`p` is a prime number and `n

p is a prime number and (2+3) s also a prime number.The number of numbers that p can assume is

Statement-I: The exponent of 3 in 100! is 48 . Statement-II: If n is a t ve integer and p is a prime number then exponent is [(n)/(p)]+[(n)/(p^(2))]+[(n)/(p^(3))]+...

If P_(1),P_(2),P_(3) are prime numbers and m,n, rare positive integers such that LCM(m,n,r)P_(1),P_(2)^(2)P_(3)^(3) and GCD(m,n,r)=P_(1)P_(2)P_(3) Then number of possible triplets of (m,n,r) are

If 25 -= 4 (mod p), where p is a prime number, then p is_________.

If 37 -= 18 (mod p), where p is a prime number then find p.

Let f(x)=[n+p sin x],x in(0,pi),n in Z,p a prime number and [x]= the greatest integer less than or equal to x.The number of points at which f(x) is not not differentiable is:

Write the contrapositive of the statement : "If n is a prime number, then n is even".

Statement-1: the highest power of 3 in .^(50)C_(10) is 4. Statement-2: If p is any prime number, then power of p in n! is equal to [n/p]+[n/p^(2)]+[n/p^(3)] + . . ., where [*] denotes the greatest integer function.