If `p ge 5` is a prime number, show that `p^2 + 2` is a composite number.

A fair die is rolled once. Statement 1: the probability of getting a composite number is 1/3. Statement2: There are three possibilities for the obtained number (i) the number is a prime number, (ii) the number is a composite number, and (iii) the number is 1. Hence, probability of getting a prime number is 1/3.

In the following question, we ask you to prove a statement. List the step in proof, and give the reason for step. If pge5 is a prime number,show that p^2+2 is divisible by 3.

For the following compound statements, identify the connecting words and then write the component statement : 13 is not a prime number or 15 is not a composite number.

Fill in the blank. The fraction whose numerator is smallest odd prime number and denominator is the smallest composite number is _____.

A number is selected at random from the first 25 natural numbers. If it is a composite number, then it is divided by 5. But if it is not a composite number, it is divided by 2. Find the probability that there will be no remainder in the division.

If p and q are positive real numbers such that p^2+ q^2=1 , then the maximum value of (p +q) is :

Greatest 2-digit prime number is: