Class 10 Maths Chapter 1: Real Numbers Extra Questions(with Questions PDF and Step by Step Handwritten Solutions)

Chapter 1) Real Numbers

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Extra Questions with solutions

Q1) Obtain HCF of 12056 and 420.

Q2) Show that any positive integer is of the form of 8q +1, 8q+3 or 8q+7, where q is some integer.

Q3) Show that cube of any positive integer is of the form of 9m, 9m+1 or 9m+8.

Q4) Use Euclid’s division algorithm to find HCF of 460 and 20468.

Q5) Show that n² -1 is divisible by 8, if n is an odd positive integer.

Q6) Consider the numbers of the form 3ⁿ (where n is a natural number). Check whether there is any value of n for which 3ⁿ ends with 2.

Q7) Find the HCF and LCM of 35 and 115 by prime factorisation method.

Q8) Find HCF of 315 and 462 and hence find their LCM.

Q9) Find HCF and LCM of the following pairs of numbers:

a)      98 and 70:

b)      112 and 64:

Q10) There are 3 alarms A, B, and C. A rings after every 3hrs, B rings after every 4hrs and C rings after every 6hrs. Find the time interval after which the 3 alarms ring together after ringing once together.

Q11) Find the largest number that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively.

Q12) Which of the following rational numbers can be represented as terminating decimals?

a)      3/5

b)      2/13

c)       7/20

Q13) Find HCF of 3675 and 43 using Euclid’s division algorithm.

Q14) Using Euclid’s division lemma, prove that difference of squares of 2 odd natural numbers is a multiple of 8.

Q15) Check whether 7ⁿ can end with the digit ‘0’ for any natural number n.

Q16) Given that HCF (189,144) = 9, find their LCM.

Q17) If a is an irrational number, them prove that -a is also a irrational number.

Q18) Prove that 2 + 21/2 is not a rational number.

Q19) Without performing the long division process state whether the following rational numbers will have terminating decimal expansion or a non-terminating decimal expansion .

a)      17/8       b) 64/455             c) 29/343              d)15/1600            e)13/3125            f)23/2³5³

Q20) Prove that 51/2 + 31/2 is an irrational number.

Answers:

Q1) 4

Q4) 4

Q7) HCF = 5, LCM = 805

Q8) HCF = 21, LCM = 6930

Q9) a) HCF = 14, LCM = 490      b)HCF = 16, LCM = 448

Q10) 12hrs

Q11) 17

Q12) a) Terminating      b)Non-Terminating      c)Terminating

Q13) HCF = 21

Q15) no

Q16) 3024

Q19) a)Terminating     b)Non-Terminating     c)Non-Terminating     d)Terminating     e)Terminating

          f)Terminating

To find handwritten step by step solution you can download handwritten_solution.pdf from the blog itself J