If n and p are both odd numbers, which of the following is an even number? `n+p` (ii) `n+p+1` (iii) `n p+2` (v) `n p`

If m , n , o, p a n d q are integers, then m (n +o) (p-q) must be even when which of the following is even? m (b) p (c) m + n (d) n + p

If p_1a n dp_2 are two odd prime numbers such that p_1> p_2, then p1 2-p2 2 is an even number (b) an odd number an odd prime number (c) a prime number

Prove the following: P(n,n)=P(n,n-1)

Prove the following: P(n,n)=2P(n,n-2)

If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1 . Here p is called the integral part of a and f its fractional part. Let neplilon N and (sqrt93)+1)^(2n)=p+f , where p is the integral part and 0ltflt1 . On the basis of bove informationi answer teh following question: The integral part p of (sqrt(3)+1)^(2n) is (A) an even number for al n epsilon N (B) an odd number for all nepsilon N (C) anodd or even number according as n is odd or even (D) an even or odd nuber according as n is odd or even

If A_n = P_n + 1 , where P_n is the product of the first n prime numbers, then consider the following statements : 1. A_n is always a composite number. 2. A_n + 2 is always an odd number. 3. A_n +1 is always an even number. Which of the above statements is/are correct ?

From the following nuclei, choose the isotopes and isobars : (i) 8p + 8n , (ii) 8p +9n , (iii)18p + 22n , (iv)20p + 20n