CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Real Numbers)

     These Mathematics Questions of Chapter {Real Number} are important for CBSE Examination 2023. So all the candidates Revise and Practices all the questions carefully.

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1. Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides q² , then will divide q³ also? Explain.
2. In a school the duration of a period in junior section is 40 minutes and senior section is 1 hour. If the first bell for each section rings at 9:00 A.M, when will the two bells ring together again.
3.  How many irrational numbers lie between √2 and √3? Write any two of them.
4.  Given that HCF (306, 1314) = 18. Find LCM (306, 1314).
5.  Find the HCF of 1656 and 4025 by Euclid’s division algorithm.
6. A rational number in its decimal expansion is 327.7081.W can you say about the prime factors of q, when this number is expressed in the form p/q? Give reason.
7.  Show the 5√6 is an irrational number.
8.  Write the denominator of the rational number 257/500 in the form 2^m X 5ⁿ, where m and n are non negative integer. Hence write in decimal expansion without actual division.
9. Show that numbers 8ⁿ can never end with the digit 0 for any natural number n.
10.  Show that (√3 + √5)² is an irrational number.
11. Use Euclid division lemma to show that the square of any positive integer cannot be of the form 5m+2, 5m +3 for some integer m.
12.  Find HCF of 90 and 126 by Euclid’s division algorithm. Also find their LCM and verify that LCM X HCF = product of numbers.
13. The decimal expansion of the rational number 43/2⁴ .5³, will terminate after how many places of decimal?
14.  Find the HCF by Euclid’s division algorithm of the numbers 92690, 7378 and 7161.
15.  The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.
16. Find the HCF of 180, 252 and 324 using Euclid’s division lemma.
17.  Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
18.  Show that one and only one out of n, n+2 or n+4 is divisible by 3. Where n is any positive integer.
19.  If p is a prime number, then prove that √p is irrational.
20.  Prove that √5 is an irrational number and hence show that 2 - √5 is also a irrational number.
21.   Prove that √2 is an irrational number.
22.  Express the number 0.317831783178…….. in the form of rationala/b.ber a/b.
23.  Check whether 6ⁿ can end with the digit 0 for any natural number n.
24.  Explain (7 X 11 X 13) + 13 and (7 X 6 X 5 X 4 X 3 X 2 X 1) + 5 are composite number.
25.  The traffic light at three different road crossing changes after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 8 a.m. at what time will they change together again?
26.  Prove that √3 + √5 is an irrational.
27.  Prove that 4 - 3√2 is an irrational.
28.  Show that n² – 1 is divisible by 8, if n is an odd positive integer.
29. Prove that n² – n is divisible by 2 for every positive integer n.
30.  Show that there is no positive integer n, for which √n-1 + √n+1 is rational.
31.  Show that the square of any positive integer is of the form 4m, 4m + 1where m is any integer.
32. Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81, 237) = 81x +237yor some x and y.
33.  Foe any positive integer n, prove that n³ – n is divisible by 6.
34.  Show that any positive odd integer is of the form 6q +1 or 6q + 3or 6q + 5, where q is some integer.
35.  If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y, find y.
36. Prove that √7 is an irrational number.
37. Using prime factorization, find the HCF and LCM of 72, 126 and 168. Also show that HCF x LCM = product of the three numbers.
38. The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.
39. The product of two numbers is 20736 and their HCF is 54, find their LCM.
40. State the fundamental theorem of Arithmetic.
41. Check whether 5ⁿ can end with the digit 0 for any natural number n.
42. Express each of the following as the product of primes. (a) 6435   (b) 8085   (c) 2184
43. Show that square of an odd positive integer is of the form 8q + 1, for some positive integer q.
44. Show that every positive even integer is of the form 2q and every positive odd integer is of the form 2q+1, where q is some integer.
45. Prove that 5 + 2 √ 3 is an irrational number.
46. Show that 514 and 224 is a composite number.

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How to High Score in Class 10 Maths

 The simplest way to score 100 Marks in Class 10 Maths Exams. Just try it to get maximum in the least number of days. It is really a fantastic way to score 100 in 100 days. Most of the students think that Class 10 Maths is a difficult subject. To score full marks in Mathematics, one should have an extraordinary brain. But it is not true. It is not impossible for a student to score above 100 marks in Class 10 Maths if you follow the following tips.

Step 1: Make Notes for Formulae, Theorems and Methods using NCERT.

Complete the NCERT textbook exercises along with examples. All the questions should be solved at least twice in suitable interval of time. Maths is all about formulae, theorems, concepts etc. So maintain a separate register for these to make it handy. You can do practice anywhere with this handy notebook. It is the best tool for when you are doing your last-minute revision.

Step 2: Try To Find Solutions of NCERT Exemplar Yourself

Go through the NCERT Exemplar book and do each and every question including the examples. First of all, you should go through all the theories and concepts of the Maths syllabus and then solve various types of problems by yourself. If you want to score more marks in 10th class Maths, you need to solve every sum by yourself, at least 3 to 4 times.

Step 3: Practicing From The Sample And Previous Year Paper

Practice 10 solved practice papers of any good publisher and learn the way to answer in board exams. Some students do not understand the value of old assets, and they even don’t try to look at the previous year’s papers. But it is well proofed that previous year papers act as the key to success in getting the high percentage in your 10th board class exam. Do practice last 5-year sample papers of board exam and revise thoroughly before your exam, you must get above 100 marks.

Step 4: Set the Target to Know Your Weak Points

Practice 10 unsolved papers in 20 days (alternatively) with the time limit of 3 hours. Know your weak points first so that you can make them strong. You should go through your answer sheets of pre-boards and class tests etc. And take a deep look into your answers, find your mistakes and try to fix these mistakes so that you will do better in your board exam.

Step 5: Cover All Your Syllabus and Be Confident

Practice last 5 years CBSE Sample Papers and CBSE Board Exams Papers including the questions of set 1, 2, and 3. Most of the students waste their time by choosing wrong heavyweight reference books. You should cover the books like NCERT in the case of CBSE board which are the best to practice for your exam.

CBSE Board Preparation Tips 2023

 CBSE Class 10 board exams are scheduled to commence from 15th February, 2023 according to the CBSE board date sheet for 2022-23 board examination. There is exactly a month left and students are equally excited and nervous for their first board exam.

The tension among the candidates has begun to rise high. We have been taught from a young age that CBSE class 10th board exams are the ultimate test in a student’s life. Although the statement isn’t inherently true, it is true that class 10 CBSE board exam is a major step in our lives towards more learning and more exposure to streams we would most likely be in our future. 

All the subjects that we study upto class 10th, including other co-curricular and extra-curricular activities, prepare us for taking on what would come next in senior secondary, undergraduate or higher and professional levels. 

To give an ‘excellent’ overall performance, it is important to prepare and perform well in each and every subject. Read this article to know how to prepare for CBSE Class 10 Board Exam 2023. 

So, if you are also contemplating about how to prepare for CBSE Class 10th board examinations, check the exam preparation tips given below:

1. GATHER ALL RESOURCES FOR PREPARATION

Believe it or not, not having all the right resources to study from is one of the worst and most common mistakes that students make. This is because students waste a lot of useful time looking for resources when they should actually be studying. The first step to begin your CBSE Class 10 Preparation is by collecting all the resources that you would require. 

2. SEGREGATE THE SUBJECTS OF CBSE CLASS 10 CURRICULUM

Although we need to be the Jack of all trades to excel in CBSE class 10 board exams with flying colours, the truth is that we all have our interests, likes and dislikes. It is imperative that we analyse and acknowledge the subjects that we are weak in and the ones which we excel in. Dividing the subjects into categories will help us in our next step.

For example, if you know that you like Social Science and Mathematics then you group them together while if you find English or Science boring then put it in a separate category.

3. DECIDE PRIORITIES 

The next tip is based on the previous tip.

Based on the list that you make by dividing subjects according to your strengths and weaknesses, you should plan on how much time and effort each subject would require from your side. Prioritise perfecting the subjects that you are not confident in while still paying attention to your strong subjects.

4. SET YOUR OWN TIME TABLE FOR BOARD EXAM PREPARATION

Remember when we asked you to gather all the resources?

Yes, now is the time to check your stack of syllabus and go through the whole syllabus, in a subject wise manner, and check the weightage of each topic.

On the basis of the CBSE Board exam date sheet and your analysis of the syllabus and marking weightage, you should now create a time table for yourself. Include more time for subjects that require more work from your side even if they aren’t your favourite. You can even study your favourite subjects as a relaxing part to boost your motivation for the preparations ahead.

5. REST & BREAKS

Go back to the time table you have created for yourself.

Now check if you have given yourself enough time for relaxation. Even if you are getting stressed about the boards, you need to provide your brain and body with a healthy amount of sleep and relaxing, fun activities.

Include time for your hobbies and sleep. Especially make your time table practical based on your weekly and daily schedule. Keep in mind the festivities and holidays where you might not be able to devote the same efforts as on other days.

Also make note of your school hours, extra-classes, coaching classes, etc. 

6. KEYWORDS

Now, when you finally begin to prepare any topic of a particular subject, you should focus on the keywords. It is around the keywords that the topics mostly revolve.

You can even make lists of different keywords in relation to different topics which will come in handy when you are trying to look back and briefly revise.

7. FAMILIARITY WITH THEORY (conceptual clarity)

Candidates often think they have a lot of time to read the topics in detail later on but that is seldom true. You should try to familiarise yourself with all the theories and concepts as early as possible in your preparation journey. Your list of keywords would be beneficial for you here.

Read and understand the topics, note down the meanings of difficult words, ask doubts to your teachers, watch relevant audio-visuals, take help of encyclopedias, etc. 

PRE - PRE BOARDS

No, that is not a typing error. Pre - Pre Boards is the test that you put yourself through by attempting sample question papers and previous year papers in the time allotted and just like how you would attempt boards. Although pre boards arranged by the schools are to test your preparations, it is always good to test yourself before and after the pre boards to see how ready you are. You also get to analyse your mistakes and weak area which require more attention and work from your end.