The geometric mean of 3 positive numbers a,b and c is 3 and the geometric mean of 3  other positive numbers d,e,f is 4.Also,atleast 3 elements in the set {a,b,c,d,e,f} are distinct.Which one of the following inequalities gives the best information about M,the arithmetic mean among 6 numbers?

If A,G and H are the arithmetic,geometric and harmonic means between a and b respectively,then which one of the following relations is correct?

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