# Important Question For Board Exam: Real Numbers Important Questions, Revision Notes and Video Lectures on Real Numbers for Class 10 Board Exam (Padhte Chalo, Badhte Chalo- Eckovation). Join Group Code 101010 to discuss your doubts with educators from IIT Delhi

• Unit-1 of Class X C.B.S.E contains only one chapter which is Real Numbers.
• It carries 06 marks of the question paper
• The following questions are the set of important questions from this chapter
• Click Here for Revision Notes and Video Lecture of the topic

## SHORT ANSWER TYPE QUESTIONS: Real Number

1. Find the H.C.F. of the smallest composite number and the smallest prime number

2. What is the HCF of (26,91) if LCM(26,91) is 182?

3. Find one rational and one irrational no. between √ 3 and √ 5

4. Solve √ 18 x√ 50.  What type of number is it, rational or irrational.

5. If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y then find y

6. Why 17 + 11 × 13 × 17 × 19 is a composite number? Explain

7. Prove that √ 2 +√ 7  is not rational number.

8. State Euclid’s Division Lemma and hence find HCF of 16 and 28.

9. Given that HCF (135, 225) = 45. Find LCM (135, 225).
10. State fundamental theorem of Arithmetic and hence find the unique factorization of 120.

## LONG ANSWER TYPE QUESTIONS: Real Number

• Click Here for Revision Notes and Video Lecture of the topic
1. Find HCF of 56, 96 and 324 by Euclid’s algorithm
2. Show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m
3. Show that any positive odd integer is of the form 6q + 1, 6q + 5 where q is some integer.
4. Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer, q.
5.  Prove that the product of three consecutive positive integers is divisible by 6.
6.  Show that one and only one of n, n + 2, n + 4 is divisible by 3.
7.  Two milk containers contains 398 l and 436 l of milk. The milk is to be transferred to another container with the help of a drum. While transferring to another container 7 l  and 11 l of milk is left in both the containers respectively. What will be the maximum capacity of the drum.
8. Check whether 5 × 6 × 2 × 3 + 3 is a composite number
9. Check whether 14n can end with the digit zero for any natural number, n
10. If a = 4q + r then what are the conditions for a and q. What are the values that r can take?

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1. 2                                                 2                                            3.. Infinite numbers                      4. 30, rational                         5.y = – 19                     8.  4                                              9.  675                                 10. 2 × 2 × 2 × 3 × 5

1.4                                                    7. 17                                      8. yes                            9. No                           10.Opposite integer r, q whole no. 0  r <

##### Free Coaching and mentoring by IITians

Get the free and most effective coaching from IIT Graduates and score less than 5000 rank in JEE Mains and Advanced. To join the program, follow the steps: