Real numbers

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

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

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

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

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

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

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

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

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.

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

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

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

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)________.

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.

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

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

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

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

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?

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

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

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

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

QUESTION 23
• 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 2 𝑖𝑠 𝑖𝑟𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙.

QUESTION 24
• 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 5 3 − 6 𝑖𝑠 𝑖𝑟𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙

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

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

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

Real numbers

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