Part - 1 (Basic Multiple Choice Questions)
1. If prime factorization of 7560 is expressible as 23 × 3p × q × 7, then the values of p and q are respectively___and__
(a) 2, 3 (b) 5, 3 (c) 3, 5 (d) 5, 2
2. The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is :
[CBSE (Standard) 2024]
(a) 5 (b) 13 (c) 40 (d) 8
3. If the HCF of 567 and 693 is expressible in the form 567x + 693 × (–4), find x.
(a) 4 (b) 2 (c) 5 (d) 3
4. Let p be a prime number and k be a positive integer. If p divides k , then which of these is DEFINITELY divisible
2
by p? [CBSE Competency Focused Practice Questions 2022-23]
k/2 k 7k k
3
(A) only k (b) only k and 7k (c) only k, 7k and k3 (d) All k/2, k, 7k and k3
5. The greatest number which when divides 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is
(a) 575 (b) 450 (c) 750 (d) 625
6. The sum of exponents of prime factors in the prime factorisation of 196 is
(a) 3 (b) 4 (c) 5 (d) 2
7. The LCM of three numbers 28, 44, 132 is :
(a) 258 (b) 231 (c) 462 (d) 924
8. If the product of two co-prime numbers is 553, then their HCF is :
(a) 1 (b) 553 (c) 7 (d) 79
9. I. The LCM of x and 18 is 36.
II. The HCF of x and 18 is 2.
What is the number x?
(a) 1 (b) 2 (c) 3 (d) 4
10. Shweta wants to organise a party. She has 336 guavas and 54 oranges at home and decided to distribute them
equally among all. What is the maximum number of guests she can invite?
(a) 5 (b) 6 (c) 7 (d) 8
Real Numbers 1
, Part - 2 (Basic Subjective Type Questions)
1. Show that 6n can not end with digit 0 for any natural number ‘n’.
2. In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively.
Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them
are of the same subject.
3. P = 2(4)(6)...........(20) and Q = 1(3)(5)..............(19). What is the HCF of P and Q.
4. If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5, then n is equal to
5. The HCF of two natural numbers is 3 and their LCM is 60. The difference of two numbers is 24. Find the numbers.
6. Vicky went to a stationery shop to buy 45 pencils and 105 pens as return gifts for his birthday party. He asked the
shopkeeper to pack them in such a way that each packet contains the same number of pencils or pens, with no
remainder. What is the greatest number of such packets that can be made for each type? Also, how many pencils
and pens will be in each packet?
7. A forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal rows (in terms of number of
trees). Also, he wants to make distinct rows of the trees (only one type of tree in one row). Find the minimum
number of rows required. [CBSE Practice Set-2, 2023]
8. Prove that n is not a rational number, if n is not perfect square.
Part - 1 (Advanced Multiple Choice Questions)
1. n is a natural number such that n > 1. Which of these can DEFINITELY be expressed as a product of primes?
[CBSE Competency Focused Practice Questions 2022-23]
n
(i) n (ii) n (iii)
2
(a) only (ii) (b) only (i) and (ii)
(c) all (i), (ii) and (iii) (d) cannot be determined without knowing n
2. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of the track is 30
minutes and p minutes respectively. If the cars meet again at the starting point for the first time after 90 minutes and
the HCF (30, p) = 15, then the value of p is [CBSE APQ (Standard) 2023-24]
(a) 45 minutes (b) 60 minutes (c) 75 minutes (d) 180 minutes
3. Find the greatest 4 digits number which leaves remainder 12 when divided by 105, 175 and 70.
(a) 9987 (b) 9462 (c) 9998 (d) 9963
4. Find the smallest 5 digits number which leaves remainder 12 when divided by 105, 175 and 70.
(a) 10500 (b) 11562 (c) 10512 (d) 11550
5. Find the least number of square tiles required to cover the floor of 630m long and 531 m broad
(a) 9 (b) 4130 (c) 81 (d) 2360
6. Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF
(a, b) = pmqn and LCM (a, b) = prqs, then (m + n) (r +s ) =
(a) 15 (b) 30 (c) 35 (d) 72
7. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result
obtained by dividing the product of the positive integers by the LCM (a, b) is :
(a) xy (b) xy2 (c) x3y3 (d) x2y2
Class - X (Module • Mathematics) 2
1. If prime factorization of 7560 is expressible as 23 × 3p × q × 7, then the values of p and q are respectively___and__
(a) 2, 3 (b) 5, 3 (c) 3, 5 (d) 5, 2
2. The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is :
[CBSE (Standard) 2024]
(a) 5 (b) 13 (c) 40 (d) 8
3. If the HCF of 567 and 693 is expressible in the form 567x + 693 × (–4), find x.
(a) 4 (b) 2 (c) 5 (d) 3
4. Let p be a prime number and k be a positive integer. If p divides k , then which of these is DEFINITELY divisible
2
by p? [CBSE Competency Focused Practice Questions 2022-23]
k/2 k 7k k
3
(A) only k (b) only k and 7k (c) only k, 7k and k3 (d) All k/2, k, 7k and k3
5. The greatest number which when divides 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is
(a) 575 (b) 450 (c) 750 (d) 625
6. The sum of exponents of prime factors in the prime factorisation of 196 is
(a) 3 (b) 4 (c) 5 (d) 2
7. The LCM of three numbers 28, 44, 132 is :
(a) 258 (b) 231 (c) 462 (d) 924
8. If the product of two co-prime numbers is 553, then their HCF is :
(a) 1 (b) 553 (c) 7 (d) 79
9. I. The LCM of x and 18 is 36.
II. The HCF of x and 18 is 2.
What is the number x?
(a) 1 (b) 2 (c) 3 (d) 4
10. Shweta wants to organise a party. She has 336 guavas and 54 oranges at home and decided to distribute them
equally among all. What is the maximum number of guests she can invite?
(a) 5 (b) 6 (c) 7 (d) 8
Real Numbers 1
, Part - 2 (Basic Subjective Type Questions)
1. Show that 6n can not end with digit 0 for any natural number ‘n’.
2. In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively.
Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them
are of the same subject.
3. P = 2(4)(6)...........(20) and Q = 1(3)(5)..............(19). What is the HCF of P and Q.
4. If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5, then n is equal to
5. The HCF of two natural numbers is 3 and their LCM is 60. The difference of two numbers is 24. Find the numbers.
6. Vicky went to a stationery shop to buy 45 pencils and 105 pens as return gifts for his birthday party. He asked the
shopkeeper to pack them in such a way that each packet contains the same number of pencils or pens, with no
remainder. What is the greatest number of such packets that can be made for each type? Also, how many pencils
and pens will be in each packet?
7. A forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal rows (in terms of number of
trees). Also, he wants to make distinct rows of the trees (only one type of tree in one row). Find the minimum
number of rows required. [CBSE Practice Set-2, 2023]
8. Prove that n is not a rational number, if n is not perfect square.
Part - 1 (Advanced Multiple Choice Questions)
1. n is a natural number such that n > 1. Which of these can DEFINITELY be expressed as a product of primes?
[CBSE Competency Focused Practice Questions 2022-23]
n
(i) n (ii) n (iii)
2
(a) only (ii) (b) only (i) and (ii)
(c) all (i), (ii) and (iii) (d) cannot be determined without knowing n
2. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of the track is 30
minutes and p minutes respectively. If the cars meet again at the starting point for the first time after 90 minutes and
the HCF (30, p) = 15, then the value of p is [CBSE APQ (Standard) 2023-24]
(a) 45 minutes (b) 60 minutes (c) 75 minutes (d) 180 minutes
3. Find the greatest 4 digits number which leaves remainder 12 when divided by 105, 175 and 70.
(a) 9987 (b) 9462 (c) 9998 (d) 9963
4. Find the smallest 5 digits number which leaves remainder 12 when divided by 105, 175 and 70.
(a) 10500 (b) 11562 (c) 10512 (d) 11550
5. Find the least number of square tiles required to cover the floor of 630m long and 531 m broad
(a) 9 (b) 4130 (c) 81 (d) 2360
6. Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF
(a, b) = pmqn and LCM (a, b) = prqs, then (m + n) (r +s ) =
(a) 15 (b) 30 (c) 35 (d) 72
7. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result
obtained by dividing the product of the positive integers by the LCM (a, b) is :
(a) xy (b) xy2 (c) x3y3 (d) x2y2
Class - X (Module • Mathematics) 2
