Number of positive integers `x` for which `f(x)=x^3-8x^2+20 x-13` is a prime number is______.

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

Number of positive integral solution of the equation |x^(2)-3x-3| gt |x^(2)+7x-13| is/are

Let f(x)=x^(2)-ax+b , 'a' is odd positive integar and the roots of the equation f(x)=0 are two distinct prime numbers. If a+b=35 , then the value of f(10)=

Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=0 has two prime numbers an roots and b+c =35. If the least value of f (x) AA x in R is lamda, then |(lamda)/(3)| is equal to (where [.] denotes greatest integer functio)

Let f(x)=x^2-bx+c,b is an odd positive integer. Given that f(x)=0 has two prime numbers as roots and b+c=35. If the least value of f(x) AA x in R" is "lambda," then "[|lambda/3|] is equal to (where [.] denotes greatest integer function)

Let f(x)=30-2x -x^3 , the number of the positive integral values of x which does satisfy f(f(f(x)))) gt f(f(-x)) is _______.

Find the number of positive integers x satisfying the equation 1/x + 1/(x+1) + 1/(x+2) = 13/12 .

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) {x : x is an even natural number} (ii) { x : x is an odd natural number } (iii) {x : x is a positive multiple of 3} (iv) { x : x is a prime number } (v) {x : x is a natural number divisible by 3 and 5} (vi) { x : x is a perfect square } (vii) { x : x is a perfect cube} (viii) { x : x + 5 = 8 }(ix) { x : 2x + 5 = 9} (x) { x : x ≥ 7 }(xi) { x : x ∈ N and 2x + 1 > 10 }

The least integer x for wich the inequality ((x-3)^(2))/(x^(2)+8x-22)lt0 is satisfied, is

Statement-1: If N the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770 , then N is divisible by 4 distinct prime numbers. Statement-2: Prime numbers are 2,3,5,7,11,13, . .