Grade 10 _ Real Numbers

Real Numbers

                                                                                                                            Grade :10

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1. Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.

2. Prove that the product of any three consecutive positive integers is divisible by 6. 

3.Apply Euclid’s division algorithm to find HCF of numbers 4052 and 420.

4. Three bells toll at intervals of 12 minutes, 15 minutes and 18 minutes respectively. If they start tolling together, after what time will they next toll together?

5. If HCF of 144 and 180 is expressed in the form 13m – 3, find the value of m.

6. Show that reciprocal of 3+2√2 is an irrational number.

7. Find HCF of 378,180 and 420 by prime factorisation method. Is HCF x LCM of three numbers equal to the product of the three numbers?

8. Find the HCF of 255 and 867 by Euclid’s division algorithm.

9. Find HCF of 65 and 117 and find a pair of integral values of m and n such that 

     HCF = 65m + 117n.

10. Using Euclid’s division algorithm, find whether the pair of numbers 847,2160 are               
      co- primes or not.

ANSWERS

1. HCF( 850, 680) = 170 liters

2. refer cbse text

3. HCF = 4

4. LCM =180

5.  m=3

6. Refer NCERT text

7. HCF = 6;  No. HCF (p, q, r) x LCM (p, q, r) ≠ p x q x r. where p, q, r are positive integers

8. HCF =51

9.The HCF of 65 and 117 is 13.
The required pair of integral values of m and n is
(2,-1) which satisfies the given relation HCF = 65m + 117n.

10. HCF =1; The numbers are co primes