a perfect question bank for chapter 01 of ncert class 10

1. CHAPTER:01
REAL NUMBERS
Q U E S T I O N S B A S E D O N L AT E S T C B S E PAT T E R N
2 0 2 0

2. QUESTION 01
• The HCF of two consecutive even number is:
a) 1 b) 2
c) 4 d) 8

3. QUESTION 02
• The HCF of smallest composite and the smallest prime number is
a) 0 b) 1
c) 2 d) 3

4. QUESTION 03
• The largest number which divides 70 and 125, leaving remainders 5 and 8
respectively is
a) 13 b) 65
c) 875 d) 1765

5. QUESTION 04
• The least number that is divisible by all the numbers from 1 to 10(both
inclusive) is
a) 10 b) 100
c) 504 d) 2520

6. QUESTION 05
• The number of decimal places after which the expansion of a
rational number
23
4 𝑥 5
is ?
a) 1 b) 2
c) 3 d) 4

7. QUESTION 06
• If P1 and P2 are odd prime numbers such that P1>P2, then
𝑃12
− 𝑃22
is ___________
a) an irrational number b) an even number
c) an even prime number d) an odd number

8. QUESTION 07
• The greatest 6 digit number exactly divisible by 4238 is
a) 993590 b) 995530
c) 995830 d) 995930

9. QUESTION 08
• State weather the following statements are true or false.
A rational number always has non-terminating and either recurring
or non-recurring decimal expansion.

10. QUESTION 09
• The unit’s place of 6 𝑛
for any positive ‘n’ is
a) 0 b) 3
c) 6 d) 4

11. QUESTION 10
• A number in the form 12q + 9 can be written as
a) 4m + 3 b) 3m + 1
c) 6q + 4.5 d) 22m + 18

12. QUESTION 11
• The only number which has only 1 factor is _______.

13. QUESTION 12
• If two positive integers a and b are expressible in the form
a=𝑝𝑞2
and b=𝑝3
𝑞 , what is the LCM(a, b)________.

14. QUESTION 13
• If
1
7
= 0.142857, then
5
7
𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜?
a) 0.871425recurring b) 0.124875recurring
c) 0.148275recurring d) 0.714285recurring.

15. QUESTION 14
• If n is any natural number then6 𝑛
− 5 𝑛
ends with?
a)5 b)9
b)6 d)1

16. QUESTION 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

17. QUESTION 16
• The decimal expansion of
15
1600
is?
a) 0.009365 b) 0.009375
c) 0.008375 d) 0.007375

18. QUESTION 17
• When 146 days is expressed as the decimal of a year, we get
a) 0.4 b) 0.004
c) 0.04 d) 0.0004

19. QUESTION 18
• There is an oval shaped park with a pathway running around it.
Babu and Raju start walking from a point Z at the same time
and in the same direction. If Babu can complete a full round in
16 mins while Raju can do it in 20 mins
a) after how many mins will they meet at point Z for the
first time?
b) if time be 400 mins, how many times will they meet at
the Z?

20. QUESTION 19
• Find the largest number which on subtracting 3 divides 120,
250 and 135.

21. QUESTION 20
• Find the HCF of 912 and 612 using Euclid’s Division Lemma.

22. QUESTION 21
• Prove that any perfect square is of the form 5m, 5m + 1 or 5m
+ 4, where m is a whole number.

23. QUESTION 22
• Prove that if ‘a’ and ‘b’ are two odd positive integers, then 𝑎2 +
𝑏2
is even, but not divisible by 4.

24. QUESTION 23
• 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 2 𝑖𝑠 𝑖𝑟𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙.

25. QUESTION 24
• 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 5 3 − 6 𝑖𝑠 𝑖𝑟𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙

26. QUESTION 25
• Show that
1
2
+
1
4
+
1
6
+
1
12
= 1

27. QUESTION 26
• Prove that the product of any three consecutive positive integer
is always divisible by 6.

28. IF YOU GET ALL THESE QUESTIONS,
THEN YOU DO HAVE REALLY
MASTERED THE CHAPTER:
REAL NUMBERS
CONGURALATIONS