Math Problem Solver

Q1: The smallest irrational number by which √20 should be multipled so as to get a rational number, is: (2024) (a) √20 (b) √2 (c) 5 (d) √5 Q2: The LCM of two prime numbers p and q (p > q) is 221. Then the value of 3p – q is: (a) 4 (b) 28 (c) 38 (d) 48

Q3: A pair of irrational numbers whose product is a rational number is (a) (√16, √4) (b) (√5, √2) (c) (√3, √27) (d) (√36, √2)

Q4: Given HCF (2520, 6600) = 40, LCM (2520, 6600) = 252 × k, then the value of k is: (a) 1650 (b) 1600 (c) 165 (d) 1625

Q5: Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announced the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to the second student. The second student also multiplied it by a prime number and passed it to the third student. In this way by multiplying by a prime number, the last student got 173250. Now, Mukta asked some questions as given below to the students: (A) What is the least prime number used by students? (B) How many students are in the class? OR What is the highest prime number used by students? (C) Which prime number has been used maximum times? Q6: The ratio of HCF to LCM of the least composite number and the least prime number is (a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 3

Q7: Find the least number which when divided by 12, 16, and 24 leaves the remainder 7 in each case.

Q8: Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Q9: Prove that √3 is an irrational number. Q10: Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers is (a) 2 (b) 3 (c) 4 (d) 1

Q11: If 'n' is any natural number, then (12)n cannot end with the digit (a) 2 (b) 4 (c) 8 (d) 0

Q12: The number 385 can be expressed as the product of prime factors as (a) 5 x 11 x 13 (b) 5 x 7 x 11 (c) 5 x 7 x 13 (d) 5 x 11 x 17 Q13: Explain why 2 x 3 x 5 + 5 and 5 x 7 x 11 + 7 x 5 are composite numbers.

Q14: The HCF and the LCM of 12, 21 and 15 respectively, are (a) 3, 140 (b) 12, 420 (c) 3, 420 (d) 420, 3

Q15: The LCM of two numbers is 182 and their HCF is 13. If one of the numbers is 26. find the other.

Q16: Given that HCF (135, 225) = 45, find the LCM (135, 225).

Q17: If HCF (336, 54) = 6. find LCM (336, 54).

Q18: The HCF of two numbers a and b is 5 and their LCM is 200. Find the product of ab.

Q19: 1f HCF of 65 and 117 is expressible in the form 65n - 117, then find the value of n.

Q20: Find the HCF of 612 and 1314 using prime factorization.

Q21: Prove that √5 is an irrational number.

Q22: Prove that √2 is an irrational number.

Q23: Prove that 2 + 5√3 is an irrational number given that √3 is an irrational number.

Q24: Write the smallest number which is divisible by both 306 and 657.