Class 10 Real Numbers Previous Year Questions
Q1:
If two positive integers p and q can be expressed as p = 18 a² b⁴ and q = 20 a³ b², where a and b are prime numbers, then LCM(p, q) is?
CBSE [2024]
EasyQ2:
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.
CBSE [2024]
MediumQ3:
Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together?
CBSE [2024]
EasyQ4:
If the product of two co-prime numbers is 553, then their HCF is:
CBSE [2024]
MediumQ5:
If the prime factorisation of 2520 is 2³ × 3ᵃ × b × 7, then the value of a + 2b is:
CBSE [2024]
MediumQ6:
Given HCF(2520, 6600) = 40, LCM(2520, 6600) = 252 × k, then the value of k is:
CBSE [2024]
EasyQ7:
Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.
CBSE [2023]
MediumQ8:
If 'p' and 'q' are natural numbers and 'p' is the multiple of 'q', then what is the HCF of 'p' and 'q'?
CBSE [2023]
MediumQ9:
Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m, when will they ring together again?
CBSE [2023]
EasyQ10:
Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
CBSE [2023]
MediumQ11:
Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and pass it to third student. In this way by multiplying to a prime number, the last student got 173250. Now, Mukta asked some questions as give below to the students: (i) What is the least prime number used by students? (ii) (a) How many students are in the class? OR (b) What is the highest prime number used by students? (iii) Which prime number has been used maximum times?
CBSE [2023]
HardQ12:
Find the smallest number which is divisible by both 644 and 462
CBSE [2025]
EasyQ13:
Two numbers are in the ratio 4 : 5 and their HCF is 11. Find the LCM of these numbers.
CBSE [2025]
EasyQ14:
Let \( x \) and \( y \) be two distinct prime numbers and \( p = x^2 y^3 \), \( q = xy^4 \), \( r = x^5 y^2 \). Find the HCF and LCM of \( p, q \) and \( r \). Further check if \( \text{HCF}(p, q, r) \times \text{LCM}(p, q, r) = p \times q \times r \) or not.
CBSE [2025]
MediumQ15:
If \( x = ab^3 \) and \( y = a^3b \), where \( a \) and \( b \) are prime numbers, then \([ \text{HCF}(x, y) - \text{LCM}(x, y)]\) is equal to: (a) 1 - a³b³ (b) ab(1 - ab) (c) ab - a⁴b⁴ (d) ab(1 - ab)(1 + ab)
CBSE [2025]
MediumQ16:
The sum of the exponents of prime factors in the prime factorisation of 4004 is :
CBSE [2025]
EasyQ17:
The least number which is a perfect square and is divisible by each of 16, 20 and 50, is : (A) 1200 (B) 100 (C) 3600 (D) 240
CBSE [2025]
EasyQ18:
Which of the following is a rational number between \(\sqrt{3}\) and \(\sqrt{5}\) (A) 1·4142387954012... (B) 2.32\( 0.\overline{6} \) (C) π (D) 1·857142
CBSE [2025]
EasyQ19:
If \((-1)^n + (-1)^8 = 0\), then n is : (A) any positive integer (B) any negative integer (C) any odd number (D) any even number
CBSE [2025]
EasyQ20:
If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n 7m is :
CBSE [2025]
EasyQ21:
Find the greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively.
CBSE [2024]
MediumQ22:
If a = 2² × 3ˣ, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM(a, b, c) = 3780, then find x.
CBSE [2024]
EasyQ23:
Can the number (15)ⁿ, n being a natural number, end with the digit 0? Give reasons.
CBSE [2024]
EasyQ24:
If p² = \(\frac{11}{2}\), then p is a/an: (a) whole number (b) integer (c) rational number (d) irrational number
CBSE [2023]
EasyQ25:
