MATHEMATICS / X / 2024-25/RO-BENGALURU
CHAPTER 1- REAL NUMBERS
KEY POINTS
13 | P a g e
, MATHEMATICS / X / 2024-25/RO-BENGALURU
Recalling the definition of prime number, composite number, rational number and irrational
number
Fundamental theorem of arithmetic: Every composite number can be expressed as a product
of primes and this factorization is unique.
Let p be a prime number. If p divides a2, then p divides a, where a is a positive integer.
For any 2 positive integers a and b, HCF (a,b) × LCM (a,b) = a × b
Proving the irrationality of √2, √3, etc using the method of contradiction
MULTIPLE CHOICE QUESTIONS (EACH CARRIES 1 MARK)
1. The sum of a rational and irrational number is always…………..
(a) Rational (b) irrational (c) 0 (d) 1
2. LCM of the numbers ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) X (b) y (c) xy (d) x+y
3. If two positive integers A and B can be expressed as A = xy3 and B = xy2; x, y being prime
numbers, the HCF (A, B) is …………….
(a) Xy (b) xy2 (c) xy3 (d) x2y
4. Express 98 as product of prime factors
(a) 7×22 (b) 72×22 (c) 72×2 (d) 7×23
5. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is……….
(a) 24 (b) 16 (c) 8 (d) 48
6. The exponent of 2 in the prime factorisation of 144, is
(a) 4 (b) 5 (c) 6 (d) 3
7. The LCM of two numbers is 1200. Which of the following cannot be their HCF?
(a) 600 (b) 400 (c) 200 (d) 500
8. The HCF of 12, 21, 15 are
(a) 3 (b) 4 (c) 12 (d) 15
9. The LCM and HCF of two rational numbers are equal, then the numbers must be
(a) Prime (b) co-prime (c) composite (d) equal
10. The ratio of LCM and HCF of the least composite number and the least prime number is
(a) 1:2 (b) 2:1 (c) 1:3 (d) 3:1
SHORT ANSWER TYPE- I QUESTIONS(EACH CARRIES 2 MARKS)
1. Express each number as a product of its prime factors:
a) 280 b) 156
14 | P a g e
CHAPTER 1- REAL NUMBERS
KEY POINTS
13 | P a g e
, MATHEMATICS / X / 2024-25/RO-BENGALURU
Recalling the definition of prime number, composite number, rational number and irrational
number
Fundamental theorem of arithmetic: Every composite number can be expressed as a product
of primes and this factorization is unique.
Let p be a prime number. If p divides a2, then p divides a, where a is a positive integer.
For any 2 positive integers a and b, HCF (a,b) × LCM (a,b) = a × b
Proving the irrationality of √2, √3, etc using the method of contradiction
MULTIPLE CHOICE QUESTIONS (EACH CARRIES 1 MARK)
1. The sum of a rational and irrational number is always…………..
(a) Rational (b) irrational (c) 0 (d) 1
2. LCM of the numbers ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) X (b) y (c) xy (d) x+y
3. If two positive integers A and B can be expressed as A = xy3 and B = xy2; x, y being prime
numbers, the HCF (A, B) is …………….
(a) Xy (b) xy2 (c) xy3 (d) x2y
4. Express 98 as product of prime factors
(a) 7×22 (b) 72×22 (c) 72×2 (d) 7×23
5. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is……….
(a) 24 (b) 16 (c) 8 (d) 48
6. The exponent of 2 in the prime factorisation of 144, is
(a) 4 (b) 5 (c) 6 (d) 3
7. The LCM of two numbers is 1200. Which of the following cannot be their HCF?
(a) 600 (b) 400 (c) 200 (d) 500
8. The HCF of 12, 21, 15 are
(a) 3 (b) 4 (c) 12 (d) 15
9. The LCM and HCF of two rational numbers are equal, then the numbers must be
(a) Prime (b) co-prime (c) composite (d) equal
10. The ratio of LCM and HCF of the least composite number and the least prime number is
(a) 1:2 (b) 2:1 (c) 1:3 (d) 3:1
SHORT ANSWER TYPE- I QUESTIONS(EACH CARRIES 2 MARKS)
1. Express each number as a product of its prime factors:
a) 280 b) 156
14 | P a g e
