Number of solutions of the equation sinx=cos4x for zero is less than equal to x is less than equal to pi

If the sum of the greatest integer less than or equal to x and the least integer than or equal to x is 5, then the solution set for x is

The number of solutions of the equation (3+cos x)^(2)=4-2sin^(8)x" in "[0, 9pi) is equal to

The number of solutions of |[x]-2x|=4, "where" [x]] is the greatest integer less than or equal to x, is

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

What is the sum of the squares of the roots of the equation x^(2)-7[x] + 5 = 0 ? (Here [x] denotes the greatest integer less than or equal to x. For example [3.4] = 3 and [-2.3] =-3).

Total number of solutions of sinx=(|x|)/(10) is equal to

The equation (x)^(2)=[x]^(2)+2x where [x] and (x) are the integers just less than or equal to x and just greater than or equal to x respectively, then number of values of x satisfying the given equation

The range of the polynomial function f is the set of real numbers less than or equal to 4. If the zeros of f are −3 and 1, which of the following could be the graph of y = f (x) in the xy-plane?

Water potential is less than ‘zero’ when