Question

Let p, q and r be three distinct prime numbers. Check whether p · q · r + q is a composite number or not. Further, give an example for 3 distinct primes p, q, r such that

Prove that √3 is an irrational number.

State true or false for each of the following statements and justify in each case :

The sum of the exponents of prime factors in the prime factorisation of 4004 is :

Assertion (A): 4ⁿ ends with digit 0 for some natural number n. Reason (R): For a number 'x' having 2 and 5 as its prime factors, xⁿ always ends with digit 0 for every natural number n.