Exam Questions & Step-by-Step Markschemes (111 Problems)
Question 1 • 2024
3 Marks
Prove that \sqrt{5} is an irrational number by contradiction using the Fundamental Theorem of Arithmetic.
Answer: \sqrt{5} \text{ is irrational (Proved)}
Question 2 • 2023
3 Marks
Show that any positive odd integer is of the form 6q + 1 , or 6q + 3 , or 6q + 5 , where q is some integer.
Answer: \text{Positive odd integers are of form } 6q + 1, 6q + 3, 6q + 5 \quad (\text{Proved})
Question 3 • 2024
3 Marks
Prove that \sqrt{3} + \sqrt{5} is an irrational number.
Answer: \text{Hence Proved, } \sqrt{3} + \sqrt{5} \text{ is irrational}
Question 4 • 2024
1 Marks
If 3825 = 3^x \times 5^y \times 17^z , then the value of x + y - 2z is:
Answer: Option (C) : 2
Question 5 • 2024
1 Marks
If the prime factorisation of 2520 is 2^3 \times 3^a \times b \times 7 , then the value of a + 2b is:
Answer: Option (A) : 12
Question 6 • 2025
1 Marks
The total number of factors of the square of a prime number is :
Answer: Option (C) : 3