iv) (a – b)x + (a + b)y = a² – 2ab – b²
(a + b) (x + y) = a² + b²

(v) 152x – 378y = 74
-378x + 152y = -604
Solution:
(i) Given pair of linear equation are
px + qy = p – q …………(1)
and qx – py = p + q ………….(2)
Multiplying (1) by q and (2) by p, we get:

or y = -1
Substitute this value of y in (1), we get:
px + q(-1) = p – q
or px – q = p – q
or px = p – q + q
or px = p
or x = 1
Hence, x = 1 and y = -1.

(ii) Given pair of linear equation are
ax + by = c
bx + ay = 1 + c
ax + by – c = 0
bx + ay – (1 + c) = 0

From I and III, we get:
\(\frac{x}{-b-b c+a c}=\frac{1}{a^{2}-b^{2}}\)
or x = \(\frac{a c-b c-b}{a^{2}-b^{2}}\)

From II and III, we get:
\(\frac{y}{-b c+a+a c}=\frac{1}{a^{2}-b^{2}}\)
or y = \(\frac{a+a c-b c}{a^{2}-b^{2}}\)
Hence, x = \(\frac{a c-b c-b}{a^{2}-b^{2}}\) and y = \(\frac{a+a c-b c}{a^{2}-b^{2}}\).

(iii) Given pair of linear equation are
\(\frac{x}{a}-\frac{y}{b}\) = 0
or \(\frac{b x-a y}{a b}\) = 0
or bx – ay = 0
or bx—ay = O …(1)
and ax + by = a² + b²
or ax + by – (a² + b²) = 0 …………..(2)

\(\frac{x}{a\left(a^{2}+b^{2}\right)-0}=\frac{y}{0+b\left(a^{2}+b^{2}\right)}=\frac{1}{b^{2}+a^{2}}\)

or \(\frac{x}{a\left(a^{2}+b^{2}\right)}=\frac{y}{b\left(a^{2}+b^{2}\right)}=\frac{1}{a^{2}+b^{2}}\)

or \(\frac{x}{a}=\frac{y}{b}=\frac{1}{1}\)
I II III
From I and III, we get:
\(\frac{x}{a}=\frac{1}{1}\)
⇒ x = a
From II and III, we get:
\(\frac{y}{b}=\frac{1}{1}\)
⇒ y = b
Hence, x = a, y = b.

(iv) Given pair of linear equation are
(a – b)x + (a + b)y = a² – 2ab – b²
or ax – bx + ay + by = a² – 2ab – b² …………….(1)
and (a + b) (x + y) = a² + b²
or ax + bx + ay + by = a² + b²
Now, (1) – (2) gives

Substitute this value of x in (1), we get:
(a – b) (a + b) + (a + b) y = a² – 2ab – b²
or a² – b² + (a + b) y = a² – 2ab – b²
or (a + b) y = a² – 2ab – b² – a² + b²
or (a + b)y = -2ab
or y = \(\frac{-2 a b}{a+b}\)
Hence, x = a + b and y = a + b

(v) Given pair of linear equation are
152x – 378y = – 74
and -378x + 152y = -604
or 76x – 189y + 37 = 0
and -189x + 76y + 302 = 0

From I and III, we get:
\(\frac{x}{59890}=\frac{1}{29945}\)
⇒ x = \(\frac{59890}{29945}\)
⇒ x = 2

From II and III, we get:
\(\frac{y}{29945}=\frac{1}{29945}\)
⇒ y = \(\frac{29945}{29945}\)
⇒ y = 1
Hence x = 2 and y = 1.

Question 8.
ABCD is a cyclic quadrilateral (see Fig.). Find the angles of the cyclic quadrilateral.

Solution:
In cyclic quadrilateral ABCD,
∠A = (4y + 20); ∠B = 3y – 5; ∠C = 4x and ∠D = 7x + 5
Sum of opposite angles of a cyclic quadrilateral are of measure 180°.
∴ ∠A + ∠C = 180°
or 4y + 20 + (4x) = 180°
or 4x + 4y = 180° – 20
or 4x + 4y = 160
or x + y = 40
or y = 40 – x ……………..(1)
and ∠B + ∠D = 180°
or 3y – 5 + (7x + 5)= 180°
or 3y – 5 + 7x + 5 = 180°
or 7x + 3y = 180° …………….(2)
Substitute the value of y from (1) in (2). we get:
7x + 3(40 – x)= 180°
or 7x + 120 – 3x = 180°
or 4x = 180 – 120
or 4x = 60
x = \(\frac{60}{4}\) = 15
Substitute this value of x in (1 ), we get:
y = 40 – 15 = 25
∴ ∠A = 4y + 20 = 4 × 25 + 20 = 120°
∠B = 3y – 5 = 3 × 25 – 5 = 70°
∠C = 4x =4 × 15 = 60°
∠D = 7x + 5 = 7 × 15 + 5 = 110°
Hence, ∠A = 120°, ∠B = 70°; ∠C = 60° and ∠D = 110°.

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 1 Real Numbers Ex 1.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2

Question 1.
Express each number as a product of its prime factors :
(i) 140 (Pb, 2019)
(ii) 156
(iii) 3825
(iv) 5005 (Pb. 2019, Set-1, II, III)
(v) 7429.
Solution:
(i) Prime factorisation of 140 = (2)² (35) = (2)² (5) (7)

(ii) Prime factorisation of 156 = (2)² (39) = (2)² (3) (13)

(iii) Prime factorisation of 3825 = (3)² (425)
= (3)² (5) (85)
= (3)² (5)² (17)

(iv) Prime factorisation of 5005
= (5) (1001)
= (5) (7) (143)
= (5) (7) (11) (13)

(v) Prime factorisation of 7429
= (17) (437)
= (17) (19) (23)

Question 2.
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the two numbers.
(i) 26 and 91 [Pb. 2017 Set-C]
(ii) 510 and 92
(iii) 336 and 54.
Solution:
(i) Given numbers are 26 and 91 Prime factorisation of 26 and 91 are
26 = (2) (13) and
91 = (7) (13)
HCF (26, 91)
Product of least powers of common factors
∴ HCF (26, 91) = 13
and LCM (26, 91) = Product of highest powers of all the factors
= (2) (7) (13) = 182
Verification :
LCM (26, 91) × HCF (26, 91)
= (13) × (182) = (13) × (2) × (91)
= (26) × (91)
= Product of given numbers.

(ii) Given numbers are 510 and 92 Prime factorisation of 510 and 92 are
510 = (2) (255)
= (2) (3) (85)
= (2) (3) (5) (17)
and 92 = (2) (46) = (2)² (23)
HCF (510, 92) = Product of least powers of common factors = 2
LCM (510, 92) = Product of highest Powers of all the factors
= (2)² (3) (5) (17) (23) = 23460

Verification:
LCM (510, 92) × HCF (510, 92)
= (2) (23460)
= (2) × (2)² (3) (5) (17) (23)
= (2) (3) (5) (17) × (2)² (23)
= 510 × 92 = Product of given numbers.

(iii) Given numbers are 336 and 54
Prime factorisation of 336 and 54 are
336 = (2) (168)
= (2) (2) (84)
= (2) (2) (2) (42)
= (2) (2) (2) (2) (21)
= (2)⁴ (3) (7)

and 54 = (2) (27)
= (2) (3) (9)
= (2) (3) (3) (3)
= (2) (3)³
HCF (336, 54) = Product of least powers of common factors = (2) (3) = (6)
LCM (336, 54) = Product of highest powers of all the factors
= (2)⁴ (3)³ (7) = 3024

Verification :
LCM (336, 54) × H.C.F. (336, 54)
= 6 × 3024
= (2) (3) × (2)⁴ (3)³ (7)
= (2)⁴ (3) (7) × (2) (3)³
= 336 × 54
= Product of given numbers.

Question 3.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12, 15 and 21 [MQP 2015, Pb. 2015 Set A, Set B, Set C]
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Solution:
(i) Given numbers are 12, 15 and 21
Prime factorisation of 12, 15 and 21 are
12 = (2) (6)
= (2) (2) (3)
= (2)² (3)
15 = (3) (5)
21 = (3) (7)
HCF (12, 15 and 21) = 3
LCM (12, 15 and 21) = (2)² (3) (5) (7) = 420

(ii) Given numbers are 17, 23 and 29
Prime factorisation of 17, 23 and 29 are
17 = (17) (1)
23 = (23) (1)
29 = (29) (1)
HCF (17, 23 and 29) = 1
LCM (17, 23 and 29)
= 17 × 23 × 29 = 11339

(iii) Given numbers are 8, 9 and 25
Prime factorisation of 8, 9 and 25 are
8 = (2) (4)
= (2) (2) (2)
= (2)³ (1)
9 = (3) (3) = (3)² (1)
25 = (5) (5) = (5)² (1)
HCF (8, 9 and 25) = 1
LCM (8, 9 and 25) = (2)³ (3)² (5)² = 1800

Question 4.
Prove that HCF (306,657) = 9, find LCM (306,657). [Pb. 2016 Set-B, 2017 Set-B]
Solution:
Given numbers are 306 and 657 Prime factorisation of 306 and 657 are
306 = (2) (153)
= (2) (3) (51)
= (2) (3) (3) (17)
= (2) (3)2 (17)

657 = (3) (219)
= (3) (3) (73)
= (3)² (73)

HCF (306, 657) = (3)² = 9
∵HCF × LCM = Product of given number
∵9 × LCM (306, 657) = 306 × 657

= 34 × 657 = 22338

Question 5.
Check whether 6ⁿ can end with the digit 0 for any natural number n:
Solution:
Let us suppose that 6ⁿ ends with the digit 0 for some n ∈ N.
6ⁿ is divisible by 5.
But, prime factor of 6 are 2 and 3 Prime factor of (6)ⁿ are (2 × 3)ⁿ
⇒ It is clear that in prime factorisation of 6ⁿ there is no place for 5.
∵ By Fundamental Theorem of Arithmetic, Every composite number can be expressed as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur.
∴ Our supposition is wrong.
Hence, there exists no natural number n for which 6ⁿ ends with the digit zero.

Question 6.
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Solution:
Consider, 7 × 11 × 13 + 13 = 13 [7 × 11 + 1]
which is not a prime number because it has a factor 13. So, it is a composite number.
Also, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
= 5[7 × 6 × 5 × 4 × 3 × 2 × 1 + 1], which is not a prime number because it has a factor 5. So it is a composite number.

Question 7.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for die same. Suppose they both start at the same point and at file same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Solution:
Time taken by Sonia to drive one round of the field =18 minutes
Time taken by Ravi to drive one round of same field = 12 minutes
They meet again at the starting point = LCM (18, 12)
Now, Prime factorisation of 18 and 12 are 18 = (2) (9)
= (2) (3) (3)
= (2) (3)²

12 = (2) (6)
= (2) (2) (3)
= (2)² (3)
LCM (18, 12) = (2)² (3)² = 4 × 9 = 36
Hence, After 36 minutes Sonia and Ravi will meet again at the starting point.

Punjab State Board PSEB 10th Class Hindi Book Solutions Hindi Grammar vilom shabd विलोम शब्द Exercise Questions and Answers, Notes.

PSEB 10th Class Hindi Grammar विलोम शब्द

निम्नलिखित शब्दों के विलोम शब्द लिखिए

उत्तर:

निम्नलिखित बहुविकल्पी प्रश्नों के उत्तर एक सही विकल्प चुनकर लिखें.

प्रश्न 1.
असली का विलोम शब्द है
(क) निष्ठुर
(ख) अनुचित
(ग) नवीन
(घ) नकली।
उत्तर:
(घ) नकली

प्रश्न 2.
चेतन का विलोम शब्द है
(क) सुप्त
(ख) जड़
(ग) जागृत
(घ) निद्रा।
उत्तर:
(ख) जड़

प्रश्न 3.
कोमल का विलोम शब्द है
(क) निष्ठुर
(ख) निकृष्ट
(ग) कर्कश
(घ) अधम।
उत्तर:
(ग) कर्कश

प्रश्न 4.
सार्थक का विलोम शब्द है,
(क) व्यर्थ
(ख) निरर्थक
(ग) निर्गुण
(घ) क्षीण।
उत्तर:
(ख) निरर्थक

प्रश्न 5.
पूर्व का विलोम है, पश्चिम (हाँ या नहीं में उत्तर लिखें)
उत्तर:
हाँ

प्रश्न 6.
दानव का विलोम है, मानव (हाँ या नहीं में उत्तर लिखें)
उत्तर:
नहीं

प्रश्न 7.
भय का विलोम है, साहस (हाँ या नहीं में उत्तर लिखें)
उत्तर:
हाँ

प्रश्न 8.
ताप का विलोम है, शीत (सही या गलत लिखकर उत्तर दें)
उत्तर:
सही

प्रश्न 9.
पतन का विलोम है, गिरावट (सही या गलत लिखकर उत्तर दें)
उत्तर:
गलत

प्रश्न 10.
मिलन का विलोम है, विरह (सही या गलत लिख कर उत्तर दें)
उत्तर:
सही।

निम्नलिखित में से किसी एक शब्द का विलोम शब्द लिखिए

वर्ष
1. कंजूस, जिंदाबाद।
उत्तर:
कंजूस = दानी
जिंदाबाद = मुर्दाबाद।

2. हानि, ईमानदार।
उत्तर:
हानि = लाभ
ईमानदार = बेईमान।

3. निंदा, हार।
उत्तर:
निंदा = स्तुति
हार = जीत।

वर्ष
1. करीब, मित्र।
उत्तर:
करीब = दूर
मित्र = शत्रु।

2. आशा, मान
उत्तर:
आशा = निराशा
मान = अपमान।

3. विधवा, स्वस्थ।
उत्तर:
विधवा = सधवा
स्वस्थ = अस्वस्थ।

वर्ष
कंजूस, विस्तार।
उत्तर:
कंजूस = खर्चीला
विस्तार = संक्षेप।

प्रश्न 1.
विलोम शब्द किसे कहते हैं? उदाहरण सहित लिखिए।
उत्तर:
परस्पर विपरीत अर्थ का ज्ञान कराने वाले किसी शब्द को विलोम शब्द कहते हैं। इसे विपरीत या विलोमार्थी शब्द भी कहते हैं। उदाहरण-
(I) रीना सदा न्याय का पक्ष लेती है।
विलोम अर्थ-रीना सदा अन्याय का पक्ष लेती है।

(II) नीरज साधारण परिवार से संबंधित है।
विलोम अर्थ-नीरज असाधारण परिवार से संबंधित है।

(III) गली में एक व्यक्ति था।
विलोम अर्थ-गली में अनेक व्यक्ति थे।

(IV) गीताजंली का व्यवहार उचित था।
विलोम अर्थ-गीतांजली का व्यवहार अनुचित था।

(V) आप की यह हरकत पाक नहीं कहला सकती।
विलोम अर्थ-आप की यह हरकत नापाक नहीं कहला सकती।

प्रश्न 2.
विलोम शब्द किस-किस प्रकार बनाए जाते हैं? उदाहरण सहित लिखिए।
उत्तर:
विलोम शब्द प्रायः तीन प्रकार से बनाए जाते हैं-
(क) उपसर्ग के योग से
(ख) उपसर्ग बदलने से
(ग) विलोम शब्द मूल रूप से।
उदाहरण-
(क) उपसर्ग के योग सेइच्छा-अनिच्छा, साधारण-असाधारण, यश-अपयश, गुण-अवगुण, सुगंध-दुर्गंध, पसंद-नापसंद।
(ख) उपसर्ग बदलने से-साक्षर-निरक्षर, ईमानदार-बेईमानदार, स्वदेश-विदेश, संपन्न-विपन्न, अधुनातन-पुरातन, आयात-निर्यात।
(ग) विलोम शब्द मूल से-उदय-अस्त, आधुनिक-प्राचीन, उजड़ा-बसा, झगड़ा-समझौता, निकास-प्रवेश, दिवस-रात।

(क) उपसर्ग के योग से बने विलोम शब्द
(i) ‘अ’ उपसर्ग के योग से बने विलोम शब्द

(ii) ‘अन्’ उपसर्ग के योग से बने विलोम शब्द

(iii) ‘अप’ उपसर्ग के योग से बने विलोम शब्द

(iv) ‘अव’ उपसर्ग के योग से बने विलोम शब्द

(v) ‘कु’ उपसर्ग के योग से बने विलोम शब्द

(vi) ‘दुः/दुर्’ उपसर्ग के योग से बने विलोम शब्द

(vii) ‘ना’ उपसर्ग के योग से बने विलोम शब्द

(viii) ‘निः/निर्’ उपसर्ग के योग से बने विलोम शब्द

(ix) ‘पर’ उपसर्ग के योग से बने विलोम शब्द

(x) ‘प्रति’ उपसर्ग के योग से बने विलोम शब्द

(xi) ‘वि’ उपसर्ग के योग से बने विलोम शब्द

(xii) ‘बे’ उपसर्ग के योग से बने विलोम शब्द

कुछ विपरीत शब्द मूल रूप में ही प्रयुक्त होते हैं। जैसे-

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 1 Real Numbers Ex 1.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1

Question 1.
Use Euclid’s division algorithm to find the HCF of:
(i) 135 and 225
(ii) 196 and 38220
(iii) 867 and 255.
Solution:
(i) By Euclid’s division Algorithm

Step 1.
Since 225 > 135,
we apply the division Lemma to 225 and 135,
we get 225 = 135 × 1 + 90

Step 2.
Since the remainder 90 ≠ 0,
we apply the division Lemma to 135 and 90,
we get 135 = 90 × 1 + 45

Step 3. Since the remainder 45 ≠ 0,
we apply the division Lemma to 90 and 45,
we get 90 = 45 × 2 + 0

Since the remainder has now become zero, so we stop procedure.
∵ divisor in the step 3 is 45
∵ HCF of 90 and 45 is 45
Hence, HCF of 135 and 225 is 45.

(ii) To find HCF of 196 and 38220
Step 1.
Since 38220 > 196,
we apply the division Lemma to 196 and 38220,
we get 38220 = 196 × 195 + 0
Since the remainder has now become zero so we stop the procedure.
∵ divisor in the step is 196
∵ HCF of 38220 and 196 is 196.
Hence, HCF of 38220 and 196 is 196.

(iii) To find HCF of 867 and 255
Step 1.
Since 867 > 255,
we apply the division Lemma to 867 and 255,
we get 867 = 255 × 3 + 102

Step 2.
Since remainder 102 ≠ 0,
we apply the divison Lemma to 255 and 102,
we get 255 = 102 × 2 + 51

Step 3.
Since remainder 51 ≠ 0,
we apply the division Lemma to 51 and 102, by taking 102 as division,
we get 102 = 51 × 2 + 0
Since the remainder has now become zero, so we stop the procedure.
∵ divisor in step 3 is 51.
HCF of 102 and 51 is 51.
Hence, HCF of 867 and 255 is 51.

Question 2.
Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer.
Solution:
Let a be any positive odd integer, we apply the division algorithm with a and b = 6.
Since 0 ≤ r < 6, the possible remainders are 0, 1, 2, 3, 4 and 5. i.e., a can be 6q or 6q + 1, or 6q + 2, or 6q + 3, or 6q + 4, or 6q + 5 where q is quotient. However, since a is odd ∵ a cannot be equal to 6q, 6q + 2, 6q + 4 ∵ all are divisible by 2. Therefore, any odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5.

Question 3.
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Solution:
Total number of members in army = 616 and 32 (A band of two groups)
Since two groups are to march in same number of columns and we are to find out the maximum number of columns.
∴ Maximum Number of columns = HCF of 616 and 32
Step 1.
Since 616 > 32, we apply the division Lemma to 616 and 32, to get
616 = 32 × 19 + 8

Step 2.
Since the remainder 8 ≠ 0, we apply the division Lemma to 32 and 8, to get
32 = 8 × 4 + 0.
Since the remainder has now become zero
∵ divisor in the step is 8
∵ HCF of 616 and 32 is 8.
Hence, maximum number of columns in which they can march is 8.

Question 4.
Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
[Hint. Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + L]
Solution:
Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2.
If x = 3 q
Squaring both sides,
(x)² = (3q)²
– 9q² = 3 (3q²) = 3m
where m = 3 q²
where m is also an integer
Hence x² = 3m ………… (1)
If x = 3q + 1
Squaring both sides,
x² = (3q + 1)²
x² = 9q² + 1 + 2 × 3q × 1
x² = 3 (3 q² + 2q) + 1
x² = 3m + 1 …. (2)
where m = 3q² + 2q where m is also an integer
From (1) and (2),
x² = 3m, 3m + 1
Hence, square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Question 5.
Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
Solution:
Let x be any positive integer and b = 3
x = 3 q + r where q is quotient and r is remainder
If 0 ≤ r < 3
If r = 0 then x = 3 q
If r = 1 then x = 3q + 1
If r = 2 then x = 3q + 2
x is of the form 3q or 3q + 1 or 3q + 2
If x = 3q
Cubing both sides,
x³ = (3q)³
x³ = 27q³ = 9 (3q³) = 9m
where m = 3q³ and is an integer .
x³ = 9m ……….. (1)
If x = 3q + 1 cubing both sides,
x³ = (3 q +1)³
x³ = 27q³ + 27q² + 9q + 1
= 9 (3q³ + 3q² + q) + 1
= 9m + 1
where m = 3q³ + 3q² + q and is an integer
Again x³ = 9m + 1 …………. (2)
If x = 3q +2
Cubing both sides,
(x)³ = (3q + 2)²
= 27 q³ + 54 q² + 36q + 8
x³ = 9 (3 q³ + 6q² + 4q) + 8
x³ = 9m + 8 ………. (3)
where m = 3 q³ + 6q² + 4q
Again x³ = 9m + 8
From (1) (2), & (3), we find that
x³ can be of the form 9m, 9m + 1, 9m + 8.
Hence, x³ of any positive integer can be of he form 9m, 9m + 1 or 9m + 8

Punjab State Board PSEB 10th Class Hindi Book Solutions Hindi Grammar anek shabdon ke liye ek shabd अनेक शब्दों के लिए एक शब्द Exercise Questions and Answers, Notes.

PSEB 10th Class Hindi Grammar अनेक शब्दों के लिए एक शब्द

निम्नलिखित वाक्यांशों के लिए एक शब्द लिखिए

उत्तर:

निम्नलिखित बहुविकल्पी प्रश्नों के उत्तर एक सही विकल्प चुनकर लिखें

प्रश्न 1.
जो कहा न जा सके के लिए एक शब्द है-
(क) अकथ
(ख) अकहानीय
(ग) अगोचर
(घ) अनंत।
उत्तर:
(क) अकथ

प्रश्न 2.
जो देखा न जा सके के लिए एक शब्द है
(क) अमूर्त
(ख) अदृश्य
(ग) निराकार
(घ) निरंजन।
उत्तर:
(ख) अदृश्य

प्रश्न 3.
जो कभी न मरता हो के लिए एक शब्द है-
(क) अवध्य
(ख) अगम
(ग) अमर
(घ) अधोरी।
उत्तर:
(ग) अमर

प्रश्न 4.
जिसका आकार हो के लिए एक शब्द है,
(क) आर्कारी
(ख) साकार
(ग) सार्कारी
(घ) आर्कारीय।
उत्तर:
(ख) साकार

प्रश्न 5.
जो सब कुछ जानता हो के लिए एक शब्द है, अज्ञानी (हाँ या नहीं में उत्तर दीजिए)
उत्तर:
नहीं

प्रश्न 6.
जो ईश्वर को न मानता हो के लिए एक शब्द है, नास्तिक (सही या गलत लिखकर उत्तर दें)
उत्तर:
सही

प्रश्न 7.
जो प्रतिदिन होता हो के लिए एक शब्द है, दैनिक (सही या गलत लिखकर उत्तर दें)
उत्तर:
सही

प्रश्न 8.
जो आकाश में उड़ते हों के लिए एक शब्द है, नभीय (हाँ या नहीं में उत्तर दीजिए)
उत्तर:
नहीं

प्रश्न 9.
जिसके माता-पिता न हो के लिए एक शब्द है, अनादि (सही या ग़लत लिखकर उत्तर दें)
उत्तर:
गलत

प्रश्न 10.
पीछे-पीछे चलने वाला के लिए एक शब्द है, अनुगामी (हाँ या नहीं में उत्तर लिखें)
उत्तर:
हाँ।

बोर्ड परीक्षा में पूछे गए प्रश्न निम्नलिखित में से किसी एक वाक्यांश (अनेक शब्दों) के लिए एक शब्द लिखिए

वर्ष
डाक बाँटने वाला, आलोचना करने वाला।
उत्तर:
डाक बाँटने वाला = डाकिया
आलोचना करने वाला = आलोचक।

ईश्वर में विश्वास रखने वाला, वर्ष में एक बार होने वाला।
उत्तर:
ईश्वर में विश्वास रखने वाला = आस्तिक
वर्ष में एक बार होने वाला = वार्षिक।

उपकार को मानने वाला, कम खाने वाला।
उत्तर:
उपकार को मानने वाला = कृतज्ञ
कम खाने वाला = अल्पाहारी, मिताहारी।

वर्ष
समाज से संबंधित, देश से द्रोह करने वाला
उत्तर:
समाज से संबंधित = सामाजिक
देश से द्रोह करने वाला = देशद्रोही।

जिसका पार न हो, डाक बाँटने वाला।
उत्तर:
जिसका पार न हो = अपार
डाक बाँटने वाला = डाकिया।

गाँव में रहने वाला, कृषि कर्म करने वाला।
उत्तर:
गाँव में रहने वाला = ग्रामीण
कृषि कर्म करने वाला = कृषक।

वर्ष
पूर्वजों से प्राप्त हुई सम्पत्ति, जो नीति का ज्ञाता हो।
उत्तर:
पूर्वजों से प्राप्त हुई सम्पत्ति = पैतृक सम्पत्ति,
जो नीति का ज्ञाता हो = नीतिज्ञ।

प्रश्न 1.
वाक्यांश बोधक शब्द किसे कहते हैं?
उत्तर:
जो शब्द अनेक शब्दों के स्थान पर अकेले ही बोलने या लिखने के लिए प्रयोग में लाए जाते हैं उन्हें वाक्यांश बोधक शब्द कहते हैं, जैसे- कृतघ्न, सदाचारी, अवसरवादी, नास्तिक आदि।

प्रश्न 2.
अनेक शब्दों के लिए एक ही शब्द/वाक्यांश का प्रयोग भाषा में क्यों किया जाता है?
उत्तर:
अनेक शब्दों के लिए केवल एक ही शब्द/वाक्यांश का प्रयोग भाषा की सहजता, सुंदरता, संक्षिप्तता और प्रभावात्मकता को बढ़ाने के लिए किया जाता है। इससे कम-से-कम शब्दों में अधिक-से-अधिक भाव अभिव्यक्त किए जा सकते हैं। इसमें एक ही शब्द संपूर्ण वाक्य को अपने भीतर समेटे रहता है। उदाहरण-
जिसका जन्म न हो सके – अजन्मा
जिसके समान कोई दूसरा न हो – अद्वितीय
जिसका कोई शत्रु न हो – अजातशत्रु
बिना वेतन के काम करने वाला – अवैतनिक
विद्या ग्रहण करने वाला – विद्यार्थी’

अनेक शब्द/वाक्यांश के लिए एक शब्द के उदाहरण-

अनेक शब्द/वाक्यांश – एक शब्द
जहाँ पहुँचा न जा सके – अगम्य
अचानक होने वाली बात या घटना – आकस्मिक
अवसर के अनुसार बदल जाने वाला – अवसरवादी
अपना मतलब निकालने वाले – स्वार्थी, मतलबी
दूसरे के पीछे चलने वाला – ‘अनुयायी, अनुचर, अनुगामी
न करने योग्य – अकरणीय
आँखों के सामने होने वाला – प्रत्यक्ष
बिना वेतन काम करने वाला – अवैतनिक
आँखों के सामने न होने वाला – परोक्ष
कम जानने वाला – अल्पज्ञ
आलोचना करने वाला – आलोचक
तेज बुद्धि वाला – कुशाग्र बुद्धि
आगे या भविष्य की सोचने वाला – दूरदर्शी
बरे मार्ग पर चलने वाला – कुमार्गी
ईश्वर में विश्वास रखने वाला – आस्तिक
हानि को पूरा करना – क्षतिपूर्ति
ईश्वर में विश्वास न रखने वाला – नास्तिक
बड़ी इमारत के टूटे-फूटे भाग – खंडहर
उपकार को न मानने वाला – कृतज्ञ
चारों वेदों को जानने वाला – चतुर्वेदी
उपकार को न मानने वाला – कृतघ्न
बहुत समय तक बना रहने वाला – चिरस्थायी
ऊपर कहा गया – उपर्युक्त

जल में रहने वाला – जलचर
कम खाने वाला – अल्पाहारी, मिताहारी
जानने की इच्छा रखने वाला – जिज्ञासु
किसी विषय का विशेष ज्ञान रखने वाला – विशेषज्ञ
छोटा भाई – अनुज
कुछ जानने की इच्छा रखने वाला – जिज्ञासु
दूसरे देश से मँगाया जाना – आयात
जिसका आदि न हो – अनादि
उपजाऊ भूमि – उर्वरा
जिसका आचरण अच्छा हो – सदाचारी
उद्योग से संबंधित – औद्योगिक
किए हुए उपकार को मानने वाला – कृतघ्न
संध्या और रात्रि के बीच का समय – गोधूलि
आकाश को छूने वाला – गगनचुंबी
रोगी का इलाज करने वाला – चिकित्सक
जनता द्वारा चलाया जाने वाला राज – जनतंत्र
तीन मास में एक बार होने वाला – त्रैमासिक
बच्चों के लिए उपयोगी – बालोपयोगी
दूसरे के काम में हाथ डालना – हस्तक्षेप
अपना नाम स्वयं लिखना – हस्ताक्षर
जिसके हाथ में वीणा हो – वीणापति
जिसके पास लाखों रुपये हों – लखपति
जिसका इलाज न हो – लाइलाज
जिसका आचरण अच्छा हो – सदाचारी
जिसका आचरण बुरा हो – दुराचारी
जिसकी आत्मा महान् हो – महात्मा
जिसका कोई अर्थ हो। – सार्थक
जिसका मूल्य न आँका जा सके – अमूल्य
जिसका कोई अर्थ न हो – निरर्थक
जिसके हाथ में चक्र हो – चक्रपाणि
जिसका आकार न हो – निराकार
जिस पर उपकार किया गया हो – उपकृत
जिसका पार न हो – अपार
जिसका कोई स्वामी या नाथ न हो – अनाथ
जिसका भाग्य अच्छा न हो – अभागा, भाग्यहीन
जिसका जन्म न हो सके – अजन्मा
जिसकी परीक्षा ली जा रही हो – परीक्षार्थी
जिसका इलाज न हो सके – असाध्य
जिसकी आयु बड़ी लम्बी हो – दीर्घायु
जिसका विश्वास न किया जा सके – अविश्वसनीय
जिसकी बहुत अधिक चर्चा हो – बहुचर्चित
जिसका मन और ध्यान दूसरी तरफ़ हो – अन्यमनस्क
जिसकी कोई फीस न ली जाए – निःशुल्क
जिसका मूल्य न आँका जा सके – अमूल्य
जिसकी गिनती न की जा सके – अगणनीय
जिसका पति मर गया हो – विधवा
जिसका कोई शत्रु न हो – अजातशत्रु
जिसकी पत्नी मर गई हो – विधुर
जिसका पति जीवित हो – सधवा/सुहागिन
जिसे क्षमा न किया जा सके – अक्षम्य
जिसने ऋण चुका दिया हो – उऋण
जिसने अपनी इन्द्रियों पर विजय पा ली हो – जितेन्द्रिय
जिस पर अभियोग लगाया गया हो – अभियुक्त/प्रतिवादी
जो हाथ से लिखित हो – हस्तलिखित
जो कुछ न करता हो – अकर्मण्य
जो लोगों में प्रिय हो। – लोकप्रिय
जो सबसे आगे रहता हो – अग्रणी, अग्रगामी, अगग्रण्य
जो शरण में आया हो – शरणागत
जो अनुकरण करने योग्य हो – अनुकरणीय
जो सरलता से प्राप्त हो – सुलभ
जो धन का अपव्यय करता है – अपव्ययी
जो स्वयं सेवा करता हो – स्वयंसेवक
जो थोड़ा बोलता हो – अल्पभाषी/मितभाषी
जो वेतन के बिना काम करे – अवैतनिक
जो सदा रहे/जो कभी मरता न हो – अमर
जो देखा न जा सके – अदृश्य
जो कानून के विरुद्ध हो – अवैध

जो साथ-साथ पढ़ते हों – सहपाठी
जो सहन न किया जा सके – असह्य
जो थोड़ी देर पहले पैदा हुआ हो – नवजात
जो पहले न पढ़ा हो – अपठित
जो थोड़ा बोलता हो – मितभाषी
जो आँखों के सामने न हो – अप्रत्यक्ष
जो कम व्यय करता हो – मितव्ययी
जो परिचित न हो – अपरिचित
जो नियम के अनुसार न हो – अनियमित
जो केवल कहने और दिखाने के लिए हो – औपचारिक
जो बात कही ना सके – अकथनीय
जो कल्पना से परे हो – कल्पनातीत
जो पहले न पढ़ा हो – अपठित क
जो व्यक्ति अपनी बुराई के लिए प्रसिद्ध हो – ुख्यात
जो परिचित न हो – अपरिचित
जो निरंतर प्रत्यनशील रहे – कर्मठ
जो कभी तृप्त न हो – अतृप्त
जो पढ़ा-लिखा न हो – अनपढ़/निरक्षर
जो बात न कही गई हो – अनकही
जो उच्च कुल में पैदा हुआ हो – कुलीन
जो कार्य कष्ट से साध्य हो – कष्ट साध्य/दुःसाध्य
जो कड़वा बोलता हो – कटुभाषी
जो क्षमा करने योग्य हो। – क्षम्य
जो टुकड़े-टुकड़े हो गया हो – खंडित
जो छिपाने योग्य हो – गोपनीय
जो जन्म से अंधा हो – जन्मांध
जिसकी मीन/मछली जैसी आँखें हों – मीनाक्षी
जिसने यश प्राप्त किया है – यशस्वी
दूसरे लोक से संबंधित – पारलौकिक
मांस खाने वाला – मांसाहारी/समिषभोजी
युद्ध में स्थिर रहने वाला – युधिष्ठर
शक्ति के अनुसार – यथाशक्ति
अत्यंत सुंदर स्त्री – रूपसी
पत्तों से बनी कुटिया – पर्णकुटी
दिन में होने वाला – दैनिक
सप्ताह में एक बार होने वाला – साप्ताहिक
पंद्रह दिन में एक बार होने वाला – पाक्षिक
तीन मास में एक बार होने वाला – त्रैमासिक
वर्ष में एक बार होने वाला – वार्षिक
घूमने फिरने वाला – घुम्मकड़
देश से द्रोह करने वाला – देशद्रोही
छात्रों के रहने का स्थान – छात्रावास
दो कामों में से करने योग्य एक कार्य – वैकल्पिक
चारों वेदों को जानने वाला – चतुर्वेदी
नई चीज़ की खोज करने वाला – आविष्कारक
एक ही जाति के – सजातीय
परदेश में जाकर बस जाने वाला – प्रवासी
हिंसा करने वाला – हिंसक
पश्चिम से सम्बन्ध रखने वाला – पाश्चात्य
शक्ति का उपासक – शाक्त
पूर्वजों से प्राप्त हुई सम्पत्ति – पैतृक
संकट से ग्रस्त – संकटग्रस्त/विपन्न
प्रशंसा करने योग्य – प्रशंसनीय
समान अवस्था का – समवयस्क
बिना विचार किया हुआ विश्वास – अंधविश्वास
युगों से चला आने वाला – सनातन
समाज से संबंधित – सामाजिक
अच्छे चरित्र वाला – सच्चरित्र
सदा रहने वाला – शाश्वत

अपना मतलब निकालने वाला – स्वार्थी
सौ वर्षों का समूह – शताब्दी
साफ़-साफ़ कहने वाला – स्पष्टवादी
हित चाहने वाला – हितैषी, शुभेच्छु
सौतेली माँ – विमाता
जिसमें संदेह हो – संदिग्ध

Punjab State Board PSEB 10th Class Hindi Book Solutions Hindi Grammar samroopi bhinnarthak shabd समरूपी भिन्नार्थक शब्द Exercise Questions and Answers, Notes.

PSEB 10th Class Hindi Grammar समरूपी भिन्नार्थक शब्द

निम्नलिखित समरूपी भिन्नार्थक शब्द-युग्म का प्रयोग वाक्य में करके अर्थ स्पष्ट कीजिए-

उत्तर:

निम्नलिखित बहुविकल्पी प्रश्नों के उत्तर एक सही विकल्प चुनकर लिखिए

प्रश्न 1.
अचल-अचला के अर्थ हैं
(क) असमर्थ-अनुरक्त
(ख) पर्वत-पृथ्वी
(ग) साधन-साध्य
(घ) हिलना-डुलना।
उत्तर:
(ख) पर्वत-पृथ्वी

प्रश्न 2.
अनल-अनिल के अर्थ हैं
(क) आग-पानी
(ख) धूप-छाँव
(ग) आग-हवा
(घ) खट्टा-मीठा।
उत्तर:
(ग) आग-हवा

प्रश्न 3.
कुल-कूल के अर्थ हैं
(क) पूर्ण-अपूर्ण
(ख) वंश-किनारा
(ग) साधन-सहारा
(घ) पूरा-ठंडा।
उत्तर:
(ख) वंश-किनारा

प्रश्न 4.
चिर-चीर के अर्थ हैं
(क) देर-तट
(ख) चीरना-घाव
(ग) देरी-वस्त्र
(घ) चिड़ना-चीखना।
उत्तर:
(ग) देरी-वस्त्र

प्रश्न 5.
क्षिति-क्षति के अर्थ हैं-पृथ्वी-हानि (सही या गलत लिखकर उत्तर दें)
उत्तर:
सही

प्रश्न 6.
सुत-सूत के अर्थ हैं-पुत्र-सारथी (हाँ या नहीं लिख कर उत्तर दें)
उत्तर:
हाँ

प्रश्न 7.
तुरंग-तरंग के अर्थ हैं-मौज-मस्ती (हाँ या नहीं लिखकर उत्तर दें)
उत्तर:
नहीं

प्रश्न 8.
बलि-बली के अर्थ हैं-भेंट-बलवान (सही या गलत लिखकर उत्तर दें)
उत्तर:
सही

प्रश्न 9.
कर्म-क्रम के अर्थ हैं-काम-सिलसिला (हाँ या नहीं लिख कर उत्तर दें)
उत्तर:
हाँ

प्रश्न 10.
अंस-अंश के अर्थ हैं-हिस्सा-कंधा (सही या गलत लिखकर उत्तर दें)
उत्तर:
गलत।

निम्नलिखित में से किसी एक समरूपी भिन्नार्थक शब्द-युग्म का प्रयोग वाक्य में इस तरह करें ताकि उनका अर्थ स्पष्ट हो जाए-

वर्ष
1. असमान-आसमान, प्रणाम-प्रमाण।
उत्तर:
असमान = सुरेश उसके असमान है।
आसमान = आसमान में अनेक तारे हैं।
प्रणाम = पुत्र ने पिता को प्रणाम किया।
प्रमाण = प्रमाण के अभाव में आरोपी को आरोप मुक्त कर दिया गया।

2. उधार-उद्धार, प्रहार-परिहार।
उत्तर:
उधार = राम ने सुरेश को सौ रुपये उधार दिए।
उद्धार = सच्चे भक्त का उद्धार परमात्मा करते हैं।
प्रहार = गुंडे ने चाकू से दो प्रहार किए।
परिहार = स्वामी जी मोहमाया का परिहार कर चुके हैं।

3. राज-राज़, माँस-मास।
उत्तर:
राज = राजा अशोक ने भारत पर कई वर्षों तक राज किया।
राज़ = मुझे नरेश से राज़ की बात जाननी है।
माँस = शेर हिरण का माँस खा रहा था।
मास = दीपावली कार्तिक मास में मनाई जाती है।

वर्ष
1. गृह, ग्रह, धरा, धारा
उत्तर;
गृह = आपका गृह तो बड़ा भव्य है।
ग्रह = कुछ लोग शनि ग्रह को कष्टकारी मानते हैं।
धरा = यह धरा ही तो हमें अनाज प्रदान करती है।
धारा = गंगा की धारा देखने योग्य है।

2. सुत, सूत, मातृ, मात्र
उत्तर:
सुत = मेरा सुत भी अभी घर पहुंचा है।
सूत = आप तो बड़ा बारीक सूत कातते हैं।
मातृ’ = हमें जन्म देने वाली मातृ तो पूजनीय है।
मात्र = मेरी तो आपसे मिलने मात्र की इच्छा थी।

3. सूखी, सुखी, सास, साँस
उत्तर:
सूखी = इस सूखी धरती पर तो फसल नष्ट हो जाएगी।
सुखी = ईश्वर आपको सदा सुखी रखे।
सास = कल मेरी सास यहाँ आएगी।
साँस = रोगी की साँस मंद होती जा रही थी।

प्रश्न 1.
‘समरूपी भिन्नार्थक’ शब्द से क्या तात्पर्य है?
उत्तर:
विश्व-भर की सभी भाषाओं में कुछ ऐसे शब्द होते हैं जो उच्चारण में प्रायः समानता रखते हैं लेकिन उनके अर्थ में भिन्नता होती है। ऐसे शब्दों को समरूपी भिन्नार्थक शब्द कहते हैं। इन्हें श्रुतिसम भिन्नार्थक शब्द भी कहते हैं। इन शब्दों का प्रयोग अलग-अलग प्रसंगों में किया जाता है। जैसे-
(क) इत्र-सुगंधित पदार्थ
इतर-अन्य, दूसरा

(ख) गृह-घर
ग्रह-नक्षत्र

(ग) कृपण-कंजूस
कृपाण-तलवार

(घ) सुत-बेटा
सूत–सारथी/धागा

(ङ) ओर-तरफ
और-तथा

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