Let a, b, c be positive integers such that `(asqrt2+b)/(bsqrt2+c)` is a rational number, then which of the following is always an integer?

Let a,b.c.d,e,f be positive integers such that (a)/(b) =b+f

Let a, b, c, d and e be integers such that a=6b=12c,and2b=9d=12e . Then which of the following pairs contains a number that is not an integer?

If a , b , c are positive integers such that a + b + c le 8, then the number of ordered triplets of the form (a,b,c) is

Let a, b, c be the positive integers such that |[b+c,c,b],[c,c+a,a],[b,a,a+b]|=4 , then abc =

Let a and b be positive integers. Show that sqrt2 always lies between a/b and (a+2b)/(a +b) .

If a, b, c are positive integers such that a^2+ 2b^2-2ab = 169 and 2bc - c^2= 169 then a + b + c is:

Let a ,b , c be positive integers such that (b)/(a) is an integer . If a , b , c are in geometric progression and the arithmetic mean of a , b , c , is b + 2 , then value of (a^(2)+a-14)/(a+1)