Real numbers Class 10 worksheet

 Class 10
CHAPTER – 1 REAL NUMBERS 

1.If n € N then 4ⁿ will never end with the digit ________

2. Which kind of decimal expansion  has ?

3. The LCM and HCF of two rational numbers are equal, then the number must be  ___                   4. What is the remainder when the square of any prime number greater than 3 is divided by 6.

5.              If n is any natural number, then 6ⁿ- 5ⁿ always ends with which digits ?

6.              how many  number of decimal places after which the decimal expansion of the rational number  will terminate  ?

7.              If two positive integers a and b are expressible in the form a = pq² and b = p³q ; p, q being prime numbers then what is L.C. M (a,b) ?

8.              What is the product of H.C.F and L.C.M of the smallest prime number and the smallest composite number.

9.               After how many places will decimal expansion 21/24 terminate.

10.  If a and b are prime numbers, then what is their L.C.M .

11.  Which of the following will have a terminating decimal expansion?

(a)               (b)                             (c)                            (d)

 

SUBJECTIVE TYPE 

12.  Three bells toll at interval of 9, 12, 15 mins respectively. If they start tolling together , after what time will they next toll together ?

13.  Check whether 4ⁿ can end with the digit 0 for any natural number n.

14.  The L.C.M of two numbers is 14 times their H.C.F. The sum of L.C.M and H.C.F is 600. If one number is 280, then find the other number.

15.  Find HCF of 96 and 404 by prime factorization method. Hence find their L.C.M

16.  Prove that √3 is irrational.

17.  Show that 5 -2√3 is irrational.

18.  Show that 3√2 is irrational.

19.  Find the largest positive integer that will divide 398, 436 and 542 leaving remainder  7,  11 and 15 respectively.

20.  Find the largest number which divides 245 and 1029 leaving remainder 5 in each case                    

21.  Find the largest number which divides 2053 and 967 and leaves a remainder 5 and 7 respectively. 

22.  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.

23.     Prove that √8 is irrational. 

24.  Prove that  is irrational

25.  The length, breadth and height of a room are 8m 25cm , 6m 75cm, and 4m 50cm., respectively. Determine the longest rod which can measure the three dimensions exactly.

26.  Find the H.C.F and L.C.M of 144, 180 and 192 by prime factorization method. 

27.Explain why 11 X 13 X 15 X 17 + 17 is a composite number.