Let `x` be a natural number and `1 le x le 200`, then the number of solutions of `[x/2] + [x/3] + [x/5] = x/2+ x/3+ x/5` is

Find the number of solutions of cos x =|1+ sin x |, 0 le x le 3 pi

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

The solution set of x^(2) + 2 le 3x le 2x^(2)-5 , is

Find the solution set of -3x + 2 le 5 and 2x -5 le 7 .

for a real number x, let [x] denote the largest unteger less than or equal to x , and let {x} = x-[x] . The number of solution x to the equation [x] {x} =5 with 0 le xle 2015 is -