Vardaan Learning Institute

Q10. \(\sqrt{0.4}\) is a/an

• (A) natural number
• (B) integer
• (C) rational number
• (D) irrational number

Q11. Which of the following cannot be the unit digit of \(8^n\), where \(n\) is a natural number?

• (A) 4
• (B) 2
• (C) 0
• (D) 6

Q20. Assertion (A): For two odd prime numbers \(x\) and \(y\), \((x \neq y)\), \(LCM(2x, 4y) = 4xy\)
Reason (R): \(LCM(x, y)\) is a multiple of \(HCF(x, y)\).

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Assertion (A) is false, but Reason (R) is true.

Q30 (a). Prove that \(\sqrt{5}\) is an irrational number.

Q30 (b). Let \(p, q\) and \(r\) be three distinct prime numbers. Check whether \(p \cdot q \cdot r + q\) is a composite number or not. Further, give an example for 3 distinct primes \(p, q, r\) such that: (i) \(p \cdot q \cdot r + 1\) is composite. (ii) \(p \cdot q \cdot r + 1\) is prime.