The number of integral values of n (where n>=2 ) such that the equation 2n{x}=3x+2[x] has exactly 5 solutions. { Here {x} is fractional part of x and [x] is integral part of x}

The number of integral values of n such that the equation 2n{x}=3x+2[x]has exactly 5 solutions.

The number of integral values of k for which the equation |x^(2)-5|x|+6|=k has four solution is

Find the number of integral value of n so that sin x(sin x+cos x)=n has at least one solution.

The number of solutions of the equation x^(2)-3={x} ,where {x} is the fractional part of x is

lim_(x rarr[a])(e^(x)-{x}-1)/({x}^(2)) Where {x} denotes the fractional part of x and [x] denotes the integral part of a.

The number of integral values of x satisfying the equation sgn([(19)/(2+x^(2))])=[1+{5x}] (where [x],{x} and sgn(x) denote the greatest integer,the fractional part and the signum functions respectively is

If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solution for x, then possible integral value of a is:

The number of integral values of n for which -1<=(x^(2)-nx-2)/(x^(2)-3x+4)<=2 holds good is

The period of x-[x] where [x] represents the integral part of x is