The sign of quadratic polynomial ax²+bx+c=0 is always positive if

Consider the following statements:

1.There exists only one prime number p such that (17p+1) is a square.

2.If x is a product of 10 consecutive prime numbers staring from 2,then (x+1) is also a prime number

Which of the above statements are correct?

Let p be a prime number other tha 2 or 5.One would like to express the vulgar fraction 1/p in the form of a recurring decimal.Then the decimal will be

The HCF and LCM of two polynomials are (x+y) and (3x^5+5x^4y+2x³y²-3x²y³-5xy^4-2y^5) respectively.If one of the polynomials is x²-y²,then the other polynomial is

Consider the following statements for the sequence of numbers given below

11,111,1111,11111,...

1.Each number can be expressed in the form (4m+3),where m is a natural number

2.Some numbers are squares

Which of the above statements are correct?

If n is a natural number and n=p1^x1*p2^x2*p3^x3,where p1,p2 and p3 are distinct prime factors,then number of prime factors of n is